Q. The ratio of half-life times of two elements A and B is $\frac{T_{A}}{T_{B}}$ . The ratio of respectively decay constants $\frac{\lambda_{A}}{\lambda_{B}}$ is
A) $\frac{T_{B}}{T_{A}}$
B) $\frac{T_{A}}{T_{B}}$
C) $\frac{T_{A} + T_{B}}{T_{A}}$
D) $\frac{T_{A} - T_{B}}{T_{A}}$
Explanation
(a) Half-life of a radioactive element
$\ \ \ T = \frac{0.693}{\lambda}or\ \ T \propto \frac{1}{\lambda}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \frac{\lambda_{A}}{\lambda_{B}} = \frac{T_{B}}{T_{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.