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 answerB$3$
- 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: $3$
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'.