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Cloud chambers let you see paths left by radioactive particles as they pass through a supersaturation of alcohol vapor. Vapor trails are formed when the radiation ionizes the alcohol.
They need to be very cold (about -15f) - so most designs require dry ice.
Originally developed by Rich Olson - this design uses inexpensive electrical "Peltier" coolers instead. Unlike other peltier-based cloud chambers - it does not require ice water to operate.
See the Make a Cloud Chamber using Peltier Coolers (Instructable) for full details on making your own.
It's fairly easy to construct - and should only cost about $100 (less if you use a cheap ATX power supply).