The excitation energy of a hydrogen-like ion in its first excited state is `40.8 eV` Find the energy needed to remove the electron from the ion

Explanation

To solve the problem, we need to find the energy required to remove the electron from a hydrogen-like ion given its excitation energy in the first excited state.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The excitation energy of the hydrogen-like ion in its first excited state is given as \( E_{exc} = 40.8 \, eV \).

2. **Use the Formula for Excitation Energy**:
...