Question

The activity of a radioactive material is $2.56\times {10}^{-3}Ci$. If the half life of the material is $5$ days, after how many days the activity will become $2\times {10}^{-5}Ci$ ?

• A. $40$ days
• B. $30$ days
• C. $35$ days
• D. $25$ days

Answer 1

The correct option is C $35$ days

$A=A_0{e}^{-\lambda t}$

$\Rightarrow 2\times {10}^{-5}=2.56\times {10}^{-3}{e}^{-\lambda t}$

$\Rightarrow e^{-\lambda t}=\frac{1}{128}={\left[\frac{1}{2}\right]}^7$

$\Rightarrow t=7t_{\frac{1}{2}}=35\text{days}$