I agree it is sad and pathetic that what was common just a generation ago is now necessitating such a question.... Nevertheless, I remember when I was 13 I know I would have gotten into mischief with my .22 or 20ga by shooting at trees, signs, random birds that flew by, etc... depending on where you live, what neighboring property/risks are within range should be taken into consideration, not just what you "think" the maturity level of your son might allow.
In one hand, responsible kids will rise to the level of responsibility bestowed upon them, but in the other, sometimes they cannot, even if it's no fault of their own... For example, does he have friends that ever come over?