Hydrogen atom is excited from ground state to another state with principal quantum number equal to 5. Then the number of spectral lines in the emission spectra will be:

Options

A. 9
B. 15
C. 8
D. 10

Explanation

To determine the number of spectral lines in the emission spectrum of a hydrogen atom when it is excited from the ground state (n=1) to a higher energy level with a principal quantum number of n=5, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Quantum Numbers**:
- The ground state corresponds to n=1.
- The excited state corresponds to n=5.

2. **Determine the Number of Energy Levels**:
- The energy levels involved in the transition are from n=1 to n=5. This means we have energy levels n=1, n=2, n=3, n=4, and n=5.

3. **Use the Formula for Spectral Lines**:
- The number of spectral lines (s) in the emission spectrum can be calculated using the formula:
\[ s = \frac{n(n-1)}{2} \]
- Here, n is the principal quantum number of the highest energy level, which is 5 in this case.

4. **Substitute the Value of n into the Formula**:
- Substitute n=5 into the formula:
\[ s = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} \]

5. **Calculate the Number of Spectral Lines**:
- Simplifying the equation:
\[ s = \frac{20}{2} = 10 \]

6. **Conclusion**:
- Therefore, the number of spectral lines in the emission spectrum when the hydrogen atom transitions from n=5 to lower energy levels is **10**.

### Final Answer:
The number of spectral lines in the emission spectra will be **10**.

---