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

Explanation

To solve the problem of finding the 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 problem states that it requires an energy of 24.6 eV to remove the first electron from a neutral helium atom.

### Step 2: Analyze the remaining atom after the first electron is removed
Once the first electron is removed, the helium atom becomes a positively charged ion (He+), which is similar to a hydrogen-like atom. The remaining electron will experience a different effective nuclear charge.

### Step 3: Calculate the energy required to remove the second electron
For hydrogen-like atoms, the energy required to remove the electron can be calculated using the formula:
\[ E = -\frac{Z^2 \cdot 13.6 \, \text{eV}}{n^2} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number. For He+, \( Z = 2 \) and since we are removing the only remaining electron, \( n = 1 \).

Thus, the energy required to remove the second electron is:
\[ E_2 = 13.6 \cdot 2^2 = 13.6 \cdot 4 = 54.4 \, \text{eV} \]

### 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:
\[ E_{\text{total}} = E_1 + E_2 = 24.6 \, \text{eV} + 54.4 \, \text{eV} = 79 \, \text{eV} \]

### Conclusion
The total energy required to remove both electrons from a neutral helium atom is **79 eV**.

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