`N_(0)//2` atoms of X(g) are converted into `X^(+)` (g) by energy `E_(1) . N_(0)//2` atoms of X(g) are converted into `X^(-)` (g) by the energy `E_(2)` . Hence ionisation potential and electron affinity of X(g) are :

Options

A. `(2E_(1))/(N_(0)) , (2(E_(1) - E_(2)))/(N_(0))`
B. `(2E_(1))/(N_(0)) , (2E_(2))/(N_(0))`
C. `((E_(1) - E_(2)))/(N_(0)) , (2E_(2))/(N_(0))`
D. `(E_(1))/(N_(0)) , (2E_(2))/(N_(0))`

Answer

To solve the problem, we need to determine the ionization potential and electron affinity of the element X based on the given information about the conversion of its atoms into ions.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have `N_0/2` atoms of X(g) being converted into `X^(+)` (g) using energy `E_1`. We also have `N_0/2` atoms of X(g) being converted into `X^(-)` (g) using energy `E_2`. We need to find the ionization potential and electron affinity of X(g).

2. **Ionization Energy Calculation**:
- The ionization energy (IE) is the energy required to remove an electron from a neutral atom to form a cation.
- Given that `N_0/2` atoms of X are converted into `X^(+)` using energy `E_1`, the energy required to ionize one atom of X can be calculated as:
\[ \text{Ionization Energy (IE)} = \frac{2E_1}{N_0} \]
- This is because the total energy `E_1` is used for `N_0/2` atoms, and we need to find the energy per atom.

3. **Electron Affinity Calculation**:
- The electron affinity (EA) is the energy released when an electron is added to a neutral atom to form an anion.
- Similarly, for the conversion of `N_0/2` atoms of X into `X^(-)` using energy `E_2`, the energy per atom can be calculated as:
\[ \text{Electron Affinity (EA)} = \frac{2E_2}{N_0} \]
- Again, this is derived from the total energy `E_2` used for `N_0/2` atoms.

4. **Final Expressions**:
- Therefore, the final expressions for the ionization potential and electron affinity of X(g) are:
\[ \text{Ionization Potential} = \frac{2E_1}{N_0} \]
\[ \text{Electron Affinity} = \frac{2E_2}{N_0} \]

### Summary of Results:
- Ionization Potential of X(g): \(\frac{2E_1}{N_0}\)
- Electron Affinity of X(g): \(\frac{2E_2}{N_0}\)