An ion of sulfur has a smaller atomic radius than a neutral atom of sulfur because it loses an electron when becoming an ion.
true or false?

Answer is FALSE. Because sulfur has no tendency to loss an electron, since its electronic configuration is 16, it always want to gain 2 electron to form S^2-, following octet rule.

The answer would be yes if it can lose an electron(because when an atom loses an electron it form cation whose nuclear charge remain as same as neutral atom but number of electron decreases. As a result the nuclear charge has to act on a fewer number of electron and hence there will be more attraction between the nuclear charge and outermost electrons resulting in decrease in size) but it is not possible in case of sulfur.