An electron jumps from `5^(th)` excited level to `2^(nd)` excited level in hydrogen atom. Maximum number of lines obtained in this transition will be

Options

A. 10
B. 12
C. 21
D. 6

Answer

To solve the problem of determining the maximum number of spectral lines obtained when an electron jumps from the 5th excited level to the 2nd excited level in a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Energy Levels**:
- The 5th excited level corresponds to the principal quantum number \( n = 6 \) (since the ground state is \( n = 1 \)).
- The 2nd excited level corresponds to the principal quantum number \( n = 3 \).

2. **Determine the Transition**:
- The electron transitions from \( n_2 = 6 \) to \( n_1 = 3 \).

3. **Use the Formula for Maximum Spectral Lines**:
- The formula to calculate the maximum number of spectral lines produced in a transition from level \( n_2 \) to \( n_1 \) is given by:
\[ \text{Number of lines} = (n_2 - n_1) \times (n_2 - n_1 + 1) / 2 \]

4. **Substitute the Values**:
- Here, \( n_2 = 6 \) and \( n_1 = 3 \).
- Calculate \( n_2 - n_1 = 6 - 3 = 3 \).
- Now substitute into the formula:
\[ \text{Number of lines} = (3) \times (3 + 1) / 2 = 3 \times 4 / 2 = 12 / 2 = 6 \]

5. **Conclusion**:
- The maximum number of spectral lines obtained in this transition is **6**.

### Final Answer:
The maximum number of lines obtained in this transition is **6**.