Show that for an ideal blackbody the product is a constant

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

Show that for an ideal blackbody the product

\lambda_{\max}^{4}R

is a constant, where

R

is the total power radiated per unit area and

\lambda_{\max}

is the wavelength of maximum emission. Hence calculate the numerical value of this constant using

\sigma = 5.67\times10^{-8}\,\text{W\,m}^{-2}\,\text{K}^{-4}

and

b = 2.898\times10^{-3}\,\text{m\,K}