Laws for Explaining the Energy Distribution

Different laws were proposed for explaining the energy distribution with respect to the wavelength. They are as follows:

(i) Wien’s displacement law 

It states that the maximum energy density (or intensity) of radiation emitted from a black body is displaced towards the shorter wavelength for the rise of temperature (T) of the black body.

It states that the wavelength corresponding to maximum energy is inversely proportional to absolute temperature (T). This law states that the product of the wavelength (λ_m) corresponding to maximum energy and the absolute temperature (T) is a constant.

Limitations: This law holds good only for shorter wavelength and not for longer wavelengths.

(ii) Stefan-Boltzmann’s law

E  = σ T⁴

Limitations: This law holds good only for shorter wavelength and not for longer wavelengths.

(iii) Rayleigh – Jean’s law

According to this law, it states that the energy distribution is directly proportional to the absolute temperature and is inversely proportional to the fourth power of the wavelength.

 (i.e.,) \text { (i.e.,) } \quad \mathrm{E}_{\lambda}=\frac{8 \pi \mathrm{kT}}{\lambda^{8}}

Limitations: This law holds good only for longer wavelength regions and not for shorter wave lengths.

It is found that, both Wien’s and Rayleigh – Jeans law do not agree with the experiment results. Therefore, we can conclude that the classical theory was not able to explain the emission of black body radiation. Thus, Max Planck used Quantum theory to explain the black radiation.