What products are obtained in the electrolysis of molten NaI?

Step 1
Reduction: ${\displaystyle N{a}^{+}\left(aq\right)+e^{-}\Rightarrow Na\left(s\right)}$
Determine the chemical equation for the reduction reaction. In the electrolysis of a pure molten salt, the cation is reduced.
Step 2
Oxidation: ${\displaystyle 2I^{-}\left(aq\right)\Rightarrow I_2\left(s\right)+2e^{-}}$
Determine the chemical equation for the oxidation reaction. In the electrolysis of a pure molten salt, the anion is oxidized.
Step 3
${\displaystyle 2N{a}^{+}\left(aq\right)+2e\Rightarrow 2Na\left(s\right)}$
${\displaystyle 2I^{-}\left(aq\right)\Rightarrow I_2\left(s\right)+2e}$
${\displaystyle 2N{a}^{+}\left(aq\right)+2I^{-}\left(aq\right)\Rightarrow 2Na\left(s\right)+I_2\left(s\right)}$
Multiply the reduction equation by 2 so that both equations have equal amounts of electrons. Then add the half-reactions to give the overall reaction, and cancel reactants and products that appear on both sides of the reaction $\Rightarrow$.
Therefore, Na and ${\displaystyle I_2}$ are the product that are obtained.

Step 1
In electrolysis, an electric current will pass through an electrolyte, and a redox reaction will take place in the electrolytic cell. The anode is positive and oxidation takes place at the anode. The cathode is negative and reduction takes place at the cathode.
Step 2
The molten Nal, the $N{a}^{+}$, and $I^{-}$ ions are present in a liquid state.
the oxidation half-reaction that takes place at the anode is as shown below:
Oxidation: $2I^{-}(l)\Rightarrow I_2(g)+2e^{-}$
The reduction half-reaction that takes place at the cathode is as shown below:
Reduction: $N{a}^{+}(l)+e^{-}\Rightarrow N{a}^{+}(l)$
to get overall reaction, multiply the reaction half-reaction with 2 and add it to oxidation half-reaction as shown below
$$\begin{gathered} 2N{a}^{+}(l)+2e^{-}\Rightarrow 2Na(l) \\ 2I^{-}(l)\Rightarrow I_2(g)+2e^{-} \\ 2N{a}^{+}(l)+2I^{-}(l)\Rightarrow I_2(g)+2Na(l) \end{gathered}$$
Therefore, the products obtained in the electrolysis of molten Nal are Na(l) and $I_2($g)