Which of the following statements are true re | vedclass

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(C) Statement $(I)$ is true: Radioactive decay follows the law $N(t) = N_0 e^{-\lambda t}$,which is an exponential decay.Statement $(II)$ is true: By

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$I, II$ and $III$

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(C) Statement $(I)$ is true: Radioactive decay follows the law $N(t) = N_0 e^{-\lambda t}$,which is an exponential decay.Statement $(II)$ is true: By definition,the half-life $(T_{1/2})$ is the time taken for the number of radioactive nuclei to reduce to half of their initial value.Statement $(III)$ is true: Radioactive dating (e.g.,uranium-lead dating) is a standard method used to determine the age of rocks and the Earth.Statement $(IV)$ is false: The relationship between half-life $(T_{1/2})$ and mean life $(	au)$ is $T_{1/2} = 	au \ln(2) \approx 0.693 	au$. Thus,the half-life is approximately $69.3\%$ of the mean life,not $50\%$.Therefore,statements $(I), (II),$ and $(III)$ are correct. The correct option is $C$.

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