Half lives of two radioactive substances A and B are respectively 20 minutes and 40 minutes. Initially the sample of A and B have equal number of nuclei. After 80 minutes, the ratio of remaining number of A and B nuclei is

(a) 1 : 16                   (b) 4 : 1
(c) 1 : 4                     (d) 1 : 1

(c) For 80 minutes, number of half lives of sample $\mathrm{A}={\mathrm{n}}_{\mathrm{A}}=\frac{80}{20}=4$ and number of half lives of sample $\mathrm{B}={\mathrm{n}}_{\mathrm{B}}=\frac{80}{40}=2$ Also by using $\mathrm{N}={\mathrm{N}}_{0}{\left(\frac{1}{2}\right)}^{\mathrm{n}}$
$⇒\mathrm{N}\propto \frac{1}{{2}^{\mathrm{n}}}⇒\frac{{\mathrm{N}}_{\mathrm{A}}}{{\mathrm{N}}_{\mathrm{B}}}=\frac{{2}^{{\mathrm{n}}_{\mathrm{B}}}}{{2}^{{\mathrm{n}}_{\mathrm{A}}}}=\frac{{2}^{2}}{{2}^{4}}=\frac{1}{4}$

Difficulty Level:

• 24%
• 15%
• 58%
• 5%