Q. A radioactive sample has $4 \times 10^{10}$ nuclei at a certain time. The number of active nuclei still remaining after 4 half lives is

A) $1 \times 10^{10}$
B) $5 \times 10^{9}$
C) $25 \times 10^{8}$
D) $5 \times 10^{8}$
Explanation

(c) Here, $N_{0} = 4 \times 10^{10}$
Number of half lives, $n = 4,$ As $\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n}$
$\therefore N = N_{0}\left( \frac{1}{2} \right)^{4} = \frac{N_{0}}{16} = \frac{4 \times 10^{10}}{16}$
$= 0.25 \times 10^{10} = 25 \times 10^{8}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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