Uranium decays chain:
http://www.uic.com.au/graphics/ral3-2.gif
Note that alpha radiation from radon isn't the only concern, its decay products are radioactive too, and many of them have shorter half-lives the radon itself.

http://www.uic.com.au/graphics/raddoses.gif
This diagram shows radon's signifance of annual natural radiation doses. What's with Australia's outdoor gamma radiation? That's not because of the ozone depletion, is it?