What should my mother do, as she vowed to celebrate my sister’s success after her graduation but was unable to fulfill her vow due to lack of money? Is an expiation for breaking an oath (kaffarat yameen) incumbent upon her? And what is the expiation for breaking an oath?

Vows (nadhr) are discouraged (makruh), and the Messenger of Allah, peace and blessings be upon him, forbade them. For a permissible vow, such as celebrating success, the one who made it has the choice between fulfilling it or offering the expiation for an oath (kaffarat al-yamin), which is feeding ten poor people, or clothing them, or emancipating a slave. If one cannot do that, then fasting for three days.