He had an argument with his wife and hit her head against the wall and she died
What the husband did, holding his wife’s head and hitting it against the wall, is an evil act and is not permissible, because Allaah has not permitted striking the wife in this manner. Rather there is a concession allowing hitting her to discipline her, after exhorting her and forsaking her in bed, on the basis that it should not be a painful blow, and should not leave a mark or break a bone, and it should not be done with motives of revenge or to express one’s anger.
What the husband has done comes under the heading of quasi-intentional killing, which the majority of scholars defined as intending to strike a person with something that does not usually kill, such as a whip or small stick.
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (6/118): Quasi-intentional is one of the categories of killing. What it means is that he intended to hit him with something that does not usually kill, either with the intention of aggression against him or with the aim of disciplining him, but he went too far in it, such as hitting with a whip, stick or small rock or striking with the hand, or anything else that does not usually kill; if it kills then it is quasi-intentional, because the aim was to strike but not to kill. The action was intentional but the killing occurred by mistake. There is no qisaas in such cases, and the diyah must be paid by the ‘aaqilah (male relatives on the father’s side), according to the majority of scholars. End quote.
Hence the husband must do two things:
He must offer expiation, which is freeing a slave; if that is not possible then he must fast for two consecutive months, and it is not acceptable for him to feed the poor instead, according to the more correct view, because Allaah says (interpretation of the meaning):
“It is not for a believer to kill a believer except (that it be) by mistake; and whosoever kills a believer by mistake, (it is ordained that) he must set free a believing slave and a compensation (blood money, i.e. Diya) be given to the deceased’s family unless they remit it. If the deceased belonged to a people at war with you and he was a believer, the freeing of a believing slave (is prescribed); and if he belonged to a people with whom you have a treaty of mutual alliance, compensation (blood money — Diya) must be paid to his family, and a believing slave must be freed. And whoso finds this (the penance of freeing a slave) beyond his means, he must fast for two consecutive months in order to seek repentance from Allaah. And Allaah is Ever All‑Knowing, All‑Wise”
The Standing Committee for Issuing Fatwas was asked: Do I have to fast after paying the diyah, and for how long? Should it be consecutive or not? Can I fast intermittently or feed poor people instead?
You have to offer expiation for killing by mistake, which is freeing a believing slave. If that is not possible then you must fast for two consecutive months, and it is not permissible for you to fast intermittently or to feed poor people as expiation for killing by mistake, because there is no proof of that as expiation for killing in the Book of Allaah or the Sunnah of His Messenger (peace and blessings of Allaah be upon him), and your Lord is not forgetful. End quote.
Fataawa al-Lajnah al-Daa’imah (21/273)
The diyah must be paid by the ‘aaqilah (male relatives on the father’s side) of the killer, unless the heirs of the wife agree to let him off.
The ‘aaqilah is what is nowadays known as the ‘aa’ilah (family), but what is meant is the males only; it does not include the females. The ‘aa’ilah includes the father, grandfather, son, brothers, paternal uncles and their sons.
The diyah for a woman is half the diyah of a man, so it is fifty camels.
And Allaah knows best.