Q. Two radioactive substances A and B have decay constants 5λ and λ respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e)² after a time interval
A) 4λ
B) 2λ
C) 1/(2λ)
D) 1/(4λ)
Explanation
[Solution from source] N_A/N_B = e^(−5λt)/e^(−λt) = e^(−4λt). Setting this equal to e^(−2) gives 4λt = 2, so t = 1/(2λ). Answers like 2λ have the wrong dimensions for a time. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.