The electron in the Hydrogen atom is excited to the `5^(th)` orbit, the number of spectral lines it is expected to emit is

Options

A. 6
B. 10
C. 12
D. 20

Answer

To determine the number of spectral lines emitted by an electron in a hydrogen atom when it is excited to the 5th orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the excited state (n)**:
The electron is excited to the 5th orbit, so we have \( n = 5 \).

2. **Use the formula for spectral lines**:
The number of spectral lines emitted when an electron transitions from an excited state to lower energy states can be calculated using the formula:
\[ \text{Number of spectral lines} = \frac{n(n-1)}{2} \]
where \( n \) is the principal quantum number of the excited state.

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

4. **Calculate the value**:
\[ = \frac{5 \times 4}{2} = \frac{20}{2} = 10 \]

5. **Conclusion**:
Therefore, the number of spectral lines expected to be emitted when the electron in the hydrogen atom is excited to the 5th orbit is **10**.

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