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At t = 0, a sample contains N1 nuclei with decay constant λ1 and N2 nuclei with decay constant λ2, and the two groups are mixed together. The decay rate of the combined sample is

1. -N1 λ2 e^(-(λ1+λ2)t)
2. -(N1/N2) e^(-(λ1+λ2)t)
3. -(N1 λ1 e⁻λ1 t + N1 λ2 e⁻λ2 t)
4. -N1 λ1 e⁻λ1 t - N2 λ2 e⁻λ2 t

Correct answer: -N1 λ1 e⁻λ1 t - N2 λ2 e⁻λ2 t

Solution

Each group decays independently: dN/dt = -lambda1*N1*e^(-lambda1 t) - lambda2*N2*e^(-lambda2 t). The combined decay rate is the sum, giving option 3.

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