# derivation of Planck distribution for photon

*label*Science

*timer*Asked: Dec 9th, 2017

*account_balance_wallet*$25

**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

## Tutor Answer

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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