(a)
Calcium is manufactured by the electrolysis of a molten mixture of calcium chloride containing some $CaF_{2}.$
$\ \ \ \ \ \ \ \ \ \ \ \ \ CaCl_{2}\ \rightleftharpoons Ca^{2 +} + 2Cl^{-}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ Ca^{2 +} + 2e^{-}\ \rightarrow Ca\ (at\ cathode)$