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Re: Nuclear rate of decay quandary



"Donald E. Simanek" wrote:

On Thu, 22 Apr 1999, Kismet Talaat wrote:


Noted above. However, this problem should be a candidate for the physics
problem hall of shame. During the last half-life represented by the data
only two atoms decayed. During the next half-life the one remaining is
supposed to decay. But due to the inherent statistical uncertainty of the
decay process itself, one atom may decay very promptly, or live nearly
forever before decaying. In short, the uncertainty in that last value "1"
in the data is *huge*, and makes any "estimate" based on it nearly
worthless in the real world of experimentation.

But the problem would be out of the "hall of shame" if the numbers
were much larger, for example, 1024*10^10 instead of 1024 etc.
I think it was a good problem to show what was intended. And a
good example of mistakes that students make. Yes, we should
emphasize that the law of exponential decay is no longer reliable
when it comes to small numbers.

Ludwik Kowalski



It would be an interesting problem for the rest of you to tackle. Based on
this data, estimate the uncertainty in the determination of half-life.
Also estimate the uncertainty of that answer of 128 atoms left after 6
minutes. Assume the uncertainties in the instrumentation, including the
times, are negligible.