Tarnishing of silver occurs due to its reaction with hydrogen sulfide (H₂S) gas present in moist air. This results in the formation of a black coating of silver sulfide (Ag₂S) on the surface of the silver object: \[ 2Ag + H_2S \rightarrow Ag_2S + H_2 \] This black layer of Ag₂S is what causes the silver spoon to appear tarnished.
The correct option is (B): \(Ag_2S\)