Radiation in Granite is not dangerous:

From what we know, here are two ways in which countertops, tiles and other finish made of granite strength emit any level of radiation. The first is by the release of small amounts of the radioactive gas radon, which can be inhaled. The second is by straight radiation from the surface itself to the homeowner. In both cases, the radiation emit is from the same process – natural radioactive decay of one element into a new. Compare to other radiation sources in the home and outside, the risk to the homeowner from radioactivity emitted from a granite countertops or tiles is practically non-existent. In fact, the quantity of radon gas emitted by a granite countertop is a lesser amount of than one millionth of that already there in the household air from other sources.

Typical Contributions to Radon Content of Indoor Air (pCi/L)