Answer: B) Ag(s) is formed at the cathode, and [tex]Mn^{2+}(aq)[/tex] is formed at the anode.
Explanation:
[tex]Ag^{+}(aq)+e^{-1}\rightarrow Ag(s)[/tex] E=0.80 V
[tex]Mn^{2+}(aq)+2e^{-1}\rightarrow Mn(s)[/tex] E=-1.18 V
Reduction takes place easily if the standard reduction potential is higher (positive) and oxidation takes place easily if the standard reduction potential is less(more negative).
Thus as reduction potential of Ag is higher , it undergoes reduction and Manganese with lower reduction potential undergoes oxidation. Here Mn undergoes oxidation by loss of electrons, thus act as anode. Ag undergoes reduction by gain of electrons and thus act as cathode.
Cathode : reduction : [tex]Ag^{+}(aq)+e^{-1}\rightarrow Ag(s)[/tex]
Anode : oxidation : [tex]Mn\rightarrow Mn^{2+}(aq)+2e^{-1}[/tex]
Ag(s) is formed at the cathode, and [tex]Mn^{2+}(aq)[/tex] is formed at the anode.