Concept:
Electrolysis is the process in which electrical energy is used to drive a non-spontaneous chemical reaction.
• Cathode: Reduction occurs (gain of electrons)
• Anode: Oxidation occurs (loss of electrons)
In molten NaCl, only \( \text{Na}^+ \) and \( \text{Cl}^- \) ions are present because there is no water.
Step 1: Identify the ions present in molten NaCl.
\[
\text{NaCl (molten)} \rightarrow \text{Na}^+ + \text{Cl}^-
\]
Step 2: Reaction occurring at the cathode (reduction).
At the cathode, sodium ions gain electrons:
\[
\text{Na}^+ + e^- \rightarrow \text{Na}
\]
Thus, sodium metal is deposited at the cathode.
Step 3: Reaction occurring at the anode.
Chloride ions lose electrons:
\[
2\text{Cl}^- \rightarrow \text{Cl}_2 + 2e^-
\]
This produces chlorine gas at the anode.
Therefore, the product formed at the cathode during electrolysis of molten NaCl is
\[
\boxed{\text{Na metal}}
\]