Chemistry · Chemical Kinetics

JEE Main 2026 — 24 January, Evening Shift — Question 68

The half-life of 65Zn^{65}\mathrm{Zn} is 245245 days. After xx days, 75%75\% of original activity remained. The value of xx in days is ____\_\_\_\_. (Nearest integer) (Given: log⁡3=0.4771\log 3 = 0.4771, log⁡2=0.3010\log 2 = 0.3010)

Answer: 102

Numerical answer — enter this value.

Step-by-step solution

Radioactive decay, we have

= \left(\frac{1}{2}\right)^{t/T_{1/2}}$$ $$0.75 = \left(\frac{1}{2}\right)^{x/245}$$ $$\log(0.75) = \frac{x}{245}\log\left(\frac{1}{2}\right)$$ $$\log\left(\frac{3}{4}\right) = 0.4771 - 0.6020 = -0.1249$$ $$\log\left(\frac{1}{2}\right) = -0.3010$$ $$\frac{x}{245} = \frac{-0.1249}{-0.3010} = 0.4147$$

x = 101.6 \approx 102

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Subject
Chemistry
Chapter
Chemical Kinetics
Topic
Integrated Rate Laws
The half-life of 65 Zn is 245 days. After x days, 75\% of original… | JEE Main 2026 PYQ with Solution · DhiX AI