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Statement I: Radioactivity of $10^{8}$ undecayed radioactive nuclei of half life of 50 days is equal to that of $1.2 x 10^{8}$ number
of undecayed nuclei of some other material with half life of 60 days.
Statement II: Radioactivity is proportional to half-life.

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Both statement I and statement II are correct

Statement I is correct and Statement II is incorrect

Statement I is incorrect and Statement II is correct

Both statement I and statement II are incorrect

answer is C.

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Detailed Solution

Radioactivity = $- \frac{dN}{dt} = λN = \frac{0.693 N}{T}$

$= \frac{0.693 x 10^{8}}{50} = \frac{0.693 x 1.2 x 10^{8}}{60} = 0.693 x 2 x 10^{6} .$

Radioactivity is proporlional to $1 / T_{1 / 2}, and not to T_{1 / 2} .$

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