[Phys-L] Re: Survey Meters

[ajm at CSUPOMONA.EDU (John Mallinckrodt)]

[Oops.  Sorry.  Let's try that again.]

Brian wrote:

> If instead of using a spreadsheet, I synthesize the effect
> of a double decay cascade like this,
> where the first species decays at one third the rate of
>   the daughter species,......
>
>    'exponential decay of double series
>      count = 1000
>      for a = 1 to 1000
>      count = count*0.99
>      count2 = count* 0.97
>      print a; " " ;count; " "; count2
>      next a
>      end
>
> .... a single exponential of this form:
> count2 = 970* exp(-0.001005 *a)
>
> leads to a fit with exceptionally good statistics
> anovar: F = 9.6E20, SE estimate = 1.4E-7
> using just a single exponential equation.
>
> Therefore, I expect I am misunderstanding some prior comments
> about the possibility of pulling details of a double decay out of an
> exponential time series. I cannot do this.
> Or was my synthetic dataset faulty?

I'm not sure I follow the above, but I have put my spreadsheet on the web at

<http://www.csupomona.edu/~ajm/special/radon.xls>

It starts with 1000 Po-218 nuclei (direct daughters of Rn-222), 8080
Pb-214 nuclei, and 6000 Bi-214 nuclei at t = -20 min.  This insures
that the sequence is very close to secular equilibrium.  Every minute
the spreadsheet calculates the number of decays of the Po-218, the
Pb-214, and the Bi-214, and accumulates the product of the final
decay as Pb-210 which has a long half life.  The Po-218 is
replenished (artificially in the model, but by the decay of Rn-222 in
the real world), maintaining the secular equilibrium, until t = 0.
After that the Po-218 is allowed to decay, mimicking the removal of
its Rn-222 source.

The spreadsheet calculates and plots the number of decays per minute
for each short-lived nuclei and also plots the composite decay rate
for the Pb-214 AND Bi-214 decays.  You will see that the composite
decay begins relatively slowly (perhaps like a 50 minute half life
and looks more like 30 minutes after a couple of hours.
--
John "Slo" Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>