Q. A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate becomes 1250 disintegration per minute. Then ,its decay constant (per minute) is
A) $0.8\log_{e}2$
B) $0.4\log_{e}2$
C) $0.2\log_{e}2$
D) $0.1\log_{e}2$
Explanation
(b) Given, $R = 1250,\ R_{0} = \ 5000\ and\ t = 5\ min$
$R = R_{0}e^{- \lambda t}$
$1250\ = \ 5000\ e^{- \lambda\ \times \ 5}$
$\lambda = 0.4\ \log_{e}2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.