The number of spectral line that can be possible when electrons in `6^(th)` shell in hydrogen atom return to the `2^(nd)` shell :

Options

A. 12
B. 15
C. 14
D. 10

Explanation

To solve the problem of determining the number of spectral lines that can be emitted when electrons in the 6th shell of a hydrogen atom return to the 2nd shell, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final Energy Levels**:
- The initial energy level (N2) is 6 (the shell from which the electron is transitioning).
- The final energy level (N1) is 2 (the shell to which the electron is transitioning).

2. **Use the Formula for Maximum Spectral Lines**:
- The formula to calculate the maximum number of spectral lines emitted during a transition from N2 to N1 is given by:
\[ \text{Number of spectral lines} = \frac{(N2 - N1)(N2 - N1 + 1)}{2} \]

3. **Substitute the Values into the Formula**:
- Substitute N2 = 6 and N1 = 2 into the formula:
\[ \text{Number of spectral lines} = \frac{(6 - 2)(6 - 2 + 1)}{2} \]

4. **Calculate the Values**:
- First, calculate \(6 - 2 = 4\).
- Then calculate \(6 - 2 + 1 = 5\).
- Now substitute these values back into the formula:
\[ \text{Number of spectral lines} = \frac{(4)(5)}{2} \]

5. **Perform the Final Calculation**:
- Calculate \(4 \times 5 = 20\).
- Now divide by 2:
\[ \text{Number of spectral lines} = \frac{20}{2} = 10 \]

6. **Conclusion**:
- The total number of spectral lines that can be emitted when electrons in the 6th shell return to the 2nd shell is **10**.

### Final Answer:
The number of spectral lines that can be emitted is **10**.