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(D) The law of radioactive decay is given by $N(t) = N_0 e^{-\lambda t}$,where $N(t)$ is the number of nuclei remaining at time $t$,$N_0$ is the initi

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(D) The law of radioactive decay is given by $N(t) = N_0 e^{-\lambda t}$,where $N(t)$ is the number of nuclei remaining at time $t$,$N_0$ is the initial number of nuclei,and $\lambda$ is the decay constant.For all nuclei to disintegrate,we require $N(t) = 0$.Setting $N_0 e^{-\lambda t} = 0$,we find that this condition is only satisfied as $t 	o \infty$.Since the decay process is exponential,the number of nuclei approaches zero asymptotically but never reaches zero in a finite amount of time.Therefore,the time taken for all nuclei to disintegrate is theoretically infinite,making the answer uncertain or undefined in a practical sense.

The half-life of a radioactive substance is $T$. The time taken for all the nuclei to disintegrate will be

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