Q. Two radioactive materials X₁ and X₂ have decay constants 5λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will be 1/e after a time
A) e/λ
B) λ
C) (1/2)λ
D) 1/(4λ)
Explanation
[Solution from source] N₁/N₂ = e^(−5λt)/e^(−λt) = e^(−4λt). Setting this to 1/e gives 4λt = 1, so t = 1/(4λ). λ and λ/2 cannot be times, since λ has units of inverse time. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.