Q127 / 150 · MHT CET 2026 (15 April Shift 2) · Physics

The electron in hydrogen atom is initially in the second excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are

  • A
    $2$
  • Correct answer
    B
    $3$
  • C
    $4$
  • D
    $5$

Solution

The ground state of a hydrogen atom corresponds to the principal quantum number $n = 1$.

The second excited state corresponds to $n = 3$.

The maximum number of spectral lines emitted when electrons transition from an excited state $n$ to the ground state is given by the formula:

Number of spectral lines = $\dfrac{n(n-1)}{2}$

Substituting $n = 3$ into the formula:

Number of spectral lines = $\dfrac{3(3-1)}{2} = 3$

The $3$ possible transitions are:
$n = 3 \rightarrow n = 1$
$n = 3 \rightarrow n = 2$
$n = 2 \rightarrow n = 1$

Answer: $3$

Hence, the correct answer is option: 'B'.

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