The rate of disintegration of a radioactive s | vedclass

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(D) The law of radioactive decay is given by the equation:$\frac{dN}{dt} = -\lambda N$where $\frac{dN}{dt}$ represents the rate of disintegration,deno

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(D) The law of radioactive decay is given by the equation:$\frac{dN}{dt} = -\lambda N$where $\frac{dN}{dt}$ represents the rate of disintegration,denoted as $R$.Thus,$R = -\lambda N$ (taking the magnitude,$R = \lambda N$).Rearranging this,we get:$\frac{R}{N} = \lambda$Since $\lambda$ (the decay constant) is a constant for a given radioactive sample,the ratio $\frac{R}{N}$ does not change with time $t$.Therefore,the graph of $\frac{R}{N}$ versus $t$ is a horizontal straight line parallel to the $X$-axis.This corresponds to the graph shown in option $(D)$.

The rate of disintegration of a radioactive sample is $R$ and the number of atoms present at any time $t$ is $N$. When $\frac{R}{N}$ is taken along the $Y$-axis and $t$ is taken along the $X$-axis,the correct graph is:

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