Deprecated: Safe\mssql_connect(): Implicitly marking parameter $servername as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/deprecated/mssql.php on line 100

Deprecated: Safe\mssql_connect(): Implicitly marking parameter $username as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/deprecated/mssql.php on line 100

Deprecated: Safe\mssql_connect(): Implicitly marking parameter $password as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/deprecated/mssql.php on line 100

Deprecated: Safe\mssql_pconnect(): Implicitly marking parameter $servername as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/deprecated/mssql.php on line 333

Deprecated: Safe\mssql_pconnect(): Implicitly marking parameter $username as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/deprecated/mssql.php on line 333

Deprecated: Safe\mssql_pconnect(): Implicitly marking parameter $password as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/deprecated/mssql.php on line 333

Deprecated: Safe\preg_replace(): Implicitly marking parameter $count as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/lib/special_cases.php on line 155

Deprecated: Safe\bzwrite(): Implicitly marking parameter $length as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/bzip2.php on line 84

Deprecated: Safe\com_print_typeinfo(): Implicitly marking parameter $dispinterface as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/com.php on line 120

Deprecated: Safe\curl_getinfo(): Implicitly marking parameter $opt as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/curl.php on line 515

Deprecated: Safe\curl_init(): Implicitly marking parameter $url as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/curl.php on line 545

Deprecated: Safe\date_sunrise(): Implicitly marking parameter $latitude as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 236

Deprecated: Safe\date_sunrise(): Implicitly marking parameter $longitude as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 236

Deprecated: Safe\date_sunrise(): Implicitly marking parameter $zenith as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 236

Deprecated: Safe\date_sunset(): Implicitly marking parameter $latitude as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 339

Deprecated: Safe\date_sunset(): Implicitly marking parameter $longitude as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 339

Deprecated: Safe\date_sunset(): Implicitly marking parameter $zenith as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 339

Deprecated: Safe\date(): Implicitly marking parameter $timestamp as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 377

Deprecated: Safe\gmdate(): Implicitly marking parameter $timestamp as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 408

Deprecated: Safe\mktime(): Implicitly marking parameter $hour as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 464

Deprecated: Safe\mktime(): Implicitly marking parameter $minute as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 464

Deprecated: Safe\mktime(): Implicitly marking parameter $second as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 464

Deprecated: Safe\mktime(): Implicitly marking parameter $month as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 464

Deprecated: Safe\mktime(): Implicitly marking parameter $day as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 464

Deprecated: Safe\mktime(): Implicitly marking parameter $year as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 464

Deprecated: Safe\strtotime(): Implicitly marking parameter $now as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/datetime.php on line 587

Deprecated: Safe\eio_busy(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 22

Deprecated: Safe\eio_chmod(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 74

Deprecated: Safe\eio_chown(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 126

Deprecated: Safe\eio_close(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 175

Deprecated: Safe\eio_dup2(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 283

Deprecated: Safe\eio_fallocate(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 355

Deprecated: Safe\eio_fchmod(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 405

Deprecated: Safe\eio_fdatasync(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 453

Deprecated: Safe\eio_fsync(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 607

Deprecated: Safe\eio_ftruncate(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 658

Deprecated: Safe\eio_futime(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 709

Deprecated: Safe\eio_grp(): Implicitly marking parameter $data as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 753

Deprecated: Safe\eio_mkdir(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 852

Deprecated: Safe\eio_mknod(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 917

Deprecated: Safe\eio_nop(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 965

Deprecated: Safe\eio_readahead(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1016

Deprecated: Safe\eio_readdir(): Implicitly marking parameter $data as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1319

Deprecated: Safe\eio_readlink(): Implicitly marking parameter $data as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1367

Deprecated: Safe\eio_rename(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1416

Deprecated: Safe\eio_rmdir(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1464

Deprecated: Safe\eio_seek(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1520

Deprecated: Safe\eio_sendfile(): Implicitly marking parameter $pri as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1572

Deprecated: Safe\eio_sendfile(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1572

Deprecated: Safe\eio_sendfile(): Implicitly marking parameter $data as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1572

Deprecated: Safe\eio_symlink(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1734

Deprecated: Safe\eio_sync_file_range(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1793

Deprecated: Safe\eio_sync(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1814

Deprecated: Safe\eio_syncfs(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1862

Deprecated: Safe\eio_truncate(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1912

Deprecated: Safe\eio_unlink(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 1960

Deprecated: Safe\eio_utime(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 2010

Deprecated: Safe\eio_write(): Implicitly marking parameter $callback as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/eio.php on line 2063

Deprecated: Safe\error_log(): Implicitly marking parameter $destination as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/errorfunc.php on line 69

Deprecated: Safe\error_log(): Implicitly marking parameter $extra_headers as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/errorfunc.php on line 69

Deprecated: Safe\system(): Implicitly marking parameter $return_var as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/exec.php on line 151

Deprecated: Safe\file_get_contents(): Implicitly marking parameter $maxlen as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/filesystem.php on line 240

Deprecated: Safe\fwrite(): Implicitly marking parameter $length as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/filesystem.php on line 925

Deprecated: Safe\touch(): Implicitly marking parameter $time as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/filesystem.php on line 1451

Deprecated: Safe\touch(): Implicitly marking parameter $atime as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/filesystem.php on line 1451

Deprecated: Safe\ftp_alloc(): Implicitly marking parameter $result as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ftp.php on line 18

Deprecated: Safe\gnupg_addsignkey(): Implicitly marking parameter $passphrase as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/gnupg.php on line 56

Deprecated: Safe\ibase_add_user(): Implicitly marking parameter $first_name as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 37

Deprecated: Safe\ibase_add_user(): Implicitly marking parameter $middle_name as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 37

Deprecated: Safe\ibase_add_user(): Implicitly marking parameter $last_name as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 37

Deprecated: Safe\ibase_connect(): Implicitly marking parameter $database as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 253

Deprecated: Safe\ibase_connect(): Implicitly marking parameter $username as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 253

Deprecated: Safe\ibase_connect(): Implicitly marking parameter $password as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 253

Deprecated: Safe\ibase_connect(): Implicitly marking parameter $charset as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 253

Deprecated: Safe\ibase_connect(): Implicitly marking parameter $buffers as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 253

Deprecated: Safe\ibase_connect(): Implicitly marking parameter $dialect as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 253

Deprecated: Safe\ibase_connect(): Implicitly marking parameter $role as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 253

Deprecated: Safe\ibase_connect(): Implicitly marking parameter $sync as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 253

Deprecated: Safe\ibase_modify_user(): Implicitly marking parameter $first_name as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 406

Deprecated: Safe\ibase_modify_user(): Implicitly marking parameter $middle_name as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 406

Deprecated: Safe\ibase_modify_user(): Implicitly marking parameter $last_name as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 406

Deprecated: Safe\ibase_pconnect(): Implicitly marking parameter $database as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 483

Deprecated: Safe\ibase_pconnect(): Implicitly marking parameter $username as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 483

Deprecated: Safe\ibase_pconnect(): Implicitly marking parameter $password as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 483

Deprecated: Safe\ibase_pconnect(): Implicitly marking parameter $charset as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 483

Deprecated: Safe\ibase_pconnect(): Implicitly marking parameter $buffers as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 483

Deprecated: Safe\ibase_pconnect(): Implicitly marking parameter $dialect as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 483

Deprecated: Safe\ibase_pconnect(): Implicitly marking parameter $role as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 483

Deprecated: Safe\ibase_pconnect(): Implicitly marking parameter $sync as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibase.php on line 483

Deprecated: Safe\db2_autocommit(): Implicitly marking parameter $value as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibmDb2.php on line 49

Deprecated: Safe\db2_bind_param(): Implicitly marking parameter $parameter_type as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibmDb2.php on line 99

Deprecated: Safe\db2_execute(): Implicitly marking parameter $parameters as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ibmDb2.php on line 307

Deprecated: Safe\getimagesize(): Implicitly marking parameter $imageinfo as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 69

Deprecated: Safe\image2wbmp(): Implicitly marking parameter $foreground as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 94

Deprecated: Safe\imageaffine(): Implicitly marking parameter $clip as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 121

Deprecated: Safe\imagefilter(): Implicitly marking parameter $arg1 as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 1370

Deprecated: Safe\imagefilter(): Implicitly marking parameter $arg2 as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 1370

Deprecated: Safe\imagefilter(): Implicitly marking parameter $arg3 as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 1370

Deprecated: Safe\imagefilter(): Implicitly marking parameter $arg4 as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 1370

Deprecated: Safe\imagewbmp(): Implicitly marking parameter $foreground as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 2554

Deprecated: Safe\imagexbm(): Implicitly marking parameter $foreground as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/image.php on line 2609

Deprecated: Safe\imap_append(): Implicitly marking parameter $options as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 25

Deprecated: Safe\imap_append(): Implicitly marking parameter $internal_date as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 25

Deprecated: Safe\imap_headerinfo(): Implicitly marking parameter $defaulthost as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 570

Deprecated: Safe\imap_mail(): Implicitly marking parameter $additional_headers as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 787

Deprecated: Safe\imap_mail(): Implicitly marking parameter $cc as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 787

Deprecated: Safe\imap_mail(): Implicitly marking parameter $bcc as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 787

Deprecated: Safe\imap_mail(): Implicitly marking parameter $rpath as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 787

Deprecated: Safe\imap_sort(): Implicitly marking parameter $search_criteria as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 1328

Deprecated: Safe\imap_sort(): Implicitly marking parameter $charset as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/imap.php on line 1328

Deprecated: Safe\getopt(): Implicitly marking parameter $longopts as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/info.php on line 195

Deprecated: Safe\ingres_connect(): Implicitly marking parameter $database as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 335

Deprecated: Safe\ingres_connect(): Implicitly marking parameter $username as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 335

Deprecated: Safe\ingres_connect(): Implicitly marking parameter $password as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 335

Deprecated: Safe\ingres_connect(): Implicitly marking parameter $options as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 335

Deprecated: Safe\ingres_execute(): Implicitly marking parameter $params as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 367

Deprecated: Safe\ingres_execute(): Implicitly marking parameter $types as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 367

Deprecated: Safe\ingres_pconnect(): Implicitly marking parameter $database as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 506

Deprecated: Safe\ingres_pconnect(): Implicitly marking parameter $username as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 506

Deprecated: Safe\ingres_pconnect(): Implicitly marking parameter $password as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 506

Deprecated: Safe\ingres_pconnect(): Implicitly marking parameter $options as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ingres-ii.php on line 506

Deprecated: Safe\ldap_add_ext(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 18

Deprecated: Safe\ldap_add(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 48

Deprecated: Safe\ldap_bind_ext(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 69

Deprecated: Safe\ldap_delete_ext(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 173

Deprecated: Safe\ldap_delete(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 193

Deprecated: Safe\ldap_exop_passwd(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 218

Deprecated: Safe\ldap_exop(): Implicitly marking parameter $reqdata as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 266

