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# A sample of hydrogen atoms are all in the n = 5 state. If all the atoms return to the ground state, how many different photon energies will be

A sample of hydrogen atoms are all in the n = 5 state. If 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 probable, what is the total number of photons that will be emitted when all the atoms have returned to the ground state?