A large collection of hydrogen atoms is initially excited to the fifth Bohr orbit and then allowed to de-excite through every possible transition. Let N(total) be the total number of distinct spectral lines and N(Balmer) be the number of distinct Balmer-series lines. Find N(total)−N(Balmer).
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A large collection of hydrogen atoms is initially excited to the fifth Bohr orbit and then allowed to de-excite through every possible transition. Let N(total) be the total number of distinct spectral lines and N(Balmer) be the number of distinct Balmer-series lines. Find N(total)−N(Balmer).

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

Total number of distinct lines from levels up to n = 5: N(total) = 5×4 ÷ 2 = 10. Balmer lines must end at n = 2. The possible upper levels are 3, 4 and 5. Therefore, N(Balmer) = 3. Hence, N(total)−N(Balmer) = 10−3 = 7.