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Question

State the law of radioactive decay. Plot s graph showing the number (N) of undebased nuclei as a function of time (t) for a given radioactive sample having half-life $$T_{1/2}$$. Depict in the plot the number of undecayed nuclei at
(i) $$t = 3T1/2$$ and
(ii) $$t = 5T1/2.$$

Solution
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Law of radioactive decay : At any instant, the rate of radioactive disintegration is directly proportional to the number of nuclei of the radioactive element present at that instant. where λ is the constant of proportionality called radioactive decay constant.

Number of undecayed nuclei at
$$t = 3T_{1/2}$$ is $$\dfrac{N_0}{8}$$ and at $$t = 5T_{1/2},$$ it is $$\dfrac{N_0}{32}.$$

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