Electron gain enthalpy and ionisation energy of an atom are `-a` and `+b` eV respectively. The electronegativity of that atom on Mulliken scale is given by

Options

A. `a-b`
B. `(b-a)/(2)`
C. `a+b`
D. `(a+b)/(2)`

Answer

To find the electronegativity of an atom on the Mulliken scale given its electron gain enthalpy and ionization energy, we can follow these steps:

### Step 1: Understand the Definitions
- **Electron Gain Enthalpy (EGE)**: This is the amount of energy released when an electron is added to a neutral isolated gaseous atom. It is given as `-a` eV, which indicates that energy is released.
- **Ionization Energy (IE)**: This is the minimum amount of energy required to remove the most loosely bound electron from a neutral isolated gaseous atom. It is given as `+b` eV, indicating that energy is required.

### Step 2: Relate to Electronegativity
- **Electronegativity** on the Mulliken scale is defined as the average of the ionization energy and the electron affinity (which is the negative of electron gain enthalpy).

The formula for electronegativity (χ) on the Mulliken scale is:
\[ \chi = \frac{\text{Ionization Energy} + \text{Electron Affinity}}{2} \]

### Step 3: Substitute the Values
- From the definitions:
- Ionization Energy = `+b`
- Electron Affinity = `-(-a)` = `a` (since electron gain enthalpy is `-a`, the electron affinity is `+a`)

Now substituting these values into the electronegativity formula:
\[ \chi = \frac{b + a}{2} \]

### Step 4: Final Expression
Thus, the electronegativity of the atom on the Mulliken scale is:
\[ \chi = \frac{a + b}{2} \]

### Conclusion
The answer to the question is:
\[ \text{Electronegativity} = \frac{a + b}{2} \]