Answer to Question #101633 in Classical Mechanics for israel

Question

by using jean number and average energy derive planks law of radiation

Answer 1

The average energy E of an oscillator is connect with density σ of radiation by formula

$σ(υ, T)=\frac{8πυ^2}{c^3} \times {E} (1)$

where υ is oscillator frequency, c is the speed of light

The average energy is given by formula

$E=\frac{hυ}{\exp{\frac{hυ}{kT}}-1} (2)$

where h is the Planck’s constant, T is the temperature, k is the Boltzman’s constant

We put (2) in (1)

$σ(υ, T)=\frac{\frac{8πhυ^3}{c^3}}{\exp{\frac{hυ}{kT}}-1} (3)$

It is a Planck’s law of radiation.