Calculate the ionisation energy of `He^(+)` if that of H atom is 13.6eV.

Answer

To calculate the ionization energy of the `He^(+)` ion, we can use the formula for ionization energy based on the atomic number (Z) of the element. The ionization energy (IE) is proportional to the square of the atomic number.

### Step-by-Step Solution:

1. **Identify the given data:**
- Ionization energy of hydrogen (H) = 13.6 eV
- Atomic number of helium (He) = 2

2. **Use the formula for ionization energy:**
\[ \text{Ionization Energy} = 13.6 \times Z^2 \text{ eV} \]
where \( Z \) is the atomic number.

3. **Substitute the value of Z for helium:**
\[ Z = 2 \quad \text{(for He)} \]
Therefore, the ionization energy of `He^(+)` becomes:
\[ \text{Ionization Energy} = 13.6 \times (2^2) \text{ eV} \]

4. **Calculate \( Z^2 \):**
\[ 2^2 = 4 \]

5. **Substitute \( Z^2 \) back into the equation:**
\[ \text{Ionization Energy} = 13.6 \times 4 \text{ eV} \]

6. **Perform the multiplication:**
\[ \text{Ionization Energy} = 54.4 \text{ eV} \]

7. **State the final answer:**
The ionization energy of `He^(+)` is **54.4 eV**.