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## Homework Statement

Here's the problem:

A group of hydrogen atoms are in n=5 state. If all atoms return to ground state, how many different photon energies will emit, assuming all transitions occur? If there are 500 atoms, assuming all transitions are equally probably, what is the total number of photons to be emitted when all atoms have returned to the ground state?

## Homework Equations

Equations:

E_gamma=hu

E_gamma=p_gamma*c

E=-13.6(Z^2/n^2)

N=W/E_gamma

## The Attempt at a Solution

How many different photon energies: 4 one from 5-4 4-3 3-2 2-1each. Using E=-13.6(Z^2/n^2). I just did E(5)-E(4) for the photon energy Ereleased

Now I need to find the work done as I already have the energies. Perhaps there is another way to find the number of photons emitted?

I could not figure how exactly to get the KE. I had a problem similar to this and I was really shaky on the KE part of it. If I can find the KE, I can find the work.

KE=Ereleased - Eion meaning for 2->1 it would be 10.2-3.4?

Using this method at E(5) I get .306-.544 which is negative :/

Anybody notice anything wrong?