The electron gain enthalpy of sodium (\( \text{Na} \)) is the negative of its ionisation energy, as it involves gaining an electron. Thus, the electron gain enthalpy is \( -5.1 \, \text{eV} \), equal to the ionisation energy value for sodium.
Step 2: Conclusion.
The correct answer is \( -5.1 \, \text{eV} \), corresponding to option (a).