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(A) The activity $A$ of a radioactive sample is given by the formula $A = \lambda N$,where $\lambda$ is the disintegration constant and $N$ is the num

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Increases,remains the same

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(A) The activity $A$ of a radioactive sample is given by the formula $A = \lambda N$,where $\lambda$ is the disintegration constant and $N$ is the number of radioactive nuclei present in the sample.Since the number of nuclei $N$ is directly proportional to the mass $m$ of the sample $(N = \frac{m}{M} N_A)$,doubling the mass $m$ doubles the number of nuclei $N$.Consequently,the activity $A$ increases because $A \propto N$.The disintegration constant $\lambda$ is a characteristic property of the radioactive isotope and depends only on the nature of the substance,not on the amount of the sample present.Therefore,$\lambda$ remains the same.

If the mass of a radioactive sample is doubled,the activity of the sample and the disintegration constant of the sample are respectively

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