ANSWER:

There’s no such thing as 40 days Iddah!

She must observe the full iddah of 4 months and 10 days of hijri calendar, however she can go out due to necessity.

Sheikh my father died one week ago and my mother wants to stay in iddah for forty days because she needs to b present for the documentation and legal work. Is this permissible for her to stay in iddah for 40 days or 4 months 10 days is mandatory for her