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

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To determine the minimum number of hydrogen atoms needed to produce all possible emission wavelengths from the n=5 state, one must consider the various decay pathways each atom can take to return to the ground state. Each hydrogen atom can emit photons of different wavelengths corresponding to the transitions from n=5 to lower energy levels (n=4, n=3, n=2, and n=1). The total number of unique transitions from n=5 is significant, and each transition produces a distinct wavelength. Therefore, to achieve a complete emission spectrum, multiple hydrogen atoms are required to cover all possible transitions. The exact minimum number depends on the specific decay paths and their probabilities.
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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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