Q. The activity of a radioactive sample is measured as N₀ counts per minute at t = 0 and N₀/e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is
A) 5 logₑ2
B) logₑ(2/5)
C) 5/logₑ2
D) 5 log₁₀5
Explanation
[Solution from source] Activity falls to 1/e in 5 min, so λ = 1/5 per minute (mean life 5 min). T½ = ln 2/λ = 5 logₑ2 min ≈ 3.47 min. 5/logₑ2 inverts the relation. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.