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[Phys-L] Re: Survey Meters



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<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>
&nbsp; the daughter species,......<br>
<br>
&nbsp;&nbsp; 'exponential decay of double series<br>
&nbsp;&nbsp;&nbsp;&nbsp; count = 1000<br>
&nbsp;&nbsp;&nbsp;&nbsp; for a = 1 to 1000<br>
&nbsp;&nbsp;&nbsp;&nbsp; count = count*0.99<br>
&nbsp;&nbsp;&nbsp;&nbsp; count2 = count* 0.97<br>
&nbsp;&nbsp;&nbsp;&nbsp; print a; &quot; &quot; ;count; &quot; &quot;;
count2<br>
&nbsp;&nbsp;&nbsp;&nbsp; next a<br>
&nbsp;&nbsp;&nbsp;&nbsp; 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>&lt;<font face="Lucida Grande" size="-3"
color="#000000">http://www.csupomona.edu/~ajm/special/radon.xls</font
&gt;</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.&nbsp; This
insures that the sequence is very close to secular equilibrium.&nbsp;
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.&nbsp; 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.&nbsp;
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.&nbsp; 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 &quot;Slo&quot; Mallinckrodt<br>
<br>
Professor of Physics, Cal Poly Pomona<br>
&lt;http://www.csupomona.edu/~ajm&gt;<br>
<br>
and<br>
<br>
Lead Guitarist, Out-Laws of Physics<br>
&lt;http://www.csupomona.edu/~hsleff/OoPs.html&gt;</div>
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