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[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>