Er, actually, I _am_ a nuclear scientist.
On sensitivity, the calim is that a microgramme of cobalt 60 can be detected.
Firstly, cobalt 60 is a beta emitter, not an alpha emitter, so I fail to understand why this follows an explanation about alpha particles.
Secondly, one microgram of cobalt 60 (half life a tad over 5 years) is about a millicurie, which gives more than 40 million disintegrations per second, and that's not what anybody sane would call a tiny amount of radioactive material. For comparison, it's about ten thousand times the typical human body load of potassium 40 (something like 125 grammes, half life a bit more than a billion years, so very roughly 4000 disintegrations per second).