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Question
The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?
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Solution
In n is the quantum number of the highest energy level involved in the transitions, then the total number of possible spectral lines emitted is
`N = (n(n-1))/2`
Third excited state means fourth energy level i.e. n = 4. Here, electron makes transition from n = 4 to n = 1 so highest n is n = 4
Thus, possible spectral lines
`N = (4 (4 -1))/2`
`=(4 xx 3)/2`
= 6
6 is the maximum possible number of spectral lines.
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