The energy required to remove the electron from a singly ionized Helium atom is `2.2` times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom ompletelyis:

Options

A. 34 ev
B. 20 eV
C. 79 eV
D. 109 eV

Answer

To solve the problem of finding the total energy required to completely ionize a helium atom, we can break it down into steps.

### Step 1: Understand the Energy Required for Ionization
The energy required to remove an electron from a singly ionized helium atom (He⁺) is given as 2.2 times the energy required to remove an electron from a neutral helium atom (He).

### Step 2: Define the Energies
Let:
- \( E_n \) = Energy required to remove an electron from a singly ionized helium atom (He⁺).
- \( E_0 \) = Energy required to remove an electron from a neutral helium atom (He).

From the problem statement, we have:
\[ E_n = 2.2 \times E_0 \]

### Step 3: Calculate the Energy for He⁺
The energy required to remove an electron from a singly ionized helium atom can be calculated using the formula for ionization energy:
\[ E_n = -\frac{Z^2 \cdot 13.6 \, \text{eV}}{n^2} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number. For helium, \( Z = 2 \) and for the ground state \( n = 1 \):
\[ E_n = -\frac{2^2 \cdot 13.6 \, \text{eV}}{1^2} = -54.4 \, \text{eV} \]

### Step 4: Calculate the Energy for Neutral Helium
Now, substituting \( E_n \) into the equation \( E_n = 2.2 \times E_0 \):
\[ -54.4 \, \text{eV} = 2.2 \times E_0 \]
To find \( E_0 \):
\[ E_0 = \frac{-54.4 \, \text{eV}}{2.2} \]
Calculating this gives:
\[ E_0 = -24.727 \, \text{eV} \approx -24.7 \, \text{eV} \]

### Step 5: Calculate the Total Energy Required for Complete Ionization
The total energy required to completely ionize the helium atom is the sum of the energies required to remove both electrons:
\[ E_{\text{total}} = E_n + E_0 \]
Substituting the values we calculated:
\[ E_{\text{total}} = -54.4 \, \text{eV} + (-24.7 \, \text{eV}) \]
\[ E_{\text{total}} = -79.1 \, \text{eV} \]

Since we are interested in the magnitude of energy required, we take the positive value:
\[ E_{\text{total}} \approx 79 \, \text{eV} \]

### Final Answer
The total energy required to completely ionize the helium atom is approximately **79 eV**.