Planck's Radiation Law | Planck's radiation formula

Planck's Radiation Law

• This is application of Bose-Einstein statistics.
• According to quantum theory, the radiant energy occurs in energy packets.
• These packets are known as quanta or photon.
• The energy of packet should be h times the frequency of photon.
• The momentum of each packet should be h/c times the frequency of photon.
• The photons are indistinguishable particles having zero rest mass and having spin quantum number 1.
• Thus photons are Bose particle and hence Bose Einstein statistics can be applied on it.
• By using Planck's radiation law, we can also establish the Rayleigh Jean’s law, Wein’s law and Stefan-Boltzmann’s law.

Planck's radiation law

• According to Planck, the energy density of radiations emitted from a black body in the wavelength range λ and λ + dλ is, u_λ dλ = (N_λ dλ) E 
• Here N_λ dλ = Number of oscillators (number of modes of vibration) in the wavelength range λ and λ + dλ
• E is average energy of Planck's oscillator.

Since

Therefore

This is Planck’s radiation formula in terms of wavelength 

Since

Therefore

This is Planck’s radiation formula in terms of frequency

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