Module 5 : MODERN PHYSICS
Lecture 23 : Black Body Radiationl
Black Body Radiation :
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 As the average energy of a mode is $ kT$, the radiant energy density, which is defined as the average energy
  per unit volume is given by
$\displaystyle u(\nu)d\nu = \frac{8\pi kT}{c^3}\nu^2d\nu$ (2)
  This is known as Rayleigh - Jeans' Law
  Exercise 1
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 The radiant intensity can be obtained from the expression for the energy density by multiplying the above
  expression by $ c/4$. The curious factor of 1/4 arises because
At any instant, on an average, half of the waves are directed towards the wall of the cavity and another half
  is directed away from it. This gives a factor of 1/2.
We need to average over all angles. In computing the radiant power, we get a factor of $ \cos^2\theta$, which averages
  to 1/2. The radiant intensity is given by
 
$\displaystyle I(\lambda) d\lambda = \frac{2\pi c}{\lambda^4}kT d\lambda$
   
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