Question

$10.24g$ radioactive substance has half life $3.8days$. After $19$ days, its remaining quantity is:

• A. $0.151g$
• B. $0.32g$
• C. $1.51g$
• D. $0.16g$

Answer 1

Answer: (B)

$0.32g$

$\begin{array}{c}\text{Given - * mass of radioactive substance initially}=10.24g\\ \text{* Half life given}{t}_{1/2}=3.8\\ \text{we want to know the amount of substance left}\\ \text{after 19 days.}\\ \Rightarrow \text{after}5\text{half lives amount of susbstance left is}\end{array}$

$\begin{array}{c}\text{where}19\text{days are equal to}5\text{times of half life.}\left(3.8\text{days}\right)\\ \Rightarrow \text{after}5\text{half lives amount of susbstance left is}\end{array}$

$\begin{array}{cc}{m}_{\text{Left}}& =10.24g\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\text{(five Half lives)}\\ & =\frac{10.24g}{32}=0.32g.\end{array}$