A radioactive element decays to form a stable | vedclass

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(C) The number of radioactive nuclei $N$ at any time $t$ is given by the radioactive decay law:$N(t) = N_0 e^{-\lambda t}$Where $N_0$ is the initial n

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(C) The number of radioactive nuclei $N$ at any time $t$ is given by the radioactive decay law:$N(t) = N_0 e^{-\lambda t}$Where $N_0$ is the initial number of radioactive nuclei at $t = 0$ and $\lambda$ is the decay constant.This equation represents an exponential decay function,which is of the form $y = a e^{-kx}$.As $t$ increases,$N$ decreases exponentially from the initial value $N_0$ and approaches zero as $t 	o \infty$.Therefore,the correct graph is the one showing an exponential decay curve starting from a positive value on the $N$-axis,which corresponds to option $C$.

$A$ radioactive element decays to form a stable nuclide. The graph representing the number of radioactive nuclei $(N)$ versus time $(t)$ is:

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