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Equilibrium radioactive decay question
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[QUOTE="nateja, post: 4496216, member: 392552"] [h2]Homework Statement [/h2] A sample of Mo-101, initially pure at time zero, beta decays to Tc-101 which then beta decays to Ru-101 (stable). The half-lives of Mo-101 and Tc-101 are nearly the same and for this problem [B]are assumed equal (14.4 min)[/B]. After a decay period of one half-life how many atoms of each isotope per initial atom of Mo-101 are present? This problem needs to be solved analytically with integrating factors or numerically with short time steps. [h2]Homework Equations[/h2] N(t) = N(0)* e^(-lambda*t) lambda = decay constant tau = half-life = ln(2)/lambda [h2]The Attempt at a Solution[/h2] My first attempt was to just integrate N(0)*e^(-lambda*t) from t = 0 to t = ln(2)/14.4 (the half-life) and then repeat the same process to get the number for Ru-101. I realized this was incorrect because A) the percent was really really small for both isotopes and B) this did not account for the fact that the Tc-101 nuclei were decaying at the same times the Mo-101 nuclei were decaying so I think i'd have to calculate them simultaneously... not sure how to do that though. I am reading up on my integrating factors and equilibrium calculations so I will be back with a better approach in an hour or so. [/QUOTE]
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Equilibrium radioactive decay question
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