The Geiger-Müller gas discharge tube is of course only one of several ways to detect ionizing radiation. It is perhaps generally the most convenient - its sensitive area is greater than optical systems; its much lower cost than photomultiplier tubes and scintillation crystals; and its a heck of a lot more portable than a cloud chamber!
But I'd quite like to try all the methods that are within my reach! One of these, the cloud chamber, I am working on. I have suitable high current power supplies and heatsinks for a small chamber cooled using Peltier effect devices - I'm just awaiting delivery of those devices! The cloud chamber is of course the best for visually demonstrating radiation, as the paths of the ejected particles are visible to the eye.
Another method is by detecting the impact of a particle or energy quanta on a semiconductor junction. Most junctions, for instance a TO-92 transistor, are tiny, but there are a number of PIN photodiodes that have rather large junction areas, in the region of 5-7mm² which, while pretty small still, represent a much greater target area. One such, the BPW34, has been used in several simple detector circuits, and can be obtained for very low cost. As the likelihood of a particle event is still quite low, wiring them in parallel to increase the effective surface area is a trivial matter. Ive ordered five for less than £1.50. My intention is to build all five into a detector, but perhaps allow switching to select the actual detection area.
Of course the big problem with using PIN photodiodes for radiation detection is keeping them from detecting the radiation they were designed for - light! And extremely light-tight enclosure is needed, plus any indicator LED has to be very well isolated optically!
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