In "Robots and Empire," Mandalamus said that Earth would be radioactive within 20 decades (e.g. 200 years). But in "Pebble in The Sky," it was said that people still were on Earth after 9000 years! Why so?
Pebble in the Sky says that while much of Earth's surface is radioactive, there are some safer patches left in between where humans can still live. I don't have the novel with me now, so I don't know where it says that, but the review in Jenkins' guide says “The Earth of the future is a patchwork of normal soil and land so contaminated with radiation that it glows”.
You should also know that there are some contradictions between the different Asimov novels about the radioactive earth. Jenkins' guide for Robots and Empire explains the retcons done by that later novel.
the final and most official reason for why the Earth became radioactive. The radioactive Earth features as a plot element in the three “Empire” novels, Pebble in the Sky, The Stars, Like Dust—, and The Currents of Space, and in all three, it is attributed to nuclear war. This was a common expectation in the early 1950’s, when these books were written; it was only later that Asimov realized that from a physics perspective, it was unreasonable to think the Earth’s crust could become radioactive as a side effect of such a conflict. With the additional perspective of nearly forty years, Asimov felt a need to provide a more rational explanation for this phenomenon, and does so here.