Q. After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half life of the isotope is
A) $15\ minutes$
B) $30\ minutes$
C) $45\ minutes$
D) $1\ hour$
Explanation
(b) $\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{t/T} \Rightarrow \left( \frac{1}{16} \right) = \left( \frac{1}{2} \right)^{2/T} \Rightarrow \left( \frac{1}{2} \right)^{4} = \left( \frac{1}{2} \right)^{2/T}$
$\Rightarrow T = 0.5\ hour = 30\ minutes$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.