An energy of `24.6 eV` is required to remove one of that electrons from a neutal helium atom. The enegy (in `eV`)required to remove both the electrons from a netural helium atom is

Options

A. `79.0`
B. `51.8`
C. `49.2`
D. `38.2`

Explanation

To find the total energy required to remove both electrons from a neutral helium atom, we can follow these steps:

### Step 1: Understand the energy required to remove the first electron
The energy required to remove the first electron from a neutral helium atom is given as \( 24.6 \, \text{eV} \).

### Step 2: Determine the remaining atom after the first electron is removed
After the removal of the first electron, the remaining atom is a hydrogen-like ion (He\(^+\)) with only one electron left. The atomic number \( Z \) for helium is 2.

### Step 3: Calculate the energy required to remove the second electron
For a hydrogen-like atom, the energy required to remove the electron can be calculated using the formula:
\[ E = 13.6 \, \text{eV} \times \frac{Z^2}{n^2} \]
Where:
- \( Z \) is the atomic number (2 for helium),
- \( n \) is the principal quantum number (1 for the ground state).

Substituting the values:
\[ E = 13.6 \, \text{eV} \times \frac{2^2}{1^2} = 13.6 \, \text{eV} \times 4 = 54.4 \, \text{eV} \]

### Step 4: Calculate the total energy required to remove both electrons
Now, we add the energy required to remove the first electron and the energy required to remove the second electron:
\[ \text{Total Energy} = \text{Energy to remove first electron} + \text{Energy to remove second electron} \]
\[ \text{Total Energy} = 24.6 \, \text{eV} + 54.4 \, \text{eV} = 79.0 \, \text{eV} \]

### Final Answer
The total energy required to remove both electrons from a neutral helium atom is \( 79.0 \, \text{eV} \).

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