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(C) The radioactive decay law states that the rate of decay is proportional to the number of radioactive nuclei present at that time,given by $\frac{d

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$\lambda$ is independent of the age of the atom.

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(C) The radioactive decay law states that the rate of decay is proportional to the number of radioactive nuclei present at that time,given by $\frac{dN}{dt} = -\lambda N$.Here,$\lambda$ is the decay constant,which represents the probability of decay per unit time for a single radioactive nucleus.Radioactive decay is a spontaneous and random process,meaning the probability of decay for a nucleus does not depend on how long the nucleus has existed.Therefore,$\lambda$ is a constant characteristic of the radioactive isotope and is independent of the age of the atom.

The decay constant of a radioactive sample is $\lambda$. The probability of decay per unit time is:

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