Q. Which one of the following statement is true, if half-life of a radioactive substance is 1 month?
A) 7/8th part of the substance will disintegrate in 3 months
B) 1/8th part of the substance will remain undecayed at the end of 4 months.
C) The substance will disintegrate completely in 4 months.
D) 1.16th part of the substance will remain undecayed at the end of 3 months
Explanation
(a) $\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n}or\ \ \frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{t/t_{1/2}}or\ \ \frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{t/1}$
For $t = 3$ months
$\ \ \ \ \ \ \ \ \ \frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{3} = \frac{1}{8}$
Therefore , disintegrated part of substance in 3 months
$= \ 1 - \frac{1}{8} = \frac{7}{8}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.