How Many Hydrogen Atoms Minimum for All Emission Spectra from n=5?

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SUMMARY

The minimum number of hydrogen atoms required to produce all possible emission spectra from the n=5 state is determined by the various decay pathways available for each atom. Each hydrogen atom can transition from the n=5 state to any lower energy level, resulting in a unique photon emission for each transition. To achieve all possible wavelengths, at least 5 hydrogen atoms are necessary, as each atom can contribute to the different transitions: n=5 to n=4, n=3, n=2, and n=1.

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sid94
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Not sure how to go ahead with this problem:

Hydrogen atoms in a sample are excited to n=5 states and it is found that photons of all possible wavelengths are present in the emission spectra. What would be the minimum no. of hydrogen atoms in the sample?

(sorry got nothin buzzin to attempt this problem.. so please help out!)

Thnxx
 
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Think of all the different ways an atom in n=5 can decay back to the ground state.
 

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