Question

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be

• A. $1:16$
• B. $4:1$
• C. $1:4$
• D. $5:4$

Answer 1

The correct option is D $5:4$

$n=n_o{e}^{-\alpha t}$
${\alpha }_A=ln2/20$
${\alpha }_B=ln2/40$
After 80 min, remaining number of nuclei for A, $n_A=n_o/16$
After 80 min, remaining number of nuclei for B, $n_B=n_o/4$
Decayed number of nuclei for A, $\Delta n_A=\frac{15}{16}{n}_o$
Decayed number of nuclei for B, $\Delta n_B=\frac{3}{4}{n}_o$
Ratio of decayed number of nuclei is
$\frac{\Delta n_A}{\Delta n_B}=\frac{15/16}{3/4}=5:4$