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(C) The rate of decay for each process is given by $\frac{dN_1}{dt} = -\lambda_1 N$,$\frac{dN_2}{dt} = -\lambda_2 N$,and $\frac{dN_3}{dt} = -\lambda_3

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$\lambda_{eff} = \lambda_1 + \lambda_2 + \lambda_3$

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(C) The rate of decay for each process is given by $\frac{dN_1}{dt} = -\lambda_1 N$,$\frac{dN_2}{dt} = -\lambda_2 N$,and $\frac{dN_3}{dt} = -\lambda_3 N$.The total rate of decay is the sum of the individual rates: $\frac{dN}{dt} = \frac{dN_1}{dt} + \frac{dN_2}{dt} + \frac{dN_3}{dt}$.Substituting the expressions,we get: $\frac{dN}{dt} = -\lambda_1 N - \lambda_2 N - \lambda_3 N = -(\lambda_1 + \lambda_2 + \lambda_3) N$.Comparing this with the general decay equation $\frac{dN}{dt} = -\lambda_{eff} N$,we find that the effective decay constant is $\lambda_{eff} = \lambda_1 + \lambda_2 + \lambda_3$.

$A$ certain radioactive material can undergo three different types of decay,each with a different decay constant $\lambda_1$,$\lambda_2$,and $\lambda_3$. Then the effective decay constant is:

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