Explanation:
Reaction equation showing ionization of NaI is as follows.
[tex]NaI(aq) \rightarrow Na^{+}(aq) + I^{-}(aq)[/tex]
Reaction equation showing ionization of water is as follows.
[tex]H_{2}O(l) \rightarrow H^{+}(aq) + OH^{-}(aq)[/tex]
At cathode, only reduction reactions take place. Hence, reactions taking place at cathode are as follows.
[tex]Na^{+}(aq) + 1e^{-} \rightarrow Na(s)[/tex] [tex]E^{o}[/tex] = -2.71
Standard reduction potential equation for hydrogen ions is as follows.
[tex]2H^{+}(aq) + 2e^{-} \rightarrow H_{2}(g)[/tex] [tex]E^{o}[/tex] = 0.00
If a cation has more negative reduction potential then that ion is difficult to reduce as compared to the cation that has lower negative reduction potential.
As [tex]Na^{+}[/tex] has less electronegative reduction potential than [tex]H^{+}[/tex].
Thus, [tex]H^{+}[/tex] will be reduced easily and you will get the product [tex]H_{2}[/tex] at cathode.