Question

Activities of three radioactive substances $A$. $B$ and $C$ are represented by the curves $A , B$ and C, in the figure. Then their half-lives $T_{\frac{1}{2}}(A): T_{\frac{1}{2}}(B): T_{\frac{1}{2}}(C)$ are in the ratio :

• A. $3: 2: 1$
• B. $4: 3: 1$
• C. $2: 1: 3$
• D. $2: 1: 1$

Answer 1

Answer: (C)

$R = R _{0} e ^{-\lambda t }$
$\ln\, R =\ln R _{0}-\lambda t$
$\lambda_{ A }=\frac{6}{10}
\Rightarrow T _{ A }=\frac{10}{6} \ln \,2$
$\lambda_{ B }=\frac{6}{5}$
$\Rightarrow T _{ B }=\frac{5 \ln 2}{6}$
$\lambda_{ C }=\frac{2}{5} $
$\Rightarrow T _{ C }=\frac{5 \,l n \,2}{2}$
$\frac{10}{6}: \frac{5}{6}: \frac{15}{6}:: 2: 1: 3$