Statement I: The half-life of a radioactive element does not depend on the initial amount of the element taken.
Statement II: Radioactive decay of unstable nuclei takes place by first order kinetics.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I.
For a first order reaction the half-life depends only on the rate constant:
\( \displaystyle t_{1/2}=\frac{0.693}{k} \)
Statement I: The half-life of a radioactive element does not depend on the initial amount of the element taken. — True. Whether a large or a small amount is taken, the same time is needed for half of it to decay.
Statement II: Radioactive decay of unstable nuclei takes place by first order kinetics. — True. All natural and artificial radioactive decay is first order.
Why Statement II explains Statement I?
Because the decay is first order, its half-life is 0.693/k, which has no concentration term.
So the half-life is the same for any initial amount of the element, which is Statement I.
NCERT (2026-27 edition):
3.3.3 Half-Life of a Reaction – “It can be seen that for a first order reaction, half-life period is constant, i.e., it is independent of initial concentration of the reacting species.”
3.3.2 First Order Reactions – “… All natural and artificial radioactive decay of unstable nuclei take place by first order kinetics.”