Deprecated: Safe\ldap_list(): Implicitly marking parameter $attributes as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 801

Deprecated: Safe\ldap_list(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 801

Deprecated: Safe\ldap_mod_add_ext(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 837

Deprecated: Safe\ldap_mod_add(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 859

Deprecated: Safe\ldap_mod_del_ext(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 880

Deprecated: Safe\ldap_mod_del(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 903

Deprecated: Safe\ldap_mod_replace_ext(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 924

Deprecated: Safe\ldap_mod_replace(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 946

Deprecated: Safe\ldap_modify_batch(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1041

Deprecated: Safe\ldap_read(): Implicitly marking parameter $attributes as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1196

Deprecated: Safe\ldap_read(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1196

Deprecated: Safe\ldap_rename_ext(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1234

Deprecated: Safe\ldap_rename(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1258

Deprecated: Safe\ldap_sasl_bind(): Implicitly marking parameter $binddn as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1282

Deprecated: Safe\ldap_sasl_bind(): Implicitly marking parameter $password as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1282

Deprecated: Safe\ldap_sasl_bind(): Implicitly marking parameter $sasl_mech as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1282

Deprecated: Safe\ldap_sasl_bind(): Implicitly marking parameter $sasl_realm as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1282

Deprecated: Safe\ldap_sasl_bind(): Implicitly marking parameter $sasl_authc_id as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1282

Deprecated: Safe\ldap_sasl_bind(): Implicitly marking parameter $sasl_authz_id as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1282

Deprecated: Safe\ldap_sasl_bind(): Implicitly marking parameter $props as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1282

Deprecated: Safe\ldap_search(): Implicitly marking parameter $attributes as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1378

Deprecated: Safe\ldap_search(): Implicitly marking parameter $serverctrls as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ldap.php on line 1378

Deprecated: Safe\mailparse_msg_extract_part_file(): Implicitly marking parameter $callbackfunc as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mailparse.php on line 29

Deprecated: Safe\mb_chr(): Implicitly marking parameter $encoding as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 16

Deprecated: Safe\mb_ereg_search_init(): Implicitly marking parameter $pattern as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 193

Deprecated: Safe\mb_ereg_search_regs(): Implicitly marking parameter $pattern as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 218

Deprecated: Safe\mb_http_output(): Implicitly marking parameter $encoding as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 292

Deprecated: Safe\mb_internal_encoding(): Implicitly marking parameter $encoding as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 323

Deprecated: Safe\mb_ord(): Implicitly marking parameter $encoding as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 347

Deprecated: Safe\mb_regex_encoding(): Implicitly marking parameter $encoding as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 395

Deprecated: Safe\mb_send_mail(): Implicitly marking parameter $additional_parameter as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 467

Deprecated: Safe\mb_str_split(): Implicitly marking parameter $encoding as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mbstring.php on line 514

Deprecated: Safe\sapi_windows_vt100_support(): Implicitly marking parameter $enable as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/misc.php on line 342

Deprecated: Safe\msql_connect(): Implicitly marking parameter $hostname as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/msql.php on line 84

Deprecated: Safe\msql_pconnect(): Implicitly marking parameter $hostname as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/msql.php on line 372

Deprecated: Safe\mysql_connect(): Implicitly marking parameter $server as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mysql.php on line 76

Deprecated: Safe\mysql_connect(): Implicitly marking parameter $username as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mysql.php on line 76

Deprecated: Safe\mysql_connect(): Implicitly marking parameter $password as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/mysql.php on line 76

Deprecated: Safe\fsockopen(): Implicitly marking parameter $timeout as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/network.php on line 307

Deprecated: Safe\oci_connect(): Implicitly marking parameter $connection_string as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 492

Deprecated: Safe\oci_connect(): Implicitly marking parameter $character_set as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 492

Deprecated: Safe\oci_connect(): Implicitly marking parameter $session_mode as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 492

Deprecated: Safe\oci_new_collection(): Implicitly marking parameter $schema as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 915

Deprecated: Safe\oci_new_connect(): Implicitly marking parameter $connection_string as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 1014

Deprecated: Safe\oci_new_connect(): Implicitly marking parameter $character_set as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 1014

Deprecated: Safe\oci_new_connect(): Implicitly marking parameter $session_mode as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 1014

Deprecated: Safe\oci_pconnect(): Implicitly marking parameter $connection_string as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 1235

Deprecated: Safe\oci_pconnect(): Implicitly marking parameter $character_set as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 1235

Deprecated: Safe\oci_pconnect(): Implicitly marking parameter $session_mode as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/oci8.php on line 1235

Deprecated: Safe\openssl_csr_new(): Implicitly marking parameter $configargs as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 212

Deprecated: Safe\openssl_csr_new(): Implicitly marking parameter $extraattribs as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 212

Deprecated: Safe\openssl_csr_sign(): Implicitly marking parameter $configargs as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 253

Deprecated: Safe\openssl_open(): Implicitly marking parameter $iv as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 363

Deprecated: Safe\openssl_pkcs12_export_to_file(): Implicitly marking parameter $args as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 436

Deprecated: Safe\openssl_pkcs12_export(): Implicitly marking parameter $args as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 484

Deprecated: Safe\openssl_pkcs7_sign(): Implicitly marking parameter $extracerts as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 621

Deprecated: Safe\openssl_pkey_export_to_file(): Implicitly marking parameter $passphrase as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 651

Deprecated: Safe\openssl_pkey_export_to_file(): Implicitly marking parameter $configargs as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 651

Deprecated: Safe\openssl_pkey_export(): Implicitly marking parameter $passphrase as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 682

Deprecated: Safe\openssl_pkey_export(): Implicitly marking parameter $configargs as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 682

Deprecated: Safe\openssl_pkey_new(): Implicitly marking parameter $configargs as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 771

Deprecated: Safe\openssl_seal(): Implicitly marking parameter $iv as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/openssl.php on line 956

Deprecated: Safe\password_hash(): Implicitly marking parameter $options as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/password.php on line 114

Deprecated: Safe\pcntl_exec(): Implicitly marking parameter $args as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pcntl.php on line 23

Deprecated: Safe\pcntl_exec(): Implicitly marking parameter $envs as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pcntl.php on line 23

Deprecated: Safe\pcntl_getpriority(): Implicitly marking parameter $pid as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pcntl.php on line 53

Deprecated: Safe\pcntl_setpriority(): Implicitly marking parameter $pid as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pcntl.php on line 86

Deprecated: Safe\preg_match_all(): Implicitly marking parameter $matches as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pcre.php on line 350

Deprecated: Safe\preg_match(): Implicitly marking parameter $matches as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pcre.php on line 587

Deprecated: Safe\pg_connect(): Implicitly marking parameter $connect_type as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 133

Deprecated: Safe\pg_copy_from(): Implicitly marking parameter $delimiter as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 216

Deprecated: Safe\pg_copy_from(): Implicitly marking parameter $null_as as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 216

Deprecated: Safe\pg_copy_to(): Implicitly marking parameter $delimiter as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 248

Deprecated: Safe\pg_copy_to(): Implicitly marking parameter $null_as as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 248

Deprecated: Safe\pg_execute(): Implicitly marking parameter $stmtname as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 406

Deprecated: Safe\pg_execute(): Implicitly marking parameter $params as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 406

Deprecated: Safe\pg_lo_export(): Implicitly marking parameter $oid as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 782

Deprecated: Safe\pg_lo_export(): Implicitly marking parameter $pathname as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 782

Deprecated: Safe\pg_lo_import(): Implicitly marking parameter $pathname as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 823

Deprecated: Safe\pg_lo_write(): Implicitly marking parameter $len as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1012

Deprecated: Safe\pg_parameter_status(): Implicitly marking parameter $param_name as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1116

Deprecated: Safe\pg_pconnect(): Implicitly marking parameter $connect_type as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1177

Deprecated: Safe\pg_prepare(): Implicitly marking parameter $stmtname as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1281

Deprecated: Safe\pg_prepare(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1281

Deprecated: Safe\pg_put_line(): Implicitly marking parameter $data as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1322

Deprecated: Safe\pg_query_params(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1388

Deprecated: Safe\pg_query_params(): Implicitly marking parameter $params as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1388

Deprecated: Safe\pg_query(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pgsql.php on line 1446

Deprecated: Safe\ps_get_parameter(): Implicitly marking parameter $modifier as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ps.php on line 781

Deprecated: Safe\ps_open_file(): Implicitly marking parameter $filename as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/ps.php on line 928

Deprecated: Safe\pspell_config_create(): Implicitly marking parameter $spelling as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pspell.php on line 93

Deprecated: Safe\pspell_config_create(): Implicitly marking parameter $jargon as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pspell.php on line 93

Deprecated: Safe\pspell_config_create(): Implicitly marking parameter $encoding as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pspell.php on line 93

Deprecated: Safe\pspell_new(): Implicitly marking parameter $spelling as nullable is deprecated, the explicit nullable type must be used instead in /home/studycon/public_html/wp-content/plugins/debloat/vendor/thecodingmachine/safe/generated/pspell.php on line 395

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Physics https://studyconcepts.in/category/physics/ A Core Of Knowledge Thu, 22 Jan 2026 16:58:35 +0000 en-US hourly 1 https://wordpress.org/?v=7.1.3 https://studyconcepts.in/wp-content/uploads/2024/12/cropped-360_F_317243574_6AEuvWN5OU9lkUecwXe2nQdt2JWSFGEC-1-32x32.webp Physics https://studyconcepts.in/category/physics/ 32 32 About Quantum Physics Part 3: Bohr’s Atomic Model, de Broglie’s Hypothesis and Wave–Particle Duality https://studyconcepts.in/about-quantum-physics-part-3-bohrs-atomic-model-de-broglies-hypothesis-and-wave-particle-duality/ https://studyconcepts.in/about-quantum-physics-part-3-bohrs-atomic-model-de-broglies-hypothesis-and-wave-particle-duality/#respond Thu, 18 Sep 2025 13:17:19 +0000 https://studyconcepts.in/?p=1398 Welcome back to the quantum physics series. In my previous article, I covered photoelectric effect, failure of the wave theory, and Einstein’s photon theory. If you haven’t read the previous article on quantum mechanics, I urge you to read all my articles one by one. All my articles are very useful and I have explained [...]

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Welcome back to the quantum physics series. In my previous article, I covered photoelectric effect, failure of the wave theory, and Einstein’s photon theory. If you haven’t read the previous article on quantum mechanics, I urge you to read all my articles one by one. All my articles are very useful and I have explained them in simple words.

In my today’s article I am going to give simple explanation on Bohr’s theory, de Broglie hypothesis and wave particle duality.

What is Bohr’s atomic model?

In 1913 Bohr gave the idea of atomic structure to explain the stability of the atom and the emission of sharp spectral lines. He modified the Rutherford model and proposed the following assumptions.

The electrons revolve around the nucleus in certain descreate orbits. While revolving in these allowed orbits the electrons do not emit or absorb electromagnetic radiation, even though they are in accelerated motion. Therefore, the atom is stable.

