The number of possible lines of Paschenc series when electron jumps from `7^(th)` excited state to ground state ( in hydrogen like atom ) is `:`

Options

A. 2
B. 5
C. 4
D. 3

Explanation

To determine the number of possible lines in the Paschen series when an electron jumps from the 7th excited state to the ground state in a hydrogen-like atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Excited State**:
- The 7th excited state corresponds to the principal quantum number \( n = 8 \) (since the ground state is \( n = 1 \), the first excited state is \( n = 2 \), and so on).

2. **Determine the Paschen Series**:
- The Paschen series involves transitions where the final state is \( n = 3 \).

3. **List Possible Transitions**:
- The electron can transition from any level higher than \( n = 3 \) to \( n = 3 \). The possible initial states for the transitions from the 7th excited state (which is \( n = 8 \)) down to \( n = 3 \) are:
- \( n = 8 \) to \( n = 3 \)
- \( n = 7 \) to \( n = 3 \)
- \( n = 6 \) to \( n = 3 \)
- \( n = 5 \) to \( n = 3 \)
- \( n = 4 \) to \( n = 3 \)

4. **Count the Transitions**:
- The transitions listed above are:
- \( 8 \to 3 \)
- \( 7 \to 3 \)
- \( 6 \to 3 \)
- \( 5 \to 3 \)
- \( 4 \to 3 \)
- Therefore, there are a total of 5 possible transitions.

### Final Answer:
The number of possible lines in the Paschen series when the electron jumps from the 7th excited state to the ground state is **5**.

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