Question 214: Atoms & Nuclei

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
${T_{{1 \over 2}}}\left( A \right)$ : ${T_{{1 \over 2}}}\left( B \right)$ : ${T_{{1 \over 2}}}\left( C \right)$ are in the ratio :
![](https://imagex.cdn.examgoal.net/jgy2xukff41t1q/b0d33f7f-0d8c-4d88-8962-596953c0530c/ab81b6e0-fd74-11ea-8293-3b6cc591631c/file-jgy2xukff41t1r-486w.png)

Accepted Answer

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

Answer

3 : 2 : 1

Answer

2 : 1 : 1

Answer

4 : 3 : 1

Answer

2 : 1 : 3

Atoms & Nuclei

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_{{1 \over 2}}}\left( A \right) : {T_{{1 \over 2}}}\left( B \right) : {T_{{1 \over 2}}}\left( C \right) are in the ratio :

Choose the correct answer: