Q. The half life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as
A) $\lambda T = 1$
B) $\lambda T = 0.693$
C) $\frac{T}{\lambda} = 0.693$
D) $\frac{\lambda}{T} = 0.693$
Explanation
(b) By using $N = N_{0}e^{- \lambda t} \Rightarrow \frac{N_{0}}{2} = N_{0}e^{- \lambda T_{1/2}} \Rightarrow 2 = e^{\lambda T_{1/2}}$
By using $l{og}_{e}$ both the side
$\log_{e}2 = \lambda T_{1/2} \Rightarrow \lambda T_{1/2} = 0.693$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.