# Calculate decay activity time [closed]

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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• You don't show any time variable. How can they cancel? – Bill N Feb 6 '17 at 22:00
• Well, the activity is defined as λN = λN_0*exp(-λ*t) – Kane Billiot Feb 6 '17 at 22:08
• Only for A, and the $\lambda$ terms could be different. The expression for activity of B is more complicated because it has the decay of A feeding into the population of B while B decays: $\dot{B}=-\lambda_B N_B(t) + \lambda_A N_A(t)$. – Bill N Feb 6 '17 at 22:16
• If I set $B'$ = $A'$ then I would I end up with 0 = $−λ_BN_B(t)+2λ_AN_A(t)$. Move one of the product to the other side, then wouldn't t cancel out again? @BillN – Kane Billiot Feb 6 '17 at 22:28