Given an initial nucleus, A, which decays to B and then B to C. I want to calculate the time when the radioactive decay activity of A and B are equal to one another. I have tried to set the $\lambda_A * N_A = \lambda_B * N_B$. But by doing that the time variable cancels out on both side. So what is the correct approach for this problem?
closed as off-topic by AccidentalFourierTransform, heather, Kyle Kanos, Jon Custer, rob♦ Feb 7 '17 at 20:01
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Once I applied all the hints from Bill N (from the comment section), I arrived at the solution of $t = [ln(λ_A/λ_B)]/(λ_A-λ_B)$.
You are on the right track--you want to solve that equation, just remember that $N_A(t)$ and $N_B(t)$ are functions of time (with $N_B(0)=0$).