Answer to Question #233282 in Molecular Physics | Thermodynamics for Arif

Question

Deduce Planck's law of radiation?

Answer 1

Answer:

Planck's law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature. The law is named after Max Planck, who originally proposed it in 1900. It is a pioneering result of modern physics and quantum theory. The spectral radiance of a body, $B_\nu$ , describes the amount of energy it gives off as radiation of different frequencies. It is measured in terms of the power emitted per unit area of the body, per unit solid angle that the radiation is measured over, per unit frequency. Planck showed that the spectral radiance of a body at absolute temperature T is given by

$B_\nu(\nu,T)=\dfrac{2h\nu^3}{c^2}\dfrac{1}{e^{\dfrac{h\nu}{k_BT}}-1}$

where k_B the Boltzmann constant, h the Planck constant, and c the speed of light in the medium, whether material or vacuum. The spectral radiance can also be measured per unit wavelength instead of per unit frequency. In this case, it is given by

$B_\lambda(\lambda,T)=\dfrac{2hc^2}{\lambda^5}\dfrac{1}{e^{\dfrac{hc}{\lambda k_BT}}-1}$ .