Why wouldn't alchemy work through radioactive decay?

I know that if a radium atom emits an alpha particle it will turn into a radon atom, so surely this goes against the whole idea that you can't change one element into another? Is there no element that would create gold through alpha emission? (I'm really not that good at science, I just learnt this at school and it got me thinking). I'm just curious, no plans to break out the cauldron just yet!