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 are assumed equal (14.4 min). 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.
N(t) = N(0)* e^(-lambda*t)
lambda = decay constant
tau = half-life = ln(2)/lambda
The Attempt at a Solution
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.