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Given below are two statements :
Statement $I:$ The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.
Statement $II:$ The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time $t =0$.
In the light of the above statements, choose the most appropriate answer from the options given below :
Both Statement $I$ and Statement $II$ are correct
Both Statement $I$ and Statement $II$ are incorrect
Statement $I$ is correct but Statement $II$ is incorrect
Statement $I$ is incorrect but Statement $II$ is correct
Solution
Since, $dN =-\lambda Ndt$ $( dN \propto N )$ statement $I$ is wrong.
$T _{1 / 2}=$ time in which active no. of nuclei becomes half therefore statement $II$ is wrong.
