<!doctype html public "-//W3C//DTD W3 HTML//EN">
<html><head><style type="text/css"><!--
blockquote, dl, ul, ol, li { padding-top: 0 ; padding-bottom: 0 }
--></style><title>Re: Survey Meters</title></head><body>
<div>Brian wrote:</div>
<div><br></div>
<blockquote type="cite" cite>If instead of using a spreadsheet, I
synthesize the effect<br>
of a double decay cascade like this,<br>
where the first species decays at one third the rate of<br>
the daughter species,......<br>
<br>
'exponential decay of double series<br>
count = 1000<br>
for a = 1 to 1000<br>
count = count*0.99<br>
count2 = count* 0.97<br>
print a; " " ;count; " ";
count2<br>
next a<br>
end<br>
<br>
... a single exponential of this form:<br>
count2 = 970* exp(-0.001005 *a)<br>
<br>
leads to a fit with exceptionally good statistics<br>
anovar: F = 9.6E20, SE estimate = 1.4E-7<br>
using just a single exponential equation.<br>
<br>
Therefore, I expect I am misunderstanding some prior comments<br>
about the possibility of pulling details of a double decay out of
an<br>
exponential time series. I cannot do this.</blockquote>
<blockquote type="cite" cite>Or was my synthetic dataset
faulty?</blockquote>
<div><br></div>
<div>I'm not sure I follow the above, but I have put my spreadsheet on
the web at</div>
<div><br></div>
<div><<font face="Lucida Grande" size="-3"
color="#000000">http://www.csupomona.edu/~ajm/special/radon.xls</font
></div>
<div><br></div>
<div>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.</div>
<div><br></div>
<div>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.</div>
<x-sigsep><pre>--
</pre></x-sigsep>
<div>John "Slo" Mallinckrodt<br>
<br>
Professor of Physics, Cal Poly Pomona<br>
<http://www.csupomona.edu/~ajm><br>
<br>
and<br>
<br>
Lead Guitarist, Out-Laws of Physics<br>
<http://www.csupomona.edu/~hsleff/OoPs.html></div>
</body>
</html>