It will be possible for an electron to revolve only in an orbit for which the orbital angular momentum is an integer multiple of h/ 2π. If L (mvr) is the angular momentum then we can write-

               mvr= nh/ 2π

n= 1,2,3,….. and h= Planck’s Constant

When an electron jumps from one allowed orbit to another the atom emits radiation.

The radiation is emitted or absorbed in the form of a single photon whose energy hv is equal to the difference in the energies “ΔE” of the electron in the two orbits.

Thus, ΔE = hv, v= frequency

How did Bohr’s theory explain the hydrogen spectrum?

The spectrum of the hydrogen atom is consist of many lines. These are divided into a number of series. Such as Lyman, Balmer, Paschen, Brackett, and Pfund series. These sharp spectral lines are the hydrogen spectrum and cannot be explained by classical theory. Bohr’s explained by applying Planck’s quantum hypothesis to Rutherford’s atomic model.

Bohr’s proposed two theories:

An electron can move only in orbits for which the angular momentum ‘L’ of the electron is an integer multiple of h/2π.

Absorption of radiation by an atom occurs when the electron jumps from one allowed orbit to another. The radiation is emitted or absorbed as a single photon whose energy ‘hv’ is equal to the difference between the energies of the electron in the two orbits.

That is, hv= E – e,

E= energy of the initial orbit and e= energy of the final orbit

When the hydrogen atom gets enough energy from outside, the electron moves from the inner orbit of lower energy to the outer orbit of higher energy. After 10⁻³ seconds the electron jumps back to the inner orbit by emitting radiation of wavelength which will be equal to.

1/ λ = R( 1/m² – 1/n²)

For,

m = 1 and n = 2,3,4…. We obtain Lyman series

m = 2 and n = 3,4,5…. We obtain Balmer series

m = 3 and n = 4,5,6…. We obtain Paschen series

m = 4 and n = 5,6,7…. We obtain Brackett series

m = 5 and n = 6,7,8….. We obtain Pfund series

Energy level diagram of hydrogen:

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What were the shortcomings of Bohr’s theory?

  1. Bohr’s theory succeeded in explaining hydrogen spectrum and also gave information about atomic structure but it has some limitations which I am going to discuss one by one.
  2. An individual line in the hydrogen spectrum consists of many blurred lines, which is called the fine structure of hydrogen. Bohr’s theory was unable to explain this. When individual lines of the hydrogen spectrum were examined, it was found that they had lines very close to each other. This is called the fine structure of hydrogen. Bohr’s theory was unable to explain this.
  3. Bohr’s theory was unable to explain the variation in the intensity of the spectral lines of an element.
  4. This theory only applies to atoms with only one electron, such as the hydrogen atom, isotopes of hydrogen (deuterium), and ions with only one electron, such as singly ionized helium (He⁺) or doubly ionized lithium (Li²⁺). It does not explain the spectra of complex atoms.
  5. This theory could not give a satisfactory explanation about the distribution of electrons in atoms.

The De Broglie hypothesis explains Bohr’s theory’s limitations by introducing the concept of wave-particle duality for matter,

What is de Broglie’s hypothesis of matter wave?

The phenomena of interference, diffraction and polarization of light can be explained on the basis of the wave nature of light. However, there are some phenomena which could not be explained on this wave theory of radiation. For example, photoelectric effect, Compton effect etc. These effects can only be explained on the basis of the particle nature of radiation. Thus, the dual nature of wave and particle became associated with light. In 1924 Louis de Broglie put forward the suggestion that matter exhibits wave like properties.

The De- Broglie’s hypothesis explains Bohr’s theory’s limitations by introducing the concept of wave-particle duality for matter. De-Broglie’s hypothesis for matter waves, also known as wave-particle duality, states that all moving particles, such as electrons, protons and all matter, have both particle-like and wave-like properties. Just as light can act as both a wave and a particle (photon).

What is wave–particle duality?

Wave particle duality is that all matter exhibits both wave like and particle like properties. in other words we can say they show wave like and particle like behavior. Wave-particle duality means that all matter exhibits both wave-like and particle-like properties. In other words, they show both wave-like and particle-like behavior. This applies to all objects, even microscopic ones.

Bohr’s model of the atom shows two features:

Electron is considered as a wave and light is considered as a particle (photon).

But this concept contradicts the earlier phenomenon that an electron behaves as a particle and light as a wave, which is provided by the relation,

(λ = h/mass × speed), that connects the mass and speed of an electron to the wavelength of the corresponding wave and E= h × frequency, which links the frequency of a light wave to the energy of the corresponding photon.

Now the question arises:

  1. what is an electron? Is it a particle or a wave?
  2. What is light? Is it a wave or a photon? The answer is wave-particle duality.

The answer is wave-particle duality, which states that all objects sometimes exhibit wave-like behavior and sometimes particle-like behavior depending on the experiment and interaction.

What is the wavelength of a matter wave? ( de Broglie wavelength)

The wavelength of a matter wave, or de Broglie wavelength, is equals to to λ = h/p.

λ is the wavelength, h is Planck’s constant (a fundamental constant of nature), and p is the momentum of the particle. Momentum (p) is equal to the product of the particle’s mass (m) and velocity (v). Therefore, we can write it as  λ = h/mv.

This equation shows that the wavelength of a matter wave is inversely proportional to the particle’s momentum. This means that heavier particles or faster-moving particles will have shorter de Broglie wavelengths. Higher velocity or larger mass will result in larger momentum and, consequently, shorter wavelength.

If you have any doubts about any topic related to quantum mechanics, please let me know in the comments section. I will definitely write an article on it.

“Stay connected, keep smiling!”

 

 

 

 

 

 

 

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About Quantum Physics Part 2: Photoelectric Effect, Failure Of Wave Theory and Einstein’s Photon Theory https://studyconcepts.in/about-quantum-physics-photoelectric-effect-failure-of-wave-theory-and-einsteins-photon-theory/ https://studyconcepts.in/about-quantum-physics-photoelectric-effect-failure-of-wave-theory-and-einsteins-photon-theory/#respond Thu, 11 Sep 2025 07:55:55 +0000 https://studyconcepts.in/?p=1276 Welcome to the series on quantum mechanics. In my last article I explained the origin of quantum mechanics. In this article I am going to explain about photoelectric effect and how Albert Einstein explained photoelectric effect using the particle nature of light. What is Photoelectric Effect? “When a beam of light of appropriate frequency incident [...]

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Welcome to the series on quantum mechanics. In my last article I explained the origin of quantum mechanics.

In this article I am going to explain about photoelectric effect and how Albert Einstein explained photoelectric effect using the particle nature of light.

What is Photoelectric Effect?

“When a beam of light of appropriate frequency incident on a metal surface, electrons are emitted from the metal surface. This phenomenon is called photoelectric effect. The emitted electrons are called photoelectrons.”

The photoelectric effect was first observed by Heinrich Hertz in 1887. This effect is one of the specific phenomena that provide evidence that photons behave like particles.

The photoelectric effect is not limited to metallic surfaces, but can also occur in gases, liquids and non-metallic solids. Light suitable for producing the photoelectric effect includes the full range of electromagnetic waves, i.e., from the gamma rays and X-rays to the infrared region of wavelengths.

 

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Explanation:

If light of appropriate frequency is fall on the plate, photo electrons will be emitted. When the potential of the plate is positive, a steady saturation current flows in the circuit. When the potential of plate is made negative, the current decreases. At a certain negative potential the photoelectric current becomes zero. This potential is the stopping potential.

If the frequency of light is increased at the stopping potential, then current starts flowing in the circuit. On increasing the stopping potential, this current stops again. Thus, the higher the frequency of the incident light, the greater will be the stopping potential.

What are the laws of photoelectric effect?

  1. The number of photoelectrons emitted per second varies directly with the intensity of the incident light.
  2. The maximum energy of photoelectrons is independent of the intensity of the incident light.
  3. The maximum energy of the photoelectrons increases linearly as the frequency of the incident light increases.
  4. If the frequency of the incident light is less than a certain value v (threshold frequency) then emission of photoelectrons cannot occur, no matter how strong the light intensity is.
  5. Emission of photoelectrons will take place immediately without any delay.

Was Maxwell’s electromagnetic theory of light wrong?

In 1865 James Clerk Maxwell proposed his theory that light is an electromagnetic wave composed of oscillating electric and magnetic fields that are perpendicular to each other and propagate through space at the speed of light.

Let me tell you one thing that Maxwell’s theory was not wrong, but when it came to applying this electromagnetic theory of light to the experimental results of the photoelectric effect, the theory could not explain the effect.

What was the difference between the explanation of experimental observations of the photoelectric effect and the explanation of the wave theory?

1) According to the wave theory, when light falls on a metal surface, the energy of the wave is transferred equally to the electrons in the surface before emission. Thus, it is clear that with increase in intensity of light, the energy absorbed by electrons must also increase.

This is against the experimental observation that the maximum energy of emitted electrons is independent of intensity of light.

2) Again, wave theory suggests that light of any frequency should be capable of ejecting electrons from a surface, provided the light is intense enough.

On the other hand, experiments show that light of frequency below a certain threshold value cannot eject photoelectrons, no matter how intense the light is.

3) Moreover, wave theory suggests that if light is incident on a metal surface, electron should take a considerable amount of time to gain enough energy to escape from the surface.

But the experimental results shows no detectable time delay between the incidence of light on the surface and the emission of photoelectrons.

Therefore, the wave theory fails to explain the experimental observations of the photoelectric effect

Einstein’s photon theory:

  1. Einstein explained the photoelectric effect with the help of the photon theory of light. He assumed that light travels through space as packets of energy called photons or quanta and that the energy of a photon is hv. Where h is Planck’s constant and v is the frequency of light.
  2. When light falls on a metal surface, a photon of energy hv is completely absorbed by an electron present in the surface. A part of this energy is used to eject the electron against the attraction of the rest of the metal and the remaining part is given to the electrons as kinetic energy.
  3. Those electrons that exit the surface from some depth lose some of their energy when they collide with atoms. Resulting in the emission of photoelectrons with a range of kinetic energies.

Photoelectric Equation:

Those photoelectrons which are emitted very close to the surface will have the maximum kinetic energy. Which is equal to.

Kinetic energy = 1/2 mv² ___ 1

‘W’ is the energy required to eject an electron against the attraction of the rest of the metal.

W = Work function

We can write-

hv = W + ( 1/2 mv²) , hv = energy of the electron

If the energy of the photon is less than w then the surface will be unable to emit electrons. If v is the threshold frequency then the threshold energy of the photon will be hν₀.

We can write-

W = hν₀  ——- 2

Using 2 and 1 the result will be

hv = hν₀ + ( 1/2 mv²)

In another way we can write-

(1/2 mv²) max = h ( v – ν₀)

This equation is called Einstein’s photoelectric equation.

