The binding energy of the electron in the ground state of `He` atom is equal to `E_(0)=24.6 eV`. Find the energy required to remove both the electrons from the atom.

Options

A. 49.2eV
B. 54.4eV
C. 79eV
D. 108.8eV

Explanation

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

### Step 1: Understand the Binding Energy
The binding energy of the electron in the ground state of the He atom is given as \( E_0 = 24.6 \, \text{eV} \). This is the energy required to remove the first electron from the atom.

### Step 2: Calculate the Energy Required to Remove the Second Electron
After removing the first electron, we are left with a He\(^+\) ion, which has only one electron. The energy of an electron in the ground state of a hydrogen-like atom can be calculated using the formula:
\[ E = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number.

For He\(^+\):
- \( Z = 2 \)
- \( n = 1 \)

Substituting these values into the formula:
\[ E = -\frac{13.6 \, \text{eV} \cdot 2^2}{1^2} = -\frac{13.6 \, \text{eV} \cdot 4}{1} = -54.4 \, \text{eV} \]
This means that the energy required to remove the second electron from He\(^+\) is \( 54.4 \, \text{eV} \).

### Step 3: Calculate the Total Energy Required
The total energy required to remove both electrons from the He atom is the sum of the energy required to remove the first electron and the energy required to remove the second electron:
\[ \text{Total Energy} = E_0 + E_{second} = 24.6 \, \text{eV} + 54.4 \, \text{eV} \]
Calculating this gives:
\[ \text{Total Energy} = 79.0 \, \text{eV} \]

### Final Answer
The energy required to remove both electrons from the He atom is \( 79.0 \, \text{eV} \).

---