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In a hydrogen-like atomic sample, electrons transition from the 4th excited state to the 2nd state. Which of the following statements are correct?

1. 10 different spectral lines are observed
2. 6 different spectral lines are observed
3. Number of lines belonging to the Balmer series is 3
4. Number of lines belonging to Paschen series is 2

Correct answer: 6 different spectral lines are observed

Solution

4th excited state = n=5; 2nd state = n=2. When electrons cascade from n=5 down to n=2, all intermediate transitions occur. Possible transitions between levels 2,3,4,5: total = C(4,2) = 6 lines (5->4, 5->3, 5->2, 4->3, 4->2, 3->2). Balmer series: transitions ending at n=2: 3->2, 4->2, 5->2 = 3 lines. Paschen series: transitions ending at n=3: 4->3, 5->3 = 2 lines. So: 6 spectral lines total, Balmer=3, Paschen=2. Statements: A (10 lines) is wrong. B (6 lines) is correct. C (Balmer=3) is correct. D (Paschen=2) is correct. Among single options, B alone is a valid single answer but B, C, D are all correct.

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