Q. Half life of a radioactive element is 10 days. The time during which quantity remains 1/10 of initial mass will be
A) 100 days
B) 50 days
C) 33 days
D) 16 days
Explanation
(c) $N = N_{0}\ e^{- \lambda t} \Rightarrow \ln{\frac{N_{0}}{N} = \lambda t}$
$t = \frac{1}{\lambda}\ln{\frac{N_{0}}{N} \Rightarrow t = \frac{2.303 \times T_{1/2}}{0.693}}\log_{10}\frac{N_{0}}{N}$
$\frac{N_{0}}{N} = 10,T_{1/2} = 10\ day \Rightarrow t = 33.23\ days$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.