Radioactive dust on air filters
The location where I have my on-line geiger counter is certainly not dust-free: I work in a library after all, and the dust sure looks like paper dust. But the air from outside is well filtered. Since a very easy way to detect radon and its daughter products in the air is to move a large quanity of air through a filter and quickly measure the activity of the picked-up dust, I've tried this out in a variety of places. The result is no radon in my basement office (A-level), no radon in the sub-basement (B-level), but a touch of it in the server room (which has a wall directly against the subsoil).
Yesterday I got lucky: I noticed a trash bin filled with the air filters for the building and took a sample. Sure enough, the readings were elevated. Yesterday it read 11.5 uR/hr with a small piece of the filter against the counter. Today, the same sample read 8.5. (The long-term background average is 7.6).
What's not clear is what radionuclide is the source. I don't know how long the filters were sitting around before I found them. With a radon filter test, it's very important to test as quickly as possible, as you are sampling the short decays of the first four daughters formed from radon-222's decay into polonium 218. That polonium-218 has a 3.05 minute half-life, its daughter lead-214 26.9 minutes, its daughter bismuth-214 19.7 minutes, and the last polonium-214's is only 0.00015 seconds; there's not much time to get a nice graph out of it.
Since the next decay, from lead-210 into bismuth 210 has a half-life of 22 years, I'll never see it unless I had a lot of it lying around. Some researchers use Pb-210 that gets embedded in glass as a long-term measurement for radon levels in old houses.
A topical point is bismuth-210 decays into polonium-210, the poison of Alexander Litvineko which ends the uranium-238 decay chain after decaying into lead-206 (Pb-206)
The whole decay chain for U-238: