Re: Nuclear rate of decay quandary

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

"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.