Blackbody Radiation

A blackbody is a body which absorbs radiations of all wavelengths which incident on it. Blackbody neither reflects nor transmits any of the incident radiation, and therefore, appears black. When any radiation enters the blackbody region through the opening, it suffers multiple reflection inside the sphere and is finally absorbed. When the walls of such a cavity are heated to temperature T, it emits the radiations which fill the cavity and it come out through the opening of cavity. These radations are known as blackbody radiations, which are the characteristic of its temperature.

Rayleigh-Jeans law of black body radiation

According to Rayleigh-Jeans law, the energy distribution in the thermal spectrum is given by

The Rayleigh-Jeans law holds good in the region of shorter frequencies but not for longer frequencies.

Wien’s displacement law of black body radiation

According to Wiens displacement law, in the energy spectrum of a black body, the product of the wavelength corresponding to maximum energy(λm) and absolute temperature is constant. i.e

The Wien’s law holds good in the region of longer frequencies but not for shorter frequencies.

Plank’s law of black body radation

According to planks theory energy is emitted in the form of packets or Quanta called photons and energy of photons is given by E=nhv where n=1,2,3 etc.

In black body, total energy of photons with the wave length range λ and λ + dλ is given by

where h is Plank’s constant, c is speed of the light and T is the temperature of the enclosure.

Plank’s law successfully anticipated black body radiation at higher and lower frequencies

Black body radiation spectrum (Characteristics of a blackbody)

1. At a given temperature, the energy is not uniformly distributed in the radiation spectrum of the blackbody.
2. At a given temperature, the intensity of radiation increases in wavelength and at a particular wavelength, its value is maximum. With further increase in wavelength, the intensity of radiation decreases.
3. With the increase in temperature, λ_m decreases, where λ_m is the wavelength at which the maximum emission of energy. takes place. The points on the dotted line represent λm at various temperatures.
4. There is increase in energy emission with the increase in temperature corresponding to all the wavelengths.
5. The area under curve gives the total energy emitted for the complete spectrum at a particular temperature. With increase in temperature, this area increases. It is also observed that the area is directly proportional to the fourth power of the temperature of the blackbody, i.e., E ∝ T⁴