Question

Which of the following is correct for a first order reaction?

• A. $t_{1/2}\propto a^0$
• B. $t_{1/2}\propto a^2$
• C. $t_{1/2}\propto a$
• D. $t_{1/2}\propto \frac{1}{a}$

Answer 1

Answer: (A)

$t_{1/2}\propto a^0$

For first order reaction, $t_{1/2}=\frac{0.693}{k}$
where, $k=$ rate constant

Hence, half-life does not depend on the concentration of the first-order reaction.

$\therefore t_{1/2}\propto a^0$ $\{a^0=1\}$

or $t_{1/2}=\frac{0.693}{k}$

$[\frac{0.693}{k}=$ constant $]$.

(All radioactive decays follow first-order kinetics)

Hence, option A is correct.