Question

Assertion: Half-life of a radioactive isotope is the time required to decrease its mass number by half.
Reason: Half-life of radioactive isotopes is independent of the initial amount of the isotope.
(A) If both (A) and (R) are correct, and (R) is the correct explanation of (A).
(B) If both (A) and (R) are correct, but (R) is not the correct explanation of (A).
(C) If (A) is correct, but (R) is incorrect.
(D) If (A) is incorrect, but (R) is correct.
(E) If both (A) and (R) are incorrect.

Answer 1

Hint: Half-life is the time required by any quantity of a substance to reduce to half of its initial value. In radioactivity, half-life is the time required for one half of the atomic nuclei of a sample to decay.

Complete Solution :
Let us know some basics of radioactivity:
From the definitions of half-life, we can say that it is the time period required by a substance to decrease the initial number of atoms or the amount of radioactive substance to half.
Radioactivity is the concept that depends on the first order process i.e. radioactivity is the first order process. Now, according to the first order process, half-life of a substance is given as:
\[{{t}_{{}^{1}/{}_{2}}}=\dfrac{0.693}{k}\]
where,
${{t}_{{}^{1}/{}_{2}}}$ = half-life
k = rate constant

Hence, we can say that the half-life for the first order reactions do not depend on the initial concentration of the reactants.
Thus, in radioactivity, half-life is independent of the initial amount of the sample.
Therefore, the Assertion is incorrect but the Reason is correct. So, the correct answer is “Option D”.

Note: Do note that when Assertion is incorrect, option (A) or (B) can never be the answers as, in these options it is required that the Assertion must be correct.