Step 1: Understanding the Concept
A process is exothermic if it releases energy, that is, its enthalpy change is negative.
Step 2: Analyse each option
Na(g) to Na+(g) is ionisation, which needs energy. Cl2 to 2Cl is bond dissociation, which needs energy. Dissolving NaCl(s) in water absorbs a small amount of heat.
Step 3: Electron gain
Cl(g) to Cl-(g) is electron gain by a halogen. Chlorine has a high negative electron gain enthalpy, so energy is released.
Step 4: Compare the options
Option (B) is exothermic.
Final Answer:
Adding an electron to a gaseous chlorine atom is the exothermic process.
\[ \boxed{\text{(B) }\text{Cl}_{(g)}\rightarrow\text{Cl}_{(g)}^{-}} \]