Q. For the first order reaction with the rate constant $k,$ which expression gives the rate half-life period? (Initial conc. = $a$)
A) $\frac{3}{2}ka^{2}$
B) $\frac{1}{ka}$
C) $\frac{1}{k}$
D) $\frac{0.693}{k}$
Explanation
(d)
$k = \frac{2.303}{t}\log_{10}\frac{a}{a - x}$
For half-life period, $x = \frac{a}{2}$
$t = \frac{2.303}{k}\log_{10}\frac{a}{a - \frac{a}{2}}$
$t = \frac{2.303}{k}\log_{10}2$
$\because t = t_{1/2}$
$t_{1/2} = \frac{2.303 \times 0.3010}{k}$
$t_{1/2} = \frac{0.693}{k}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.