Explanation of photoelectric laws by Einstein’s photoelectric equation:

  1. If the intensity of light of a given frequency v is increase the number of photons striking at the surface per second will also increase. However, the energy hv of each photon will remain the same.
  2. Therefore, the number of electrons emitted per second will increase but their maximum energy ( 1/2 mv²) will remain the same. Therefore, we can say that the equation successfully explains photoelectric laws 1 and 2
  3. It is also clear from Einstein’s equations that the maximum energy of photoelectrons will increase linearly with an increase in the frequency ‘v’ of the incident light. This explains the third law of photoelectric emission.
  4. It is clear from the photoelectric equation that if v is less than ν₀, then the kinetic energy of photoelectrons will be negative which is impossible. This means that if the frequency v of the incident light is less than the threshold frequency ν₀ then photoelectrons will not be emitted. This explains the fourth law of photoelectric emission.
  5. Eventually, as soon as the first photon hits the surface, the electron will instantly absorb this energy and escape from it immediately. Hence, it will happen instantly without any delay. This explains the fifth law of photoelectric emission.

Einstein’s explanation of the photoelectric effect suggests that electromagnetic radiation is made up of discrete packets of energy, called photons. Which demonstrates the particle nature of light. Photons are fundamental and discrete units of energy. Each photon has energy E = hv and momentum p = hv/c.

Additionally, photons are stable, electrically neutral and massless elementary particles and always travel at the speed of light. The mass of a photon is m = hv/c²  and do not exist at rest. Photons always travel at the speed of light whether in a vacuum or in a medium.

Applications of Photoelectric effect:

  • In photo controlled circuits. For example, alarms, auto switch off street lights, automatic traffic control and control of railway crossings etc.
  • Automatic counting of the people entering a hall, to find the capacity of a substance, control of furnace temperature.
  • Determination of relative colour of face, detection of smoke and for fast transmission in T.V broadcast etc.

My next article will be on wave-particle duality.

If you have any doubts on this topic, please drop your comments in the comment box below. I will try to answer all your questions.

“Stay connected, keep smiling!”

 

 

 

 

 

 

 

 

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About Quantum Physics Part 1: Black Body Radiation, Ultraviolet Catastrophe, Planck’s Radiation Law https://studyconcepts.in/about-quantum-physics-black-body-radiation-ultraviolet-catastrophe-plancks-radiation-law/ https://studyconcepts.in/about-quantum-physics-black-body-radiation-ultraviolet-catastrophe-plancks-radiation-law/#respond Mon, 08 Sep 2025 18:26:04 +0000 https://studyconcepts.in/?p=1231 In this article I am going to tell you about quantum physics. But as we all know that quantum physics is a vast branch of physics. Therefore, it is difficult to explain quantum physics in one article. So, today in this article I will tell how and who laid the foundation of quantum physics. “Quantum [...]

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In this article I am going to tell you about quantum physics. But as we all know that quantum physics is a vast branch of physics. Therefore, it is difficult to explain quantum physics in one article. So, today in this article I will tell how and who laid the foundation of quantum physics.

“Quantum Physics was first introduced when Max Planck derived the correct mathematical law for the distribution of energy in black body radiation.”

Before I begin with this it is important to know what is classical physics and what is the need of quantum physics.

What is Classical Physics?

Classical physics also known as Newtonian mechanics is the system, in which Newton’s laws of motion are used and time and distance are considered absolute and invariant. This system has been used successfully for nearly three centuries to deal with a wide variety of problems in physics.

Classical physics developed over several centuries based on observations of moving objects. It correctly explains the motion of celestial bodies, macroscopic and microscopic terrestrial bodies moving with non- relativistic speed.

By the end of the 19th century, it was a common view among physicists that all types of problems could be solved with the help of classical physics. Moreover, there was no limitations on the accuracy of the results.

You may be wondering what is the meaning of “absolute time” and “non-relativistic speed”?

Absolute time: Time passes uniformly for everyone, everywhere, independently of the motion of observers or external factors. According to Newton’s view, time is a distinct dimension, separate from space and absolute, that is same for all observers.

Non-relativistic speed: Speeds much less than the speed of light. Where Newtonian mechanics accurately describes the motion of a moving body. (i.e. v<<c, c= speed of light)

What are the drawbacks of classical physics?

In cases of our everyday experience, which involve relatively large particles and relatively slow-moving objects, the results of classical physics match experiments quite well, but classical physics had certain drawbacks.

Classical physics cannot be used at the atomic level. This means when it comes to describing the motion of electrons in atoms, vibrations of atoms, etc.

It was unable to explain the stability of atoms and the absorbed spectrum of black body radiation.

It could not explain the origin of discrete spectra of atoms and observed variation of specific heat of metals and gases.

Moreover, classical physics was unable to explain phenomenon like photoelectric effect, compton effect and Raman effect etc.

“The inadequacy of classical physics led to the development of quantum physics.”

What is Quantum Physics?

Quantum Physics explains the behavior of matter and energy at the atomic and subatomic levels. Where classical physics (like Newtonian mechanics) fails.

According to quantum physics the energy changes are not continuous but discrete. the absorption and emission of energy in atoms is in bundles of energy hv.

V= Frequency, h= Planck’s constant

Quantum Physics is able to explain stability of atoms, spectrum of black body radiation. Moreover, it is also able to explain phenomena like photoelectric effect, Compton effect and theory of alpha decay.

Let’s understand quantum physics in more detail:

What is thermal radiation?

The radiation emitted by the source depending upon its temperature is called thermal radiation. light is produced as a result of their temperature. Hence they are called thermal sources. A thermal source produces a continuous spectrum because thermal radiation is electromagnetic in nature and its energy is distributed over all wavelengths.

At low temperatures the radiation is mainly lies in the infra red region. As body temperature increases, the maximum intensity component shifts to a higher frequency. As the current increases through the filament. It appears initially red, orange and then yellow and finally it emits white light.

What is blackbody?

A perfect black body is a body that absorbs all the radiation that falls on it, regardless of the frequency of the radiation. A black body is an ideal body that neither reflects nor transmits any incident radiation. Therefore, it appears black whatever is the colour of the incident radiation.

If a black body is placed in an isothermal envelope(sphere) , it will emit the entire radiation of the envelope(sphere). Thus, the radiation emitted from an isothermal sphere is similar to that emitted from a black body at the same temperature and is called black body radiation.

Can we create a black body?

Yes, we can also make a black body by making a small hole in a sphere. The hole will act as a perfect absorber. The light entering the cavity reflects multiple times on the walls and gets trapped inside the cavity. As a result, the hole will appear completely dark.

Conversely, when the cavity is heated, the radiation produced in the cavity passes out through the hole, which will include all the wavelengths. Therefore, the whole will act as an perfect emitter.

What are the laws of black body radiation?

This includes the Stefan-Boltzmann law and Wien’s law:

Stefan-Boltzmann’s law: It states that the total radiation emitted from a black body at temperature T is proportional to the fourth power of the absolute temperature of the body.

Wien’s law: It states that the peak wavelength at which the maximum emission occurs for any given temperature is inversely proportional to the absolute temperature of the body.

What were the experimental results?

The experimental results showed that at a given temperature the radiation energy density initially increases with frequency, then peaks at a particular frequency and then finally decreases to zero at a very high frequency.

Various efforts were made to calculate theoretically the frequency distribution of thermal radiation. Rayleigh and jeans also tried and gave Rayleigh jeans law to explain this but there was one drawback.

Raleigh-Jeans Law?

Rayleigh and Jeans assumed that every standing wave must have energy ‘KT’ (according to Boltzmann’s principle of equipartition of energy, each simple harmonic oscillator has an average thermal energy of ‘KT’ at thermal equilibrium) and derived an expression for the energy density of the radiation distribution within the cavity.

The expression is –

E(v) = 8 π v² kT/ c³

 k = Boltzmann constant and T = Temperature

This result is known as Raleigh-Jeans Law

What is ultraviolet Catastrophe?

The energy density calculated from the upper formula matched the experimental result well at long wavelengths of the spectrum, but it was predicting an infinite amount of energy for very short wavelengths.

This meant that the radiation emitted by a hot body must consist of a large portion of UV rays. This violates the law of conservation of energy. This is known as the “Ultraviolet Catastrophe.”

The result was showing inconsistencies between observations and the predictions of classical physics.

This showed the need for a new approach to physics. Max Planck later developed his theory to solve this problem, incorporating the concept of quantized energy into his formula and providing the correct blackbody radiation curve by introducing his law know as ” The Planck’s Radiation Law”.

The Planck’s Radiation Law:

 

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According to the classical theory of radiation, energy changes in radiators occur continuously. Classical mechanics could not explain the experimental observation i.e. the distribution of energy in the spectrum of a black body.

After a long struggle, in 1900 Planck succeeded in obtaining the correct mathematical law for the distribution of energy in black body radiation. He recognized that the cause of the ultraviolet catastrophe was Rayleigh’s assumed that standing waves consist of an infinite number of harmonic modes of vibration.

Each of these modes was assumed to have an energy KT, leading to the absurd result that the total energy in the cavity would be infinite. Therefore Max Planck put forward a postulate that an oscillating atom can absorb or emit energy only in quantities that are integer multiples of “hv”. The invisible discrete unit of energy hv is called an energy quantum.

Energy of an oscillator will be

E = nhv

n = Quantum number of the oscillator ( n = 1,2,3,….)

h = Planck ‘s constant

Eventually, Max Planck gave the final result by using Maxwell Boltzmann distribution law and including the discreteness in the emission of energy.

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This is  “Planck’s radiation law” . This formula given by Max Planck correctly describes blackbody radiation at all wavelengths.

The failure I have described exposed the limitations of classical physics and set the stage for Max Planck’s quantum theory.

The inability of classical physics to explain the continuous spectrum emitted by a black body gave birth to quantum physics. Planck’s hypothesis of a discreet quanta of energy was the foundation of quantum physics. 

In my next article I will explain about photoelectric effect.

If you have any doubt regarding this article, please drop your question in the comment box below, I will definitely try to answer it.

“Stay connected, keep smiling!”

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Origin of Thermodynamics, Isothermal Process and Adiabatic Process https://studyconcepts.in/origin-of-thermodynamics-isothermal-process-and-adiabatic-process/ https://studyconcepts.in/origin-of-thermodynamics-isothermal-process-and-adiabatic-process/#respond Fri, 29 Aug 2025 17:32:56 +0000 https://studyconcepts.in/?p=1132 Today my article will tell you how thermodynamics originated and who laid the foundations of modern thermodynamics. What is heat? Heat is a type of energy that is transferred from one body to another due to difference in temperature. Heat always flows from a hotter object to a colder object until they reach a state [...]

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Today my article will tell you how thermodynamics originated and who laid the foundations of modern thermodynamics.

What is heat?

Heat is a type of energy that is transferred from one body to another due to difference in temperature. Heat always flows from a hotter object to a colder object until they reach a state of thermal equilibrium. The measure of the average heat in a substance is called temperature.

What is thermodynamics?

