Q. Two first order reaction have half-lives in the ratio $8\ :1.$ Calculate the ratio of time intervals $t_{1}\ :t_{2}.$ The time $t_{1}\$and$\ t_{2}$ are the time period for $(1/4)th\$and$\ (3/4)th$ completion
A) $1\ :0.602$
B) $2\ :301$
C) $0.256\ :0.603$
D) $0.2\ :0.301$
Explanation
(a)
$t_{1} = \frac{\left( t_{1/2} \right)_{1}}{0.693}\ln\left( \frac{1}{1 - (1/4)} \right)$
And $t_{2} = \frac{\left( t_{1/2} \right)_{2}}{0.693}\ln\left( \frac{1}{1 - (3/4)} \right)$
$\frac{t_{1}}{t_{2}} = \frac{8}{1} \times \frac{\ln(4/3)}{\ln 4}$
$= \frac{8 \times 0.125}{0.602} = \frac{0.001}{0.602}$
$= 1\ :\ 0.602$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.