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 :

  • [NEET 2022]
  • A

    Both Statement $I$ and Statement $II$ are correct

  • B

    Both Statement $I$ and Statement $II$ are incorrect

  • C

    Statement $I$ is correct but Statement $II$ is incorrect

  • D

    Statement $I$ is incorrect but Statement $II$ is correct

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$x$ fraction of a radioactive sample decay in $t$ time. How much fraction will decay in $2t$ time

A $1000 \;MW$ fission reactor consumes half of its fuel in $5.00\; y$. How much $_{92}^{235} U$ (in $kg$) did it contain initially? Assume that the reactor operates $80 \%$ of the time, that all the energy generated arises from the fission of $_{92}^{235} U$ and that this nuclide is consumed only by the fission process.

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  • [IIT 2004]