What is the energy of the electron in `He+ ion in the ground state ?

Explanation

To find the energy of the electron in the He+ ion in the ground state, we can use the formula for the energy of an electron in a hydrogen-like atom:

\[ E = -\frac{13.6 \, \text{eV} \times Z^2}{n^2} \]

where:
- \( E \) is the energy of the electron,
- \( Z \) is the atomic number,
- \( n \) is the principal quantum number (state of the electron).

### Step-by-Step Solution:

1. **Identify the Atomic Number (Z)**:
- For the Helium ion (He+), the atomic number \( Z \) is 2.

2. **Determine the Principal Quantum Number (n)**:
- In the ground state, the principal quantum number \( n \) is 1.

3. **Substitute the Values into the Formula**:
- Plugging in the values into the energy formula:
\[ E = -\frac{13.6 \, \text{eV} \times (2)^2}{(1)^2} \]

4. **Calculate the Energy**:
- Calculate \( (2)^2 \) which is 4.
- Now substitute this back into the equation:
\[ E = -\frac{13.6 \, \text{eV} \times 4}{1} \]
- This simplifies to:
\[ E = -54.4 \, \text{eV} \]

5. **Final Answer**:
- The energy of the electron in the He+ ion in the ground state is:
\[ E = -54.4 \, \text{eV} \]