The post About Quantum Physics Part 1: Black Body Radiation, Ultraviolet Catastrophe, Planck’s Radiation Law appeared first on StudyConcepts.
]]>“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:
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.
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!”
The post About Quantum Physics Part 1: Black Body Radiation, Ultraviolet Catastrophe, Planck’s Radiation Law appeared first on StudyConcepts.
]]>