I am afraid I don't have the numbers to back up my claim but when I was at university, my thermodynamics lecturer showed us a calculation that background dose from radioactive material at a coal powered fire station is higher than that of a nuclear power station. This is because of the shear amount of coal power stations burn through, and in that fuel, there is a trace amount of radioactive material that eventually gets out into the atmosphere.

I've previously worked on a nuclear licenced site and we were not even allowed to throw smoke alarms in the general rubbish due to there being radioactive material inside.