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A radioactive sample has initial concentration $N_{0}$ of nuclei. Select the correct statement(s)

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The number of undecayed nuclei present in the sample decays exponentially with time.

The activity $(R)$ of the sample at any instant is directly proportional to the number of undecayed nuclei present in that sample at that time.

The number of decayed nuclei grows exponentially with time.

The number of decayed nuclei decreases exponentially with time.

answer is A, B, C.

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Detailed Solution

Number of undecayed nuclei N = ${N_{0}}^{- λ t}$

Number of undecayed nuclei = $N_{0} - N = N_{0} (1 - e^{- λ t})$

Activity A = $λ N$

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