Mulliken defined the electronegativity of an atom as the arithmetic mean of its ionisation energy and electron affinity.
`X_(A)=(1)/(2)(I.P.+E.A.)`
One more relationship given by him, if the values are given in eV is
`X_(A)=("Ionisation potential"+ "Electron affinity")/(5.6)`
When there is pure covalent bond between A-B
`((IP)_(A)+(EA)_(A))/(5.6)=((IP)_(B)+(EA)_(B))/(5.6)`
`implies X_(A)=X_(B)`
When there is formation of `overset(delta-)(A)-overset(delta+)(B)` bond then condition will be

Options

A. `((IP)_(A)+(EA)_(A))/(5.6)gt((IP)_(B)+(EA)_(B))/(5.6)`
B. `((IP)_(A)+(EA)_(B))/(5.6)gt((IP)_(A)+(EA)_(B))/(5.6)`
C. `((IP)_(A)+(EA)_(B))/(2.8)=((IP)_(A)+(EA)_(B))/(2.8)`
D. `((IP)_(A)+(EA)_(B))/(5.6)gt((IP)_(A)+(EA)_(A))/(5.6)`

Answer

To solve the question regarding Mulliken's definition of electronegativity and the conditions for bond formation between two atoms A and B, we can break it down into the following steps:

### Step 1: Understand Mulliken's Definition of Electronegativity
Mulliken defined the electronegativity (X) of an atom as the arithmetic mean of its ionization potential (I.P.) and electron affinity (E.A.). The formula is given by:
\[ X_A = \frac{1}{2}(I.P._A + E.A._A) \]
Alternatively, when values are given in electron volts (eV):
\[ X_A = \frac{I.P._A + E.A._A}{5.6} \]

### Step 2: Analyze the Condition for Pure Covalent Bonds
According to the problem, when there is a pure covalent bond between atoms A and B, the electronegativities are equal:
\[ X_A = X_B \]
This implies:
\[ \frac{I.P._A + E.A._A}{5.6} = \frac{I.P._B + E.A._B}{5.6} \]

### Step 3: Consider the Case of Polar Covalent Bonding
When there is a bond formed where atom A carries a partial negative charge (δ-) and atom B carries a partial positive charge (δ+), it indicates that atom A is more electronegative than atom B. This means:
\[ X_A > X_B \]
Thus, the relationship can be expressed as:
\[ \frac{I.P._A + E.A._A}{5.6} > \frac{I.P._B + E.A._B}{5.6} \]

### Step 4: Evaluate the Options
Now, we need to evaluate the provided options based on the derived relationship:
1. **Option 1**: \( \frac{I.P._A + E.A._A}{5.6} > \frac{I.P._B + E.A._B}{5.6} \) - This is correct as it indicates \( X_A > X_B \).
2. **Option 2**: \( \frac{I.P._A + E.A._B}{5.6} > \frac{I.P._B + E.A._A}{5.6} \) - Incorrect, as it mixes the electron affinity of B with the ionization potential of A.
3. **Option 3**: \( \frac{I.P._B + E.A._A}{5.6} > \frac{I.P._A + E.A._B}{5.6} \) - Incorrect for the same reason as above.
4. **Option 4**: \( \frac{I.P._A + E.A._A}{5.6} < \frac{I.P._B + E.A._B}{5.6} \) - Incorrect, as it contradicts the derived relationship.

### Conclusion
The correct answer is **Option 1**: \( \frac{I.P._A + E.A._A}{5.6} > \frac{I.P._B + E.A._B}{5.6} \).