Question

At any instant, the ratio of the amounts of two radioactive substances is $2:1$. If their half-lives be, respectively, $12h$ and $16h$, then after two days, what will be the ratio of the substances?

• A. $1:1$
• B. $2:1$
• C. $1:2$
• D. $1:4$

Answer 1

Answer: (A)

$1:1$

$N1=N{1}_o{e}^{-{\lambda }_{1}t}$
$N2=N{2}_o{e}^{-{\lambda }_{2}t}$
$\frac{N1}{N2}=2e^{-({\lambda }_1-{\lambda }_2)t}$
$t_{1/2}=\frac{ln2}{\lambda }$
$\frac{N1}{N2}=2e^{-ln2(1/12-1/16)t}$

After $2$ days $=48$ hours
$\frac{N1}{N2}=2e^{-ln2(1/12-1/16)48}$
$\frac{N1}{N2}=1$