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Lagraaaange
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Homework Statement
Two isotopes N1, N2. You are given the value of the proportions N1(t1)/N2(t1) and N1(t2)/N2(t2). From this calculate Δt.
Homework Equations
dN/dt = -λN
The Attempt at a Solution
Solve dN1/N = -λdt and dN2/N = -λdt
obtain: N1(t2) = N1(t1)exp(-λ1(t2-t1)) (1)
and N2(t2) = N2(t1)exp(-λ2(t2-t1)). (2)[/B]
Divide (1) by (2) and take ln of both sides
=> ln[(N1(t2)/N2(t2))/(N1(t1)/N2(t1))] = (-λ1+λ2)(Δt)
Okay so if I'm given the proportions (say X) I can get a numerical result for left hand side
ln(X)/(-λ1+λ2) = Δt
But if I'm not given the λ's how can I obtain them? I feel like I'm missing some relationships between λ and the proportionality constants.