When the electron of a hydrogen atom jumps from the n=4 to the n=1 state , the number of all pos - sible spectral lines emitted is :-

Options

A. 15
B. 6
C. 3
D. 4

Answer

To determine the number of possible spectral lines emitted when an electron of a hydrogen atom jumps from the n=4 state to the n=1 state, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final States:**
- The electron is transitioning from the n=4 state (higher energy level) to the n=1 state (lower energy level).
- Here, \( n_2 = 4 \) and \( n_1 = 1 \).

2. **Use the Formula for Spectral Lines:**
- The formula to calculate the total number of possible spectral lines emitted is:
\[ \text{Number of spectral lines} = \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2} \]

3. **Substitute the Values:**
- Substitute \( n_2 \) and \( n_1 \) into the formula:
\[ \text{Number of spectral lines} = \frac{(4 - 1)(4 - 1 + 1)}{2} \]

4. **Calculate the Values:**
- Calculate \( (4 - 1) \):
\[ 4 - 1 = 3 \]
- Calculate \( (4 - 1 + 1) \):
\[ 4 - 1 + 1 = 4 \]
- Now substitute these values back into the formula:
\[ \text{Number of spectral lines} = \frac{(3)(4)}{2} \]

5. **Final Calculation:**
- Multiply and divide:
\[ \text{Number of spectral lines} = \frac{12}{2} = 6 \]

### Conclusion:
The total number of possible spectral lines emitted when the electron jumps from the n=4 state to the n=1 state is **6**.