If ioinsation potential of hydrogen atom is 13.6 eV, then ionisation potential of `He^(+)`will be

Options

A. 54.4 eV
B. 6.8 eV
C. 13.6 eV
D. 24.5 eV

Explanation

To find the ionization potential of \( He^+ \) given that the ionization potential of hydrogen is 13.6 eV, we can follow these steps:

### Step 1: Understand the Ionization Potential Formula
The ionization potential (IP) for a hydrogen-like atom can be expressed using the formula:
\[ IP = 13.6 \, \text{eV} \times Z^2 \]
where \( Z \) is the atomic number of the element.

### Step 2: Identify the Atomic Number
For hydrogen (\( H \)), the atomic number \( Z \) is 1. For helium ion (\( He^+ \)), the atomic number \( Z \) is 2.

### Step 3: Substitute the Values into the Formula
Now we can substitute the atomic number of \( He^+ \) into the formula:
\[ IP_{He^+} = 13.6 \, \text{eV} \times (2^2) \]

### Step 4: Calculate the Ionization Potential
Calculating \( 2^2 \):
\[ 2^2 = 4 \]
Now substituting this back into the equation:
\[ IP_{He^+} = 13.6 \, \text{eV} \times 4 \]
\[ IP_{He^+} = 54.4 \, \text{eV} \]

### Conclusion
The ionization potential of \( He^+ \) is **54.4 eV**.

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