The correct balanced equation for the reaction between sodium (Na) and iodine gas (I₂) to form sodium iodide (NaI) is:
\[ 2 \text{Na} + \text{I}_2 \rightarrow 2 \text{NaI} \]
This reaction shows that two sodium atoms react with one molecule of iodine gas to produce two formula units of sodium iodide. Therefore, the first option is the correct representation.