Step 1: Understanding the Concept
An exothermic change releases heat, so its enthalpy change is negative.
Step 2: Check each option
Ionisation of gaseous Na needs energy, so it is endothermic.
Atomisation of methane needs energy to break the C-H bonds, so it is endothermic.
Dissolving NaCl in water is slightly endothermic, because the lattice enthalpy is a little larger than the hydration enthalpy.
Step 3: Electron gain
When a gaseous chlorine atom gains an electron, it attains the stable noble gas configuration and releases energy. This change is exothermic.
Final Answer:
The exothermic change is the electron gain of gaseous chlorine atoms, which is option (B).
\[ \boxed{\text{(B) }\text{Electron gain enthalpy of one mole of gas phase atoms of chlorine}} \]