# derivation of Planck distribution for photon

Anonymous
timer Asked: Dec 9th, 2017
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Question description

see attachment it is about derivation of Planck distribution for photon and then derive in term of wavelength and then determine the wavelength in term of T. i can send to u my lecture note and see what we did

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Barbartos
School: Carnegie Mellon University

Sorry about the holdup; the equations were a little messy to type up. Here's the final copy.

Planck Distribution
December 9, 2017

Frequency Derivation
We derive Planck’s law by counting how many photons there are at each energy
state, multiplying that by the energy, and then taking the sum over all possible
energy states.
X
U=
n(E)g(E)E
E

Where n(E) is the average number of photons with a given energy, g() is the
number of photons with energies between E and E + dE. In the infinitesimal
limit, this becomes
Z ∞
U=
n(E)g(E) dE
0

First, since the photon is spin-1, there are two possible spins for every
position-momentum combination, so gi = 2. Next, the photon is a boson with
chemical potential µ = 0, so s...

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Anonymous
Outstanding Job!!!!

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