Thermodynamics is a branch of physics that studies about heat and the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale.

“French mechanical engineer and physicist Nicolas Leonard Sadi Carnot is known as the the father of thermodynamics.” For publishing Reflections on the Motive Power of Fire in 1824.

History of thermodynamics:

Aristotle (ancient Greek philosopher) believed that a vacuum, or a space without matter was is impossible because “nature abhors a vacuum”. Aristotle believed that empty space could not exist, because nature continually fills any empty space with denser surrounding material, preventing a true void. According to Aristotle, a vacuum was an illogical concept, that would allow for impossible motion.

Otto von Guericke’s ( German scientist, inventor, and politician) invention (the world’s first vacuum pump in 1650) and his famous Magdeburg Hemisphere experiment proved Aristotle’s theory wrong.

Robert Boyle and his colleague Robert Hooke used this vacuum pump, based on Otto von Guericke’s design, for experiments. This led to the development of a law known as Boyle’s Law. Which states that the pressure of a fixed amount of gas is inversely proportional to its volume at constant temperature.

Contribution of Thomas Savery:

In 1698 Thomas Savery invented the first commercially used steam-powered device, a steam pump known as the Miner’s Friend. His invention was a water pump that would draw water up by creating a vacuum using condensed steam and then push the water out using the pressure of the steam.

Then later inventors such as Thomas Newcomen and James Watt used Savory’s work to develop more efficient and powerful steam engines.

Limitations of Savery’s engine: Savery’s engine was dangerous. It was not very safe because of the risk of boiler bursting from the high steam pressure, and its pumping height was also limited. In addition, it was inefficient.

Contribution of Thomas Newcomen:

Thomas Savory’s design was to create a vacuum by using steam to pump water. On the other hand, another inventor, Thomas Newcomen, improved the efficiency by adding a piston to separate the steam from the water in 1712. This improvement made it safer than Savory’s design.

Thomas Newcomen’s atmospheric engine became the first widely successful steam engine. It was widely used for mine drainage and set the stage for later innovations.

Limitation of Thomas Newcomen’s engine: Newcomen’s engine was safer and more efficient, but was still inefficient. Newcomen’s engine were inefficient due to the repeated heating and cooling of the cylinders, wasting a lot of energy

Contribution of James Watt:

Since, Newcomen’s engine were inefficient James Watt realised that the cylinder could stay hot if the steam was condensed in a separate chamber, away from the main cylinder. James Watt realized that if the steam was condensed in a separate chamber away from the main cylinder, the cylinder could stay hot.

This idea was influenced by Black’s work on latent heat. It was the first major improvement to the steam engine. It made the engines much more efficient, saving three-fourths of the fuel compared to the Newcomen engines.

 Contribution of Sadi Carnot:

“Sadi Carnot’s (father of thermodynamics) 1824 theoretical Carnot engine laid the foundation for modern thermodynamics by introducing the concepts of ideal heat engines, maximum efficiency, and the relationship between heat, work, and temperature..”

Sadi Carnot created the first theoretical framework for a heat engine, establishing the Carnot cycle and the Carnot theorem, which defines the maximum possible efficiency for any heat engine.

He did this by proposing an ideal, reversible engine that operates in a four-step cycle of isothermal and adiabatic expansions and compressions between a hot and cold reservoir, setting a standard of performance that no other engine could surpass.

Before Carnot, there was no way to know the maximum possible efficiency of a heat engine. He provided the scientific basis for this limit, showing that efficiency depends only on the temperatures of the hot and cold reservoirs.

What is isolated system?

An isolated system cannot exchange energy or mass with its surroundings. This means that neither heat nor work can cross the system’s boundary, and no matter can enter or leave the system. An isolated system in the universe has a definite amount of energy. This energy is called internal energy.

The internal energy is the sum of the kinetic and potential energies. The internal energy of an isolated system is conserved. Because no energy can enter or leave the system.

What is Thermodynamic System?

It consist of a large number of particles(atoms or molecules) and exists in the form of solid, liquid or gas or a combination of two or more states.

Equation of state of the thermodynamic system:

The thermodynamic state of a system is described by four parameters. These parameters are temperature (T), pressure (P), volume (V) and heat content (Q).

the relation between temperature (T), pressure (P), volume (V) and heat content (Q) is called equation of state of the thermodynamic system:

For n moles the equation is-

PV=nRT

P= Pressure, V= Volume, T= Temperature, R= Universal gas constant

What is Isothermal Process?

When the pressure and volume of a gas change, without any change in its temperature, it is called an isothermal process. It allows the free exchange of heat between the gas and its surroundings. When a gas is compressed in an enclosure, work is done on the gas which generates heat, causing the temperature to rise. The temperature of the gas will remain constant.

Similarly when the pressure on the gas is decreased, it expands, work is done by the gas.Some heat energy is lost and the temperature decreases. Thus, for an isothermal change, there should be a free exchange of heat between the gas and its surroundings.

Hence, the two essential conditions for a perfect isothermal change are:

  • The walls of the container should be perfectly conducting
  • The process of compression or expansion should be slow

Examples of Isothermal changes are-

  1. When an ideal gas expands or is compressed Slowly (ideal gas Expansion/Compression).
  2. Melting of Ice
  3. Boiling of Water

What is Adiabatic Process?

When the pressure and volume of a gas change along with changing temperature it is called an area that a process. When a gas in an enclosure compressed suddenly, heat is produced which if not allowed to escape will increase the temperature of the gas.

Similarly, if the gas is allowed to expand suddenly, heat energy will be spent and the volume of the gas expands. If this heat is not gained from the surroundings, the temperature of the gas would fall. Thus, for an adiabatic process, no change of heat between the gas and the surroundings should take place. Hence, the two essential conditions for a perfect adiabatic change are:

  1. The walls of the container must be perfectly non conducting.
  2. The process of compression or expansion should be sudden.

Perfect adiabatic changes are practically impossible. Examples of nearly perfect adiabatic changes are

  1. Sudden compression or expansion of a gas in a container with perfectly non conducting walls.
  2. Sudden bursting of the tube of a bicycle tyre.
  3. Propagation of sound waves in air and other gases.
  4. Expansion of steam in the cylinder of a steam engine
  5. Expansion of hot gases in an internal combustion engine.

If you have any doubt on thermodynamics topic, please let me know in the comment box. I will try to write more articles on your requested topics.

“Stay connected, keep smiling!”

 

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The Simplest Explanation Ever of Electric Charge https://studyconcepts.in/the-simplest-explanation-ever-given-of-electric-charge/ https://studyconcepts.in/the-simplest-explanation-ever-given-of-electric-charge/#respond Fri, 15 Aug 2025 13:42:35 +0000 https://studyconcepts.in/?p=1013 Today in my article I will explain everything about Electric Charge. Like what is electric charge, how it is generated and some properties of Electric Charge etc. I am going to explain it in very simple language so that you do not have any problem in understanding it. What is electric charge? The study of [...]

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Today in my article I will explain everything about Electric Charge. Like what is electric charge, how it is generated and some properties of Electric Charge etc. I am going to explain it in very simple language so that you do not have any problem in understanding it.

What is electric charge?

The study of electric charge, especially when the electric charge is at rest, falls under the branch of physics called electrostatics. Electrostatics focuses on the behavior of electric charges that are not in motion. It involves the study of the forces, fields, and potentials associated with these static charges.

Electric charge is a fundamental property of matter. It is produced by the rubbing of two substances and experiences a force when placed in an electromagnetic field (electric and magnetic fields). There are two types of electric charges: positive and negative. Like charges (positive-positive or negative-negative) repel each other, while opposite charges (positive-negative) attract.

Who gave the name positive and negative to electric charges?

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“Benjamin Franklin one of the Founding Fathers of the United States is credited with naming electric charges as positive and negative.”

In the 18th century, while experimenting with electricity, Franklin identified two types of electrical states and named them as positive and negative. He observed that when certain materials were rubbed together, they attracted or repelled each other, and he used these observations to develop his theory of electric charge.

What is Benjamin Franklin’s electrical theory?

Before Franklin’s work, scientists believed that electricity involved the interaction of two different fluids. Franklin, on the other hand, proposed a single-fluid model of electricity. According to him, electricity was a type of fluid that could flow between objects.

Moreover, when this fluid is transferred from one object to another, the object losing the fluid becomes positively charged, and the object gaining the fluid becomes negatively charged. While the choice of which charge should be called positive and which negative was basically arbitrary. Franklin gave his theory before the discovery of the electron and proton.

He defined the direction of electric current as flow from positive to negative. However, we all know that the direction of electron flow, which constitutes electric current, is from negative to positive. But we still use the convention of flowing current from positive to negative.

How charges are produced?

When two objects are rubbed together, charges are generated due to friction.

  • When the glass rod is rubbed with silk, the glass rod loses electrons and the silk gains electrons. This means the glass rod becomes positively charged and the silk becomes negatively charged.
  • Similarly, when rubber is rubbed with fur the rubber gains electrons and the fur loses electrons. This means the rubber becomes negatively charged and the fur becomes positively charged.
  • Suppose there are two glass rods that have been rubbed with silk and two rubber rods that have been rubbed with fur.
  • When we bring two glass rods (rubbed with silk) close to each other they repel each other. Similarly, when we bring the two rubber rods (rubbed with fur) close to each other they repel each other. On the other hand, when we bring the rubber rod (rubbed with fur) close to the glass rod (rubbed with silk) they will attract each other.

In this way, charges are produced by the interaction of two substances.

“When we bring two glass rods (rubbed with silk) and rubber rods (rubbed with fur) near a piece of paper, they also attract that piece of paper.”

How does a charged object attract a neutral object?

This happens due to polarization of charges:

Charges are usually distributed evenly throughout the object. When a positively charged object is brought near a neutral object, it attracts that neutral object towards itself. Since the object is positively charged, it attracts the negatively charged particle inside the neutral object.

As a result, the part near the positively charged object becomes negative and the other part becomes positive. There will be a redistribution of charges within the neutral object, and there will be a slight separation between the positive and negative charges. As a result, positively charged objects will attract neutral objects.

Similarly, when a negatively charged object is brought near a neutral object, it attracts that neutral object. In this case also there will be redistribution of charges within the neutral object. In this case too, there will be a slight separation between the positive and negative charges. As a result, positively charged objects will attract neutral objects.

“The separation of positive and negative charges within a material due to an external electric field is indeed called the polarization of electric charges.”

What is ionization?

Atoms are made up of three types of particles, negatively charged electrons, positively charged protons, and neutral neutrons. The charge of a proton or electron is the ultimate, natural unit of charge.  If the atom is undisturbed. That is, no electron is removed or added from it then the entire atom will become electrically neutral. That is, the algebraic sum of the positive charge of protons and the negative charge of electrons is zero.

If one or more electrons are removed, the remaining positively charged structure is called a positive ion. A negative ion is formed when an atom gains one or more electrons. The process of losing gaining electrons is called ionization.

What is additive nature of charges?

