Attic Rat,
Welcome back, mate.
You could probably do that with something like a current-held relay to switch an alarm.

I remember reading Popular Mechanics magazine back in the mid-80's and pretty much every single issue had an ad for a radon alarm.
Now at the time, we didn't have the Google (or the Net either) where you could go and see what this was, it actually sounded pretty scary at the time.
Is this a US-wide thing or is it confined to certain areas?