Question

Activity of a radioactive sample decreases to (1/3)rd of its original value in 3 days. Then, in 9 days its activity will become:

• A. $\frac{1}{27}$ of the original value
• B. $\frac{1}{9}$ of the original value
• C. $\frac{1}{18}$ of the original value
• D. $\frac{1}{3}$ of the original value

Answer 1

The correct option is A $\frac{1}{27}$ of the original value

Activity of radioactive sample, $A=A_0{e}^{-\lambda t}$

$A_0$ is the initial activity at time $t=0$.

After 3 days:

$A=\frac{A_0}{3}=A_0{e}^{-3t}\Rightarrow e^{-3t}=\frac{1}{3}$

After 9days:

$A=A_0{e}^{-9t}=A_0{\left(e^{-3t}\right)}^3{e}^{-9t}={\left(\frac{1}{3}\right)}^3=\frac{1}{27}$

Activity, $A=\frac{A_0}{27}$

Hence, option A is correct.