Step 1: Understand the concept
An ionic bond forms by complete transfer of electrons from a metal to a non-metal. The metal becomes a cation and the non-metal becomes an anion. These ions then attract each other.
Step 2: Condition for the metal
Forming the cation needs energy equal to the ionization enthalpy. A low ionization enthalpy makes it cheap for the metal to lose its electron.
Step 3: Condition for the non-metal
Forming the anion releases energy equal to the electron gain enthalpy. A highly negative value means more energy is released, so the anion forms readily.
Step 4: Check the options
Option (A) has a poorly negative electron gain enthalpy, so the non-metal is unwilling to accept electrons. Option (C) makes the metal reluctant to lose electrons. Option (D) has both factors unfavourable. Only option (B) has both factors favourable, and a large lattice energy then stabilises the solid.
Final Answer:
Low ionization enthalpy of the metal with high negative electron gain enthalpy of the non-metal favours ionic bonding. This is option (B).
\[ \boxed{\text{(B) }\text{Low IE of metal, high negative } \Delta_{eg}H \text{ of non-metal}} \]