Is expiation obligatory for one who swore, saying: "By Allah, no more playing," intending to frighten his son and encourage him to study, and not intending an oath?

Swearing without intending an oath falls under 'laghw al-yameen' (unintentional oaths), for which the person is not held accountable, as Allah Almighty says: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what your hearts have earned." This includes slips of the tongue uttering an oath without intent, or swearing about one thing and the tongue inadvertently slips to another.

If the oath was not intended at all, but merely uttered by the tongue without intent, then the oath is not binding, and nothing is required. However, if the intention was to prevent the child from playing and to encourage him to read, this does not negate the intention of the oath and its binding nature.

If the oath is binding, then the swearer breaks his oath by the child playing, and he is obligated to offer an expiation for the oath. The expiation is binding on the one who swore the oath, not on the one who caused him to break it.