The number of spectral lines obtained in Bohr spectrum of hydrogen atom when an electron is excited from `5^("th")` orbit to ground level is:

Options

A. 10
B. 5
C. 8
D. 15

Explanation

To find the number of spectral lines obtained in the Bohr spectrum of a hydrogen atom when an electron transitions from the 5th orbit to the ground level (1st orbit), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final Energy Levels**:
- The electron is excited from the 5th orbit (n = 5) to the ground level (n = 1).

2. **Determine the Number of Transitions**:
- The number of possible transitions when an electron falls from a higher energy level (n) to a lower energy level (1) can be calculated using the formula:
\[ \text{Number of spectral lines} = \frac{n(n-1)}{2} \]
- Here, \( n \) is the principal quantum number of the initial state, which is 5 in this case.

3. **Substitute the Value of n**:
- Substitute \( n = 5 \) into the formula:
\[ \text{Number of spectral lines} = \frac{5(5-1)}{2} \]

4. **Calculate the Expression**:
- First, calculate \( 5 - 1 = 4 \).
- Then, calculate \( 5 \times 4 = 20 \).
- Finally, divide by 2:
\[ \frac{20}{2} = 10 \]

5. **Conclusion**:
- The number of spectral lines obtained in the Bohr spectrum of the hydrogen atom when an electron is excited from the 5th orbit to the ground level is **10**.

### Final Answer:
The number of spectral lines is **10**.