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(C) According to the law of radioactive decay,the number of undecayed nuclei $N$ at time $t$ is given by $N = N_0 e^{-\lambda t}$,where $N_0$ is the i

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(C) According to the law of radioactive decay,the number of undecayed nuclei $N$ at time $t$ is given by $N = N_0 e^{-\lambda t}$,where $N_0$ is the initial number of nuclei and $\lambda$ is the decay constant.The rate of decay is given by the derivative of $N$ with respect to time $t$:$\frac{dN}{dt} = -\lambda N_0 e^{-\lambda t}$The magnitude of the rate of decay is $|\frac{dN}{dt}| = \lambda N_0 e^{-\lambda t}$.This expression shows that the rate of decay decreases exponentially with time $t$. Among the given options,Figure $C$ represents an exponential decay curve,which correctly depicts the relationship between the rate of decay and time.

$A$ radioactive element decays to form a stable nuclide. The rate of decay of the reactant $\left( \frac{dN}{dt} \right)$ will vary with time $(t)$ as shown in which figure?

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