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Topic: 2 Step Nuclear Decay  (Read 2388 times)

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Offline jacobcolbert

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2 Step Nuclear Decay
« on: February 17, 2007, 01:18:49 PM »
I recently have been trying to model 2 step nuclear decay. I said that X decays into Y with a rate constant kx. And Y decays into Z with rate constant kx. I then set up the differential equation dy/dt=kxx-kyY. I then substituted in X=X0e-kxt for X in the differential equation. The result when I solve the equation however has the term (ky-kx) in the demominator of a fraction which makes no sense to me because because what if they are equal? And what if kx is greater than ky? There shouldnt be a negative amount of Y. Once i find a place to host my work as a picture I can post that. Anyways if anyone knows of a correct equation to model this or could confirm or reject my original differential equation it would be appreciated. Thanks.
« Last Edit: February 21, 2007, 12:08:07 AM by Mitch »

Offline Mitch

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Re: 2 Step Nuclear Decay
« Reply #1 on: February 21, 2007, 12:08:12 AM »
The equation doesn't work when ky equals kx. Great catch! Are you sure you are in high school though?
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Offline Yggdrasil

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Re: 2 Step Nuclear Decay
« Reply #2 on: February 21, 2007, 01:30:20 AM »
In the case where kx = ky = k you can derive a different model for Y by choosing a particular solution of the form tekt.

In the case where kx > ky the equation will still be positive since this implies that ekxt < ekyt for all t > 0 and two negative expressions will multiply to give a positive value.

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