Q. If $T$ is the half life of a radioactive material, then the fraction that would remain after a time $\frac{T}{2}$ is
A) $\frac{1}{2}$
B) $\frac{3}{4}$
C) $\frac{1}{\sqrt{2}}$
D) $\frac{\sqrt{2} - 1}{\sqrt{2}}$
Explanation
(c) Fraction remains after $n$ half lives $\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n} = \left( \frac{1}{2} \right)^{t/T}$
$\therefore\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{\frac{T/2}{T}} = \left( \frac{1}{2} \right)^{1/2} = \frac{1}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.