Is divorce considered effective merely by intention, and how is a wife divorced while she is at her family's home without knowledge of her purity?

Divorce does not occur merely by the wife sending herself to her parents' house with the intention of divorce; for divorce does not happen by mere intention without utterance. If the husband resolves to divorce his wife, he must divorce her during a period of purity in which he has not touched her, and the woman must remain in her home and not leave it until her 'iddah (definition) (waiting period) expires; as Allah Almighty says: "O Prophet, when you [men] divorce women, divorce them for [the commencement of] their waiting period and keep count of the waiting period, and fear Allah, your Lord. Do not expel them from their houses, nor should they leave, unless they commit a clear immorality." (At-Talaq (definition):1).