Number of possible spectral lines which may be emitted in brackett series in H-atom, if electrons in 8th excited state returns to ground state are:

Options

A. 5
B. 45
C. 6
D. 21

Explanation

To determine the number of possible spectral lines emitted in the Brackett series when an electron in the 8th excited state of a hydrogen atom returns to the ground state, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Energy Levels**:
- In a hydrogen atom, the energy levels are denoted by \( n = 1, 2, 3, \ldots \).
- The ground state corresponds to \( n = 1 \). The excited states are \( n = 2, 3, 4, \ldots \).
- The 8th excited state corresponds to \( n = 9 \) (since the ground state is counted as the 1st state).

2. **Determine the Brackett Series**:
- The Brackett series involves transitions to the \( n = 4 \) level.
- Therefore, we need to consider transitions from the 9th level down to the 4th level.

3. **Calculate Possible Transitions**:
- The electron can transition from \( n = 9 \) to \( n = 4 \) in several ways:
- \( n = 9 \) to \( n = 8 \)
- \( n = 8 \) to \( n = 7 \)
- \( n = 7 \) to \( n = 6 \)
- \( n = 6 \) to \( n = 5 \)
- \( n = 5 \) to \( n = 4 \)

4. **Count the Spectral Lines**:
- Each transition results in the emission of a spectral line.
- The transitions are:
- \( 9 \rightarrow 4 \)
- \( 9 \rightarrow 8 \rightarrow 4 \)
- \( 9 \rightarrow 7 \rightarrow 4 \)
- \( 9 \rightarrow 6 \rightarrow 4 \)
- \( 9 \rightarrow 5 \rightarrow 4 \)
- Therefore, there are a total of 5 possible transitions.

5. **Conclusion**:
- The total number of possible spectral lines emitted in the Brackett series when an electron in the 8th excited state returns to the ground state is **5**.

### Final Answer:
The number of possible spectral lines emitted in the Brackett series when electrons in the 8th excited state return to the ground state is **5**.

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