Question
The half-life of ^ 65 Zn is 245 days. After x days, 75 \% of original activity remained. The value of x in days is \_\_\_\_. (Nearest integer) (Given: 3=0.4771 and 2=0.3010)
JEE Main
Chemistry
Chemical Kinetics
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Chemistry Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
Using radioactive decay: A = A_0 ( 1 2 )^ t/t_ 1/2 . With 75% activity remaining: 0.75 = ( 1 2 )^ x/245 . Taking log base 10: (0.75) = x 245 (0.5). Calculate: (0.75) = 3 - 4 = 0.4771 - 2(0.3010) = -0.1249 and (0.5) = -0.3010. Thus -0.1249 = x 245 (-0.3010), giving x = 0.1249 245 0.3010 = 101.66 102 days (nearest integer).
Related: Chemistry — Chemical Kinetics · All PYQ Banks