The total charge on an object is equal to the algebraic sum of all the electric charges distributed on the different parts of the object. If q1,q2, q3,……. are electric charges present on different parts of an object, and if q is the total electric charge on the object then

q=q1 + q2 + q3 +…..

What is quantization of charge?

The magnitude of charge on the proton and electron is e= 1.6 × 10⁻¹⁹ C. Since, protons and electrons are the only charged particles that make up matter, the charge on an object must be an integer multiple of ±e. The charge on any object must be equal to-

q= ±ne (where n is an integer)

The charge on an object can be increased or decreased in steps of e. “The fact that all charges are always some integral multiples of an elementary charge (e= 1.6 × 10⁻¹⁹ C) is known as quantization of charge.”

What is law of conservation of charge?

You must have read in mechanics, that the total linear momentum of an isolated system always remains constant. Electric charge also obeys the similar law.

“For an isolated system, the net charge always remains constant. In any physical process the charge may get transferred from one part of the system to another, but net charge remains the same. In other words charges can neither be created nor destroyed. This is called the law of conservation of charge.”

With the help of some examples it will become more clear to you how charge is conserved:

1) As I have already told that when a glass rod is rubbed with silk the glass rod becomes positively charged and the silk becomes negatively charged. The amount of positive charge on the glass rod is exactly equals to the negative charge on the silk.

Thus, the glass rod and silk, which had zero net charge before rubbing, still possesses zero net charge after rubbing.

2) In all nuclear changes, the proton number is found to be unchanged. For example, in nuclear fission of Uranium (₉₂U²³⁵) by one neutron (₀n¹), Barium (₅₆Ba¹⁴¹), krypton (₃₆kr⁹²) and three neutrons (₀n¹) are produced along with liberation of energy.

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Proton number before fission = Proton number Proton number after fission= 56 + 36 +3(0)= 92

Thus, net charge (proton number) is same before and after the nuclear fission of Uranium.

3) Annihilation of matter ( A positron and an electron combine to produce a Gamma ray Photon) and pair production (a Gamma ray Photon materialises into an electron and positron pair) are two important nuclear phenomena. Charge is conserved in both the process.

Some properties of electric charge:

  1. Like charges (positive-positive or negative-negative) repel each other, while opposite charges (positive-negative) attract.
  2. The magnitude of elementary negative or positive charge is same and is equal to 1.6 × 10⁻¹⁹ C.
  3. The electric charge is additive in nature. it means that that the total charge on an object is the algebraic sum of the charges located at different points on the object.
  4. The electric charge is quantized. it means charge carried by any charge object is equal to ±ne (“n” is an integer).
  5. Electric charge obeys the law of conservation of charge.
  6. Unlike mass, the electric charge on an object is not affected by the motion of the object.

I hope all your doubts are cleared but still if you have any queries then you are welcome. If you want me to write more articles on electrostatics please let me know in the comment box below.

“Stay connected, keep smiling!”

 

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Unified Theory of Electricity, Magnetism, and Light by Maxwell https://studyconcepts.in/unified-theory-of-electricity-magnetism-and-light-by-maxwell/ https://studyconcepts.in/unified-theory-of-electricity-magnetism-and-light-by-maxwell/#respond Wed, 16 Jul 2025 15:54:47 +0000 https://studyconcepts.in/?p=532 In this article, we will learn about, how Maxwell changed our understanding of light. He showed electricity, magnetism, and light are interconnected and derived a set of equation called Maxwell’s equation that predicted Electromagnetic waves. Let us first look at Newton and Huygen’s approach to the description of light: What is Newton’s Corpuscular theory of [...]

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In this article, we will learn about, how Maxwell changed our understanding of light. He showed electricity, magnetism, and light are interconnected and derived a set of equation called Maxwell’s equation that predicted Electromagnetic waves.

Let us first look at Newton and Huygen’s approach to the description of light:

What is Newton’s Corpuscular theory of light?

This theory describes light as a stream of tiny elastic and massless particles, called corpuscular. These corpuscular are emitted by the light source and travel in straight lines at high speeds through space. In short, he supported the particle nature of light.

What is Huygen’s wave theory?

Huygens’ wave theory, known as Huygens’ Principle. According to this theory, The wavefront is the locus of all points on the wave that are in the same phase of oscillation. Each point on the wavefront acts as a source of secondary spherical wavelets that propagate outward. The new wavefront is then the tangent or envelope of all the secondary wavelets. In short, he supported the wave nature of light.

“Newton’s particle theory dominated, however Young’s double-slit experiment provided strong evidence for the wave nature of light.”

What is Maxwell’s theory of Electromagnetism?

James Clerk Maxwell, a Scottish physicist, his groundbreaking equations predicted the existence of radio waves before they were discovered. Maxwell’s important contributions to the kinetic theory of gases laid the foundation for modern thermodynamics. Additionally, his theory forms the backbone of modern physics and engineering, influencing technologies from radio and television to radar.

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“Maxwell developed the classical theory of electromagnetic induction, unifying electricity, magnetism, and light into a comprehensive theory. He proposed that light is a form of electromagnetic radiation and composed of oscillating electric and magnetic fields traveling at the speed of light.”

Heinrich Hertz experimentally confirmed Maxwell’s theory by generating and detecting electromagnetic waves, specifically radio waves. Maxwell observed inconsistency in Ampere’s circuital laws and symmetry in the laws of electromagnetism. The concept of displacement current removed the inconsistency in Ampere’s circuital law and the laws of electromagnetism also becomes symmetrical.

The above four fundamental laws of physics were stated by Maxwell in the form of four equations, called, “Maxwell’s equations.” The equations predict that time and space dependent electric and magnetic fields propagate as transverse waves, called electromagnetic waves, with a velocity equal to that of light.

The equations are:

1. Gauss’s law in electrostatics:

This law gives the total electric flux in terms of the charge enclosed by a closed surface, where A is the total surface area.

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2. Gauss’s law in magnetism:

A direct consequence of Gauss’s law in magnetism is that an isolated magnetic monopole does not exist.

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3. Faraday ‘s law of electromagnetic induction:

This law states that the line integral of the electric field along a closed path is equal to the rate of change of magnetic flux through the surface bounded by the closed path.

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4. Maxwell ampere’s circuital law:

This law states that conduction current and displacement current together have a property of continuity and at an instant, in a circuit, the conduction current is equal to the displacement current.

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Based on these equations, Maxwell made the following predictions:

  • Electromagnetic waves are produced by accelerating electric charges.
  • Electromagnetic waves propagate in space at the speed of light (=  3 × 10⁸ m/s). Electromagnetic waves are transverse in nature.
  • Light itself is an electromagnetic wave, it is transverse in nature and it travels through space at a speed of (3 × 10⁸ m/s).

What are Electromagnetic Waves?

Maxwell predicted the existence of electromagnetic waves based on these equations. According to him an accelerating charge produces a sinusoidal time varying magnetic field, which produces a sinusoidal time varying electric field. The two fields thus generated are perpendicular to each other and are sources of each other.

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The mutually perpendicular time wearing electric and magnetic fields constitute electromagnetic waves, which propagate in space in a direction perpendicular to the direction of both the field. The electric and magnetic fields are perpendicular to each other and also perpendicular to the direction of wave propagation. Therefore, electromagnetic waves are transverse in nature.

The speed of electromagnetic waves in free space is given by:

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Where, μο (absolute permeability) and ∈o (absolute permittivity) of the free space. The velocity of electromagnetic waves in free space (vacu ght in vacuum, i. e. (3 × 10⁸ m/s).

Examples of Electromagnetic Waves:

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  • Radio waves: Radio waves have the lowest frequency and longest wavelength and used for broadcasting radio and television signals.
  • Microwaves: Used in microwave ovens, radar, and some telecommunications.
  • Infrared radiation: Used in thermal imaging, remote controls, and some heating applications.
  • Visible light: The portion of the spectrum that humans can see, enabling vision.
  • Ultraviolet radiation: Can be harmful in large doses but is also used in sterilization and tanning lamps.
  • X-rays: Used in medical imaging to see bones and other internal structures.
  • Gamma rays: Gamma rays have the highest frequency and shortest wavelength and used in cancer treatment and sterilization.

 

Electromagnetic waves propagate as varying electric and magnetic fields, with two fields are perpendicular to each other and also perpendicular to the direction of propagation of the wave. In other words, electromagnetic waves are transverse in nature. Electromagnetic waves are produced by accelerated charges, obey the principle of superposition And  do not require any medium to propagate. The electric field vector in an electromagnetic wave is responsible for the optical effect For this reason, the electric vector is called the light vector.

“In upcoming article, we will learn how wave particle duality explained every mystery of light, how it opened the doors of quantum mechanics.” If you have any doubts regarding this topic, please leave your question in the comment section below.

“Stay connected, keep smiling!”

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Simple and Brief Explanation on Zener Diode https://studyconcepts.in/simple-and-brief-explanation-on-zener-diode/ https://studyconcepts.in/simple-and-brief-explanation-on-zener-diode/#respond Tue, 08 Jul 2025 19:11:36 +0000 https://studyconcepts.in/?p=427 Are you puzzled by the concept of the Zener Diode? Looking for a reliable platform to understand it easily? Don’t worry, you’re absolutely in the right article! Today In this article, we are going to explore everything about Zener Diode. We’ll focus on some key areas such as, what a Zener diode is, some prerequisites [...]

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Are you puzzled by the concept of the Zener Diode? Looking for a reliable platform to understand it easily? Don’t worry, you’re absolutely in the right article!

Today In this article, we are going to explore everything about Zener Diode. We’ll focus on some key areas such as, what a Zener diode is, some prerequisites to understand the topic, its classification, diagrams, and a few more extra concepts to strengthen the understanding.

By the end of this article, you’ll have a complete understanding of Zener diode. So, let’s get started! But before diving into the Zener diode itself, we have to understand some of it’s pre-requisites first, so let’s start..

What is Semiconductor?

A Semiconductor is a material whose electrical conduction is due to the movement of electrons in the conduction band and the movement of holes in the valence band. Its electrical conductivity lies between a conductor and an insulator.

Semiconductors are classified into two types:

1. Intrinsic Semiconductor:

A pure semiconductor which is free of every impurity is called intrinsic semiconductor. The electrical conductivity of a pure semiconductor is completely controlled by electrons. For example: Silicon (Si) and Germanium (Ge).

2. Extrinsic Semiconductor:

A doped semiconductor or a semiconductor with suitable impurity atoms added to it, is called extrinsic semiconductor.

Extrinsic semiconductors are further classified into two types:

1. N-type Semiconductor:

When a pure semiconductor of silicon (Si), is doped with a controlled amount of pentavalent atoms. For example: arsenic, phosphorus, antimony or bismuth, is called n-type semiconductors.

2. P-type Semiconductor:

When a pure semiconductor of germanium (Ge), is doped with controlled amount of trivalent atoms. For example: gallium (Ga), indium (In), boron (B) or aluminium (Al), is called p-type semiconductors.

What is Doping?

