Having read the Robot, Empire, and Foundation novels in a haphazard order, I was wondering when the Earth was turned radioactive and was it ever explained why?
It's addressed in one of his later books, Robots and Empire: It's some kind of global nuclear activation, not nuclear war. It's done:
- by the man activating it: To kill Earth humans.
- by the robot mentally controlling him: To force Earth humans to expand into the galaxy.
In The Stars, Like Dust a character claims it's the result of a nuclear war, but in Robots and Empire it's explained by the people doing it to be a nuclear intensifier, which causes the radiation increase over 150 years, force most of humanity to leave early.
http://www.sikander.org/foundation.php says that it happens about 3700 C.E.