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)

$R=R_0{e}^{-\lambda t}$
$\ln R=\ln R_0-\lambda t$
${\lambda }_A=\frac{6}{10}<br/><br/>\Rightarrow T_A=\frac{10}{6}\ln 2$
${\lambda }_B=\frac{6}{5}$
$\Rightarrow T_B=\frac{5\ln 2}{6}$
${\lambda }_C=\frac{2}{5}$
$\Rightarrow T_C=\frac{5ln2}{2}$
$\frac{10}{6}:\frac{5}{6}:\frac{15}{6}::2:1:3$