Hydrogen atoms are excited to the $n = 6$ level and all possible downward transitions occur. How many distinct spectral lines have a wavelength longer than that of the $n = 3 \to n = 2$ line (H-alpha)?

Answer: B

A longer wavelength means a smaller energy gap than

3 \to 2

, where

1/ n_{f}^{2} - 1/ n_{i}^{2} = 5/36 = 0.139

. Checking all 15 transitions among

n \leq 6

, the lines that qualify are

4 \to 3

5 \to 3

5 \to 4

6 \to 3

6 \to 4

6 \to 5

. That is 6 lines.