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. 9
C. 6
D. 3

Answer

To solve the problem of determining the number of possible spectral lines emitted when an electron in 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 initial state (n2) is 4.
- The final state (n1) is 1.

2. **Use the Formula for Spectral Lines**:
- The formula to calculate the number of spectral lines emitted when an electron transitions between two energy levels is given by:
\[ \text{Number of spectral lines} = \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2} \]

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

4. **Calculate the Number of Spectral Lines**:
- Simplifying the expression:
\[ \text{Number of spectral lines} = \frac{(3)(4)}{2} = \frac{12}{2} = 6 \]

5. **Conclusion**:
- Therefore, the number of possible spectral lines emitted when the electron jumps from n=4 to n=1 is **6**.

### Final Answer:
The number of all possible spectral lines emitted is **6**.

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