Q. A radioactive substance has a half-life of $1\ year$. The fraction of this material, that would remain after $5\ years$ will be
A) $\frac{1}{32}$
B) $\frac{1}{5}$
C) $\frac{1}{2}$
D) $\frac{4}{5}$
Explanation
(a) Number of half lives $n = \frac{5}{1} = 5$
Now $\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n} \Rightarrow \frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{5} = \frac{1}{32}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.