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## Homework Statement

A sample of hydrogen atoms are all in the n=5 state. I all the atoms return to the ground state, how many different photon energies will be emitted , assuming all possible transitions occur? If there are 500 atoms in the sample and assuming that from any state all possible downward transitions are equally probably, what is the total number of photons that will be emitted when all atoms return to the ground state

## Homework Equations

I don't think there is an equation.

## The Attempt at a Solution

In the first part of the problem, wouldn't the ground state, be n=1. If true, then wouldn't there be four different photon energies emitted? Energies would be emitted from n=5 to n=1, Other energies would be emitted from n=5 to n=2 , n=5 to n=3 , and n=5 to n=4. I'm not sure how to figure out the second answer to the problem.

Actually for the first part of the problem, the back of my book says that there are 10 possible transitions instead of 4 . I do not understand why there are 10 possible transitions

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