JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Modern Physics

The number of spectral lines emitted by atomic hydrogen that is in the

4^{th}

energy level, is

(A)6✓ Correct
(B)0
(C)3
(D)1

Answer: (A)

Solution

When a hydrogen atom sits in the

n = 4

level, it can drop to any lower level, and each distinct pair of levels gives one spectral line. The number of ways to choose 2 levels out of

n

N = (2 n) = \frac{n ( n - 1 )}{2}

For

n = 4

N = \frac{4 \times 3}{2} = 6

These correspond to the transitions

4 \to 3, 4 \to 2, 4 \to 1, 3 \to 2, 3 \to 1, 2 \to 1

, giving 6 spectral lines.

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Single correct option

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