Alpha radiation has alot of high-energy to it but cannot penetrate through anything thinker than paper or skin. With skin, it would kill the skin cell and would be like a slow tanning process.

Bad news is, once the particles get inside the body - through a cut, inhaling or by ingesting it... it releases all this high-energy to your organs all the time its stuck in your body - doing extensive damage in the mean time.

Infact in the 1930s they made watches painted with alpha radiation (they didnt know it was dangerous!) because it reacted with a chemical to "glow-in-the-dark". Breaking the bezel and inhaling the radioactive gas is very bad for you. Info all over the web, google for it here.