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

E_{\lambda}d\lambda=\frac{8\Pi hc}{\lambda^{5}}\frac{1}{\left( e\frac{hc}{\lambda kT} \right)-1}d\lambda

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.

E_{\lambda}d\lambda=\frac{8\Pi hc}{\lambda^{5}} e^{\frac{-hc}{\lambda kT}}d\lambda

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.