Radioactive sources can be hard to come by, but there are a few common household items that can be used as radioactive sources. The most common source to come by is Americium 241 which is the source of alpha particles used in smoke detectors. of you take it apart you'll find a little piece of metal half a centimeter wide that contains Americium 241 (in picture). Another source can be ceramic dishes which naturally contain isotopes of uranium and thorium, however the glaze can contain uranium oxides and be potent emitters as well. Even some paints containing uranium or cadmium may be emitters, but you don't necessarily need a source to see particle paths in a cloud chamber since the background (mostly muons from space) can also be seen occasionally.
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