Black body Radiation | Ultraviolet Catastrophe (UV- Destruction)

Download

What is Black body Radiation?

What is the Ultraviolet Catastrophe (UV- Destruction)?

Answer:

Black body radiation refers to an object or system which absorbs all radiation incidents upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation that is incident upon it. So, the Black Body is an object which absorbs 100% incident radiation and there is no reflection occurs.

It is seen that there is no material available in nature which absorbs all incoming radiation but carbon is one of the material which absorbed maximum radiation; it is also known as a perfect absorber / emitter of radiation. At a particular temperature, the black body would emit the maximum amount of energy possible for that temperature. This value is known as black body radiation. It would emit at every wavelength of light as it must be able to absorb every wavelength to be sure of absorbing all incoming radiation. The maximum wavelength emitted by a blackbody radiator is infinite.

The amount of radiation emitted in a frequency range should be proportional to the number of modes in that range. The best of classical physics suggested all modes had an equal chance of being produced and that the number of modes went up proportional to the square of the frequency.

For example: In the case of the furnace; If there is a very small hole in the door of the furnace heat energy can enter from the outside; inside the furnace, the inside walls absorbed this. The walls become very hot and are also emitting thermal radiation. This may be absorbed by another part of the furnace wall or it may escape through the whole in the door. This radiation that escapes may contain any wavelength. The furnace is in equilibrium as when it absorbs some radiation it emits some to make up for this and eventually a small amount of this emitted radiation may escape compensating for the radiation that entered through the hole.

A black body has the following features

1. The Black body is a perfect absorber as well as perfect emitter.
2. At a particular temperature and wavelength, a black body emits more radiation energy.
3. It absorbs all incident radiation of wavelength and direction
4. It emits radiation energy uniformly in all directions.

BLACK BODY RADIATION CURVES

Figure: Black body radiation curves showing peak wavelengths at various temperatures.

This graph shows how the blackbody radiation curves change at various temperatures. These all have their peak wavelengths in the infra-red part of the spectrum as they are at a lower temperature. In this graph, the peak wavelength of emitted light by the black body decreases when the temperature increases. If we begin to move from IR region to the visible region the power radiation is increasing at a particular point after that it will decrease till the visible region. As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.

Ultraviolet Catastrophe (UV- Destruction)

The major problem for physicists was at a specific wavelength to predict the intensity of radiation emitted by a black body. At long wavelengths, Wilhelm Wien’s theory disagreed with experimental data. Later-on Rayleigh and Jeans then produced a formula by considering the radiation within the black body cavity to be made up of a series of standing waves.

The radiation intensity (I) is given as:

I = (2πCkT/ l⁴)              {l = Lembda : wavelength}

With the help of this formula, large wavelengths fitted the experimental data but it had major problems at shorter wavelengths; i.e if wavelength tended to zero, the curve would tend to infinity. However we know that there is a peak wavelength for each temperature, and the energy emitted at either side of this peak dropped. The Rayleigh-Jeans Law predicted no peak wavelength. This problem is known as the ultraviolet catastrophe.

Similarly Rayleigh Jean’s distribution formula in terms of energy density:

u_l  dl = (8πkT/ l⁴) d_l

For lower wavelength tended to zero the energy density goes to ∞ but experimentally it found that when we decrease l; the energy density u_l  also decreases below the minimum l and at l=0, u_l = 0. So that this law did not explain the experimental curve at lower l; We know this Drawback as the ultraviolet catastrophe.