Q. The activity of a radioactive sample is measured as 9750 counts $per\ minute$ at $t = 0$ and as 975 counts $per\ minute$ at $t = 5\ minutes$. The decay constant is approximately
A) $0.230\ per\ minute$
B) $0.461\ per\ minute$
C) $0.691\ per\ minute$
D) $0.922\ per\ minute$
Explanation
(b) $A = A_{0}e^{- \lambda t} \Rightarrow 975 = 9750\ e^{- \lambda \times 5} \Rightarrow e^{5\lambda} = 10$
$\Rightarrow 5\lambda = \log_{e}{10 = 2.3026\log_{10}{10 = 2.3026}}$
$\Rightarrow \lambda = 0.461$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.