Doping is a process of adding desirable impurity atoms to a pure semiconductor. The impurity, atoms added are called dopants.

What is P-N Junction?

When a p-type semiconductor is brought into close contact with n-type semiconductor crystal, the resulting arrangment is called p-n Junction diode.

There are two methods of biasing in the P-N Junction:

1. Forward Biasing:

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A p-n junction is said to be forward biased if the positive terminal of the external battery is connected to p-side and the negative terminal to the n-side of p-n junction.

2. Reverse Biasing:

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A p-n junction is said to be reverse biased if the positive terminal of the external battery is connected to n-side and the negative terminal to p-side of the p-n junction.

Characteristics of a P-N Junction Diode:

1. Forward Voltage Drop:

A small voltage across a conducting diode, is called the forward voltage drop and is about 0.7 V for normal diodes which are made from Silicon. The forward voltage drop of a diode is almost constant whatever the current passing through the diode so they have a very steep characteristic.

2. Reverse Voltage:

When a reverse voltage is applied a perfect diode does not conduct, but all real diodes leak a very tiny current. This can be ignored in most circuits because it will be very much smaller than the current flowing in the forward direction. However, all diodes have a maximum reverse voltage (usually 50V or more) and if this is exceeded the diode will fail and pass a large current in the reverse direction, this is called breakdown.

3. Rectifier Diodes:

Rectifier diodes are used in power supplies to convert alternating current (AC) to direct current (DC), a process called rectification. All rectifier diodes are made from silicon and therefore have a forward voltage drop of 0.7V.

There are two types of characteristics of a p-n junction diode:

1. Forward Characteristics:

This gives, how diode behaves, when the positive terminal of a voltage source is connected to the P-type side and the negative terminal to the N-type side. This causes the depletion region to narrow,  because majority charge carriers attracted towards the junction. When the voltage is low, small current flows. At threshold voltage or knee voltage current starts to increase rapidly. Threshold voltage for Silicon diodes is around 0.7V and for Germanium around 0.3V. After threshold voltage current increases exponentially with voltage.

2. Reverse Characteristics:

This gives, how diode behaves , when the positive terminal of a voltage source is connected to the n-side and the negative terminal to the p- side. This increases the width of the depletion region, because of majority charge carriers are attracted away from the junction, which blocks current to flow. Small reverse saturation current, flow due to the presence of minority carriers. At breakdown, the diode’s resistance drops sharply, and a large current flow, resulting in damage to the diode.

The Zener Effect:

In the presence of sufficient reverse voltage, a p-n junction experiences rapid avalanche breakdown and conducts current in the reverse direction. Under the influence of an applied electric field the free valence electrons can be accelerated so much that they can free other electrons and the subsequent collision quickly become an avalanche. When this process is taking place, very small changes in voltage can cause very large changes in current. The breakdown process depends upon the applied electric field, so by changing the thickness of the layer to which the voltage is applied, zener diodes can be formed which break down at voltages from about 4 volts to several 100 volts.

What is Zener Diode?

The Zener effect was discovered by Clarence Melvin Zener. With details of electrical characteristics of diode and Zener effect.In which current flows in the opposite direction due to electron tunneling in the heavily doped p-n junction.

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The zener diode uses a p-n junction in reverse bias to make use of the zener effect which is a breakdown phenomenon which holds the voltage close to a constant value called the zener voltage. The basic principle of diodes is that they allow current to flow in one direction. When the direction is reversed (reverse bias) the diode does not allow any current to flow in the circuit. This also applies to zener diode as it does not allow current to flow in reverse bias, the zener diode will work like a standard diode.

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Zener diodes have a specified reverse breakdown voltage known as the Zener voltage. In reverse bias, the Zener diode prevents current from flowing through the circuit only up to a certain voltage. If the breakdown voltage of the zener diode is 10V and the supply voltage is 5V. In this condition, current will not flow in the circuit. However, when the circuit voltage rises above the Zener diode breakdown voltage i.e. above 10 volts, current will start flowing in the circuit due to increased Zener diode breakdown voltage.

“You may be wondering, what is the advantage of a diode that can conduct current in both directions?”

So here are the all applications, which can answer above question:

  • Zener diode as a Voltage Regulator: The zener diode is used as a Shunt voltage regulator for regulating voltage across small loads.
  • Zener diode in clipping circuits: Zener diode is used for modifying AC waveform clipping circuits by limiting the parts of either one or both the half cycles of an AC waveform
  • Zener diode in clipping circuits: Zener diode is used for modifying AC waveform clipping circuits by limiting the parts of either one or both the half cycles of an AC waveform.

What are Zener and Avalanche Breakdown?
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Zener Breakdown:

In highly doped diodes, the depletion region becomes narrow. This high electric field causes the electrons to pass through the depletion region even at relatively low reverse voltage, which leads to zener breakdown. The breakdown voltage decreases with increasing temperature.

Avalanche Breakdown:

In lightly doped diodes the depletion region is wide. The strong electric field at higher reverse voltage accelerates the free electrons, which result in collisions with atoms, creating many new electron-hole pairs. These electron-hole pairs contribute to a significant increase in the current, which leads to avalanche breakdown. The breakdown voltage increases with increasing temperature.

I hope by now all your doubts related to Zener diode have been cleared. If you still have any doubts on this topic or you want me to come up with more articles on semiconductor devices then please, please drop your question in the comment section, I will try my best to answer all your doubts.

“So stay connected, keep smiling!”

 

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Cruelty Knows No Limit https://studyconcepts.in/cruelty-knows-no-limit/ https://studyconcepts.in/cruelty-knows-no-limit/#respond Thu, 03 Jul 2025 16:45:52 +0000 https://studyconcepts.in/?p=268 If I had foreseen Hiroshima and Nagasaki , I would have torn my formula in 1905. —Albert Einstein An explosion that killed 2 lakh people. When the human mind starts feeling that it has no option left, it finds a way to commit crime. “I am talking about the explosion that happened in Japan in [...]

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If I had foreseen Hiroshima and Nagasaki , I would have torn my formula in 1905.
—Albert Einstein

An explosion that killed 2 lakh people. When the human mind starts feeling that it has no option left, it finds a way to commit crime.

“I am talking about the explosion that happened in Japan in 1945 which shook everyone. “In a civil war or a world war, only one country wins. But the common people have to suffer its consequences.”

During the Second World War, atomic bombs were used by America on two Japanese cities, “Hiroshima” and “Nagasaki.

On August 6, 1945, people saw an American Boeing B-29 plane flying in the sky, nobody had any information about that plane till then. For them it was a normal plane, they did not know that this plane was carrying a nuclear bomb.

The Boeing B-29 aircraft flew over the city of Hiroshima carrying the “Little Boy” atomic bomb. This was the world’s first atomic bomb. This bomb was dropped on Hiroshima and with this America became the first and only country in the world to use nuclear weapons. Three days later, on August 9, 1945, another Boeing B-29 aircraft “Fat Man” flew over Nagasaki carrying the atomic bomb. America dropped another atomic bomb on Nagasaki.

What happened after the giant explosion?

  1. 200,000 people were killed in this bombing.
  2. First there was a blinding light that temporarily blinded people Immediately.
  3. there was such a powerful explosion that many people lost their hearing ability forever.
  4. A temperature of 4000 degrees Celsius fell on the ground, that instantly vaporised people in the radius.
  5. People’s skin was peeling off, they were so dehydrated they were in agony.
  6. Those who did not die immediately, that is, died a few days, weeks or months later. The sunny sky that day was covered with black toxic fumes.

Who developed the Atomic Bomb?

American physicist,  “J. Robert Oppenheimer” considered the “Father of the Atomic Bomb”, led the Manhattan Project. Under this project, he developed the atomic bomb.

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How did “J. Robert Oppenheimer “develop the atomic bomb?

Before understanding the mechanism of an atomic bomb, let us understand some important points :

What is nuclear fission??

The process in which a larger nucleus splits into two or more smaller nuclei releasing particles. Such as, neutrons and energy in the form of radiations, alpha beta and gamma.

For example:

When a neutron strikes a larger nucleus such as Uranium, it’s nucleus splits into two smaller nuclei.

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What is Alpha, Beta and Gamma radiation?

Alpha particle is a positively charged particle which contains two neutrons and protons, with weakest penetrating power and high ionization power. Produced in the process of alpha decay. Beta particle is high energy electron and positron emitted during beta decay, with moderate penetrating power and lower ionizing power than alpha. Gamma particle is a penetrating form of electromagnetic radiation, with highest penetrating power and least ionizing power.

What is Radioactive decay?

Atoms are made up of subatomic particles: protons, neutrons, and electrons. Protons and neutrons reside in the nucleus, while electrons orbit around the nucleus. The nucleus of a radioactive element like uranium contains large amounts of protons and neutrons. As a result, nucleus of radioactive elements become unstable due to high repulsion. To make it stable, radioactive elements like uranium undergo radioactive decay and emit particles and energy in the form of radiations like alpha, beta and gamma. This process is known as radioactive decay.

Now, let us come to the point and understand the mechanism behind how the atomic bomb was developed???

As I have already discussed above that if a large nucleus like Uranium collides with a particle (usually a neutron) then it splits into two smaller nuclei. If the total mass of the two small nuclei is less than the mass of uranium then the missing mass is converted into energy.

By the equation:

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The greatest scientist of all time, “Albert Einstein”, proposed this equation, it is a fundamental part of his theory of special relativity proposed in 1905. This equation simply says that, “the energy is equals to mass multiplied by the speed of light squared.” Showing that even a little bit of mass can release tremendous amount of energy. This means, “energy and mass are related.

In the case of Uranium-235 and Plutonium 239, when these are bombarded with a neutron they split into two less massive nuclei with the emission of particles and huge amounts of energy in the form of radiations. If there is enough fissionable nuclei, in high enough concentration, then it is possible for released neutron to hit three more nuclei. As a result, there will be three more fission. This will further leads to 9 then 27 more fission. This will cause chain reaction. At last, this chain reaction ends up creating nuclear bomb, which releases massive amount of energy. As a result there will be three more fission.

Why only Uranium-235 (U-235) and Plutonium-239 (Pu-239) are used in atomic bombs?

Uranium- 235 is an isotope of Uranium and is naturally occurring while Plutonium-239 is an artificially created isotope usually obtained by bombarding U-238 with a neutron. Uranium-235 and Plutonium-239, fissions easily releasing immense energy making them more suitable for atomic bombs.

Is nature destructive??

You might be thinking that, since Uranium-235 is naturally present in nature. That means nature is destructive. Before you jump to any conclusions and before I answer this question. let me tell you what half-life is.

Half-life:

Ernest Rutherford introduced the concept of half-life. Half-life refers to the time required for half of the atoms in a radioactive substance to undergo radioactive decay.

