When the husband of a wife passes away, the religion prescribes an iddah (mourning) period of four months and ten days for the wife of the husband.
There is no iddah period for the husband in the case of his wife dying.
During this time of Iddah, it is suggested that the wife do not partake in unnecessary social activities.
The wife is allowed to perform mandatory tasks like working depending in her circumstances.
Learned Scholars must be consulted for more detail around the various interpretations of the above.