Why are metals such as sodium and calcium extracted by electrolytic reduction instead of heating with carbon?

The correct option is: They have greater affinity for oxygen than carbon.

Highly reactive metals like sodium (Na), calcium (Ca), magnesium (Mg), and aluminium (Al) are placed at the top of the reactivity series. These metals form very stable oxides because they have a much stronger chemical affinity for oxygen than carbon does.

If we attempt to reduce their oxides (such as sodium oxide or calcium oxide) by heating them with carbon, carbon is unable to break the strong metal-oxygen bonds. Carbon cannot attract the oxygen atoms away from these highly reactive metals to form carbon dioxide or carbon monoxide. Consequently, carbon reduction is ineffective for these metals.

Therefore, to extract these metals from their ores, a more powerful reduction method is required. This is achieved through electrolytic reduction (electrolysis) of their molten salts (usually chlorides or oxides). During electrolysis, a powerful electric current is passed through the molten compound, forcing the metal ions to gain electrons at the cathode and deposit as pure metal, bypassing the need for a chemical reducing agent like carbon.