From `N` atoms of an element `A`, when half the atoms transfer one electron to the another atom. `405 kJ mol^(-1)` of energy was found to be consumed. An additional energy of `745 kJ mol^(-1)` was further required to convert all the `A^(ɵ)` ions to `A^(o+)`. Calculate the ionisation energy and the electron gain enthalpy of atom `A` in `eV (1 eV = 96.48 kJ)`.

Explanation

To solve the problem step by step, we will analyze the energy changes involved in the ionization and electron gain processes for the element A.

### Step 1: Understand the Energy Changes
We have `N` atoms of element A. When half of these atoms (i.e., `N/2`) transfer one electron each, an energy of `405 kJ/mol` is consumed. This energy corresponds to the ionization energy (IE) of the atoms.

### Step 2: Set Up the Equation for Ionization Energy
Let the ionization energy of atom A be denoted as `X`. Since half of the atoms are involved, the energy consumed can be expressed as:
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