Let’s discuss the half-life of uranium and plutonium:

The half-life is as I mentioned above. So the half-life of Uranium-235 is 703.8 million years. This means that it takes about 703.8 million years for half of a given amount of uranium 235 to undergo radioactive decay. Similarly, the half-life of plutonium-239 is about 24,100 years. This means that it takes 24,100 years for half of a given amount of Plutonium-239 to undergo radioactive decay.

Nature also knew how dangerous these radioactive elements can be for our lives, that is why their half-life is so high. Therefore, it is not nature but the human mind that is destructive. It is man who triggers the decay of dangerous radioactive elements like uranium and plutonium and develops atomic bombs with the help of chain reaction.”

I hope now all your doubts are cleared, if not then please leave a comment and let me know where you are feeling difficulty and what you felt after reading this article. I will come up with a new article soon, till then take care.

“Stay connected and keep smiling!”

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Take Off Your Blindfold and Live in the Moment https://studyconcepts.in/take-off-your-blindfold-and-live-in-the-moment/ https://studyconcepts.in/take-off-your-blindfold-and-live-in-the-moment/#respond Sat, 21 Jun 2025 16:47:01 +0000 https://studyconcepts.in/?p=394 Have you ever heard of the calendar of one year being a doppelganger of another year’s calendar? Yes, you heard it right. The 2025 calendar is a doppelganger of the 1941 calendar. Both 1941 and 2025 are non leap years and both years started on the same day i.e. Wednesday. This fact has raised many [...]

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Have you ever heard of the calendar of one year being a doppelganger of another year’s calendar?

Yes, you heard it right.

The 2025 calendar is a doppelganger of the 1941 calendar. Both 1941 and 2025 are non leap years and both years started on the same day i.e. Wednesday. This fact has raised many questions in many minds.  Such as, if 1941 was the bloodiest and most tragic year of the 20th century, then so will 2025 be?

Is World War III approaching?

Will the past of Hiroshima and Nagasaki be repeated?

1941 was a year of great change and ferocity in World War II, including the entry of the United States, the opening of the Eastern Front, and continued tremendous expansion in many areas. Now let’s explore some of it’s incidents:

Attack on Pearl Harbor:

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The Japanese Navy suddenly attacked the United States naval base Pearl Harbor on 8 December 1941. As a result of this attack, the United States also jumped into the Second World War. Japan also attacked the US-occupied Philippines, British-occupied Malaya, Singapore, and Hong Kong.

The Battle of Hong Kong:

On 8 December 1941, British and Canadian forces attacked the Japanese army to protect Hong Kong. The Japanese army displayed outstanding skills and forced the British colonial authorities to surrender after a violent conflict, on 25 December 1941.

Mass shooting at Babi Yar:

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One of the many mass shootings carried out by Nazi German’s. The first documented of the massacres took place on 29-30 September 1941, in which some 33,771 Jews were murdered. Other victims of the massacre included Soviet prisoners of war, communists, and Romani people. A total of 100,000 to 150,000 people were murdered at Babi Yar during the German occupation.

“In 2025, ongoing conflicts and tensions show that the entire world is struggling.”

The war in Ukraine, now in its third year, remains a major focal point with increased missile and drone attacks. The Israel-Hamas conflict in Gaza also remains a source of instability, fueling military operations and regional tensions. In addition, conflict continues in Sudan, Myanmar, and the Sahel region of Africa, and the humanitarian crisis in many of these areas is getting worse.

Pahalgam attack:

On 22 April 2025, a suicide attack occurred at Baisaran Valley near Pahalgam in Anantnag district of Jammu and Kashmir, India, killing 26 tourists and injuring more than 17 people. The attack was one of the deadliest in the region, with specific details from Jammu and Kashmir, in which Hindus were massacred.

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On the night of 6th and 7th  May India launched “Operation Sindoor“, attacking “terrorist infrastructure.” Missile strikes by Indian Air Force jets are also included. Pakistan also retaliated, but eventually both countries agreed on a ceasefire. However, India’s position remained strong in the end.

Some similar incidents of 1941 and 2005:

1. Plane crash incidents:

There were a number of air accidents in Britain in 1941, many of which involved mid-air collapses. In one incident a Hampden 83 aircraft crashed at Wickham Ford on 14 August. Another group of incidents involved RAF Airspeed Oxfords colliding mid-air, two near RAF South Cerney and two near RAF Shawbury. In addition, two Westland Whirlwinds of 263 Squadron collided over Saltford, Somerset.

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On 12 June 2025, a Boeing 787-8 Dreamliner aircraft crashed into the hostel block of B. J. Medical College in the Meghani Nagar area of Ahmedabad, about thirty seconds after take-off. A few seconds after takeoff, the plane began losing altitude while its wing was nearly level and the nose pointed upward. The flight crew issued a mayday call, reporting a loss of power and thrust. The accident resulted in several explosions. As a result of the incident, 241 of the 242 people on board the plane died. One British man.

2. Attack on Iran:

In August 1941, during World War II, Britain and the Soviet Union launched a joint invasion of Iran, known as Operation Countenance. The offensive was aimed at securing a vital supply route to the Soviet Union, protecting British oil in Iran, and reducing German influence in the region.

On June 13, 2025, Israel launched surprise attacks on Iran’s key military and nuclear installations. Israeli air and ground forces killed some of Iran’s key military leaders, nuclear scientists, and politicians; and damaged or destroyed Iran’s air defenses and some of its nuclear and military facilities. The Iran-allied Houthis in Yemen have also fired several missiles at Israel.

3. Stampede:

In June 1941, a series of Japanese bombings took place in Chongqing, China, including a major air raid, The result was a tragic accident in which thousands of civilians were killed. The incident, often referred to as the Great Tunnel Disaster, involved a stampede and suffocation in a crowded air raid shelter during a prolonged bombing raid.

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The RCB stampede refers to the tragic stampede that occurred during the victory celebrations of the Royal Challengers Bengaluru (RCB) in Bengaluru on 4 June 2025. Celebrations at the M. Chinnaswamy Stadium after RCB won the IPL resulted in a stampede near the stadium gate, killing 11 people and injuring over 56.

After winning the IPL 2025, RCB held a victory parade and celebrations at the M. Chinnaswamy Stadium in Bengaluru. A stampede broke out during the celebrations. As a result, at least 11 people died and many were injured. This led to public criticism. Resulting, at least 11 deaths and numerous injuries.

Before you start believing this and the fear of the future starts bothering you, let me give you a logical explanation. The Gregorian calendar is the most widely used calendar including India

According to this calendar:

  1. Leap year calendar repeats its pattern every 28 years.
  2. Years which are divisible by 4 and century years which are divisible by 400 are called leap years.
  3. Non-leap year calendar repeats its pattern after 6 or 11 years.
  4. Moreover, The calendar of 2025 is not only the same as that of 1941 but also of years, 1958, 1969, 1986, 1997, 2003 and 2014.

“It is advisable to do some research before believing anything. As I mentioned, “similar incidents,” but they are not exactly same, there are differences in their results. I have explained the reason behind the repetition of the calendar pattern and the repetition of the incident is just a coincidence.”

“The future is unpredictable. Enjoy every moment as much as you can, don’t believe in irrational things. I request you not to be superstitious and spread superstitions.”

If you still don’t agree with my explanation then please let me know in the comment box below.

 “Stay connected, keep smiling!”

 

 

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The Mystery of Time Travel https://studyconcepts.in/the-mystery-of-time-travel/ https://studyconcepts.in/the-mystery-of-time-travel/#respond Wed, 18 Jun 2025 16:47:03 +0000 https://studyconcepts.in/?p=216 Imagine you are traveling in a plane which is supposed to take you to your destination, but what if it doesn’t take you to your destination and when you get off the plane you find out that three decades have passed. In this article, I will discuss about: Mysterious incidents that happened in the past, [...]

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Imagine you are traveling in a plane which is supposed to take you to your destination, but what if it doesn’t take you to your destination and when you get off the plane you find out that three decades have passed.

In this article, I will discuss about:

  1. Mysterious incidents that happened in the past, which made people think that time travel is possible.
  2. Newton and Einstein’s views on time travel, which will ultimately answer the question: Is time travel possible?

1) In 1955, “Flight 914,  Douglas DC-4″, took off from New York to Miami, Florida, carrying 57 passengers and 5 crew members. The plane disappeared from radar mid-way without a trace. Search operations were launched, but all were unsuccessful and failed. After many attempts at last, the airline declared the plane missing and the case was closed.

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“In 1992 a mysterious incident occurred at the airport of Caracas, the capital of Venezuela.”

A flight that was not on the air traffic control radar contacted the airport control room and asked for permission to land. When the air traffic control chief “Juan De La Corte” was asked the name of the plane and where it was coming from, the chief was completely shocked to know that the name of the plane was “Flight-914, Douglas DC-4” and wanted to land in “Miami, Florida.” The chief said that this is not Miami but Caracas airport in Venezuela. The pilot asked for permission  to land the plane, the plane was allowed to land in Venezuela.

“The pilot panicked when he saw the view of the airport. He panicked even more when he realized that it was 1992 and almost three decades had passed. Suddenly he started the plane and took off from the airport and the plane was never seen again.”

What happens when you and your friend are discussing time travel and a third person comes and says I am a time traveler from 2036?

2) In the early 2000s an anonymous man named, “John Titor,”appeared on Internet forums. “He introduced himself as an American soldier and claimed to be a time traveler
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Many questions arose in people’s minds:

What he is doing here? how he reached?

This news went viral and caught everyone’s attention. In addition, he said that he is on a mission to retrieve a 1975 IBM 1500 computer in order to fix a software bug in the computer of his time. Everyone was surprised but still people did not believe it, they thought that all this is a fantasy.

On this John Titor posted the design of his time machine and made some predictions:

  1. Civil war in America,
  2. global nuclear conflict,
  3. technological breakthroughs.

One day John Titor mysteriously vanished and left no evidence behind. Some of his predictions were accurate but some were not. But it was also quite surprising that how someone’s predictions could be so accurate.

Before accepting this incident as true, let us see what “Newton and “Einstein ” said about “time travel:

  1. According to “Newton,” time is absolute and moves only in forward direction and it is same for everyone irrespective of their place. So, for Newton time travel was not possible.
  2. According to “Einstein,” time is relative and it’s value can change. “Time travel is possible only when the speed is close to or equal to the speed of light and in places where gravity is high such as- black hole.”
  3. This theory supports time travel to the future but if I talk about time travel to the past then it is even more difficult.

Theories like wormholes support time travel to the past and future but this “theory gives rise to a paradox called grandfather paradox. In short, theoretically time travel is possible but there is no practical proof of it. Till now no such time machine has been made that can take us on time travel.

I have presented the past events and the physics behind it in front of you all. Because I am a physics student. So, it would be a bit difficult for me to believe this incident to be true.

There was disagreement among people about these events:

According to one group, this was a true event, while according to the other group, this was merely a fictional story that was spread among the people. so what is your opinion on this? Was this a true incident or just a fictional story”?

If you want to know about “time travel, black hole and grandfather paradox then please let me know in the comment box below.”

“Stay connected, keep smiling! “

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