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I was not available over the weekend when much of this discussion took place. I actually do this experiment in a home-made vacuum chamber and using an alpha source from a smoke detector. It works extremely well and points out several interesting facts about detection of radiation with Geiger-Mueller tubes.
A photograph of the home-made apparatus, and a fairly detailed explanation, and some actual data and graphs are available on my web space. If you are at all interested in this topic, I recommend that you take a look at this document. It is two pages of text plus two graphs, and is in PDF format.
Here is the link...