Starting from Planck’s quantum theory of radiation arrive at Wein’s law and Rayleigh-Jean’s law.

Starting from Planck’s quantum theory of radiation arrive at Wein’s law and Rayleigh-Jean’s law.

Answer:-

Planck’s law could be reduced to Wien’s distribution law and Rayleigh-Jeans law in the shorter and longer wavelength regions respectively. Thus the Plack’s law explains the distribution of energy in the blackbody radiation spectrum completely. Planck’s law is given by

here c is the velocity of light,k is Boltzmann constant and h is Planck’s constant.

Reduction to Wien’s law:-

Consider the shorter wavelength region in the black body radiation spectrum.

For very small values of \lambda,e\frac{hc}{\lambda kT}\ >> 1 .

Thus 1 in the denominator can be neglected compared to e\frac{hc}{\lambda kT}.

Hence the equation 3.4 reduces to.

Thus Planck’s law reduces to Wien’s distribution law and hance explains lower wavelength region in the blackbody radiation spectrum.

Reduction to Rayleigh-Jeans law:-

Consider the longer wavelength region in the black body radiation spectrum.

For very large values of \lambda the term \frac{hc}{\lambda kT} is very small.

Thus e\frac{hc}{\lambda kT} could be expanded as a power series.