How many times is the ionization energy of `He^(+)` ion as compared to that of H-atom?

Explanation

To determine how many times the ionization energy of the `He^(+)` ion is compared to that of the hydrogen atom (H), we can use the formula for ionization energy for hydrogen-like atoms.

### Step-by-Step Solution:

1. **Understanding Ionization Energy**:
- Ionization energy is the amount of energy required to remove an electron from an atom or ion. For hydrogen-like atoms (which have only one electron), the ionization energy can be calculated based on the atomic number (Z).

2. **Formula for Ionization Energy**:
- The ionization energy (IE) of a hydrogen-like atom is given by the formula:
\[ \text{IE} = Z^2 \times \text{IE}_H \]
where \( \text{IE}_H \) is the ionization energy of hydrogen and Z is the atomic number of the element.

3. **Identify the Atomic Number**:
- For the helium ion `He^(+)`, the atomic number (Z) is 2. Thus, we can substitute Z into the formula:
\[ \text{IE}_{He^+} = 2^2 \times \text{IE}_H \]

4. **Calculate the Ionization Energy of `He^(+)`**:
- Substituting Z = 2 into the formula:
\[ \text{IE}_{He^+} = 4 \times \text{IE}_H \]

5. **Comparing Ionization Energies**:
- This means that the ionization energy of the `He^(+)` ion is 4 times that of the hydrogen atom:
\[ \text{IE}_{He^+} = 4 \times \text{IE}_H \]

### Final Answer:
The ionization energy of `He^(+)` is **4 times** that of the hydrogen atom.

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