A photons was absorbed by a hydrogen atom in its ground state, and the elctron was prompted to the fifth orbit. When the excited atom returuned to its ground state, visible and other quanta were emitted. In this process, how many maximum spectral lined could be obtained-

Options

A. `2rarr1`
B. `5rarr2`
C. `3rarr1`
D. `4rarr1`

Explanation

To determine the maximum number of spectral lines that can be obtained when a hydrogen atom transitions from the fifth orbit (n=5) to the ground state (n=1), we can use the formula for calculating the number of spectral lines produced during transitions between energy levels.

### Step-by-Step Solution:

1. **Identify Initial and Final Energy Levels**:
- The electron is excited from the ground state (n1 = 1) to the fifth orbit (n2 = 5).

2. **Use the Formula for Spectral Lines**:
- The formula for the maximum number of spectral lines (N) that can be obtained from transitions between two energy levels is given by:
\[ N = \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2} \]
- Here, \(n_2\) is the higher energy level (5) and \(n_1\) is the lower energy level (1).

3. **Substitute the Values into the Formula**:
- Substitute \(n_2 = 5\) and \(n_1 = 1\) into the formula:
\[ N = \frac{(5 - 1)(5 - 1 + 1)}{2} \]
- This simplifies to:
\[ N = \frac{(4)(5)}{2} \]

4. **Calculate the Number of Spectral Lines**:
- Performing the multiplication:
\[ N = \frac{20}{2} = 10 \]

5. **Conclusion**:
- Therefore, the maximum number of spectral lines that can be obtained when the hydrogen atom returns to its ground state from the fifth orbit is **10**.