How many spectral lines are seen for hydrogen atom when electron jump from `n_(2) = 5 ` to `n_(1) = 1` in visible region ?

Options

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

Answer

To determine how many spectral lines are seen for a hydrogen atom when an electron jumps from \( n_2 = 5 \) to \( n_1 = 1 \) in the visible region, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Series**:
- The transition from \( n_2 = 5 \) to \( n_1 = 1 \) falls into the Lyman series, which corresponds to transitions where the final energy level is \( n = 1 \). However, since we are interested in the visible region, we need to consider transitions that end at \( n = 2 \) (the Balmer series).

2. **List Possible Transitions**:
- From \( n = 5 \), the electron can transition to the following levels:
- \( n = 4 \)
- \( n = 3 \)
- \( n = 2 \)
- \( n = 1 \)
- However, only transitions to \( n = 2 \) will produce visible light.

3. **Calculate the Transitions to \( n = 2 \)**:
- The possible transitions from \( n = 5 \) to \( n = 2 \) are:
- \( 5 \rightarrow 2 \)
- The transition from \( n = 4 \) to \( n = 2 \):
- \( 4 \rightarrow 2 \)
- The transition from \( n = 3 \) to \( n = 2 \):
- \( 3 \rightarrow 2 \)

4. **Count the Spectral Lines**:
- The transitions that result in spectral lines in the visible region are:
- \( 5 \rightarrow 2 \)
- \( 4 \rightarrow 2 \)
- \( 3 \rightarrow 2 \)
- Therefore, there are **3 spectral lines** in the visible region.

### Final Answer
The number of spectral lines seen for the hydrogen atom when the electron jumps from \( n_2 = 5 \) to \( n_1 = 1 \) in the visible region is **3**.

---