The Earth was made radioactive due to a plot by the Spacers.

On the other hand, the Foundation - the civilization using miniature nuclear reactors - is happening many millennial later and far away from Earth.

So the "miniature nuclear tech" and "radioactive Earth" aren't related in the plot.

I was going to say that you're probably thinking of Trantor, the imperial capital, and that the earth was protected by R Daneel Olivaw and his "descendants", but now I just want to wave the nerd flag and link Wikipedia, because you're right about the radioactive but (apparently) wrong about the habitability.

https://en.wikipedia.org/wiki/Earth_(Foundation_universe)

You win this round, sir.

Edit: What petre was referring to was that the eponymous Foundation was deliberately founded on a world poor in radioactives (and other metals), so that they'd be forced to make the most out of what they had, resulting in extremely small, low power equipment.