Was the mother's action of asking her son to swear on the Qur'an not to smoke correct? Will the son be held accountable if he breaks the oath? And does informing the mother that he will smoke in the future absolve him from his oath?

The questioner is keen on the righteousness of her son and on him avoiding smoking. She must employ beneficial means and successful methods to keep him away from it, through encouragement and deterrence, by explaining its harms, by choosing righteous companions for him, and by enrolling him in Quran memorization circles or lessons of knowledge. Making him swear on the Quran to abandon it is a good thing, but his oath is not binding due to his young age. He does not incur sin if he disobeys and smokes before reaching puberty, and there is no expiation for him if he disobeys and smokes after reaching puberty, according to the correct opinion of the scholars. However, he might be considered an adult by another sign other than age, in which case his oath becomes binding, and he is obligated to fulfill it because he swore to abandon a sin. If he informs the questioner before smoking, he does not break his oath.