IPhone 4 from AT&T to sprint?

Okay need a little help here.
I have AT&T. I just upgraded my iPhone 4 to the iPhone 5. But I still have my 4 because I decided not to trade it in.
Now my mom & brother have a contract with Sprint. My mom needs a new phone. I offered her my old iPhone.
If they go to Sprint with my old phone that has been restored to factory settings, will they be able to use it?

Nope - totally different technology.AT&T uses GSM, sprint does not.