Question

A certain radio-isotope ${}_{Z}^{A}X$ (Half life = 10 days) decays to ${}_{Z - 2}^{A - 4}Y$. If 1 g of atoms of ${}_{Z}^{A}X$ is kept in sealed vessel, how much helium will accumulate in 20 days

• A. 16800 Ml
• B. 17800 mL
• C. 18800 mL
• D. 15800 mL

Answer 1

Answer: (A)

16800 Ml

Answer 2

${}_{Z}^{A}X \rightarrow_{Z - 2}^{A - 4}Y +_{2}^{4}He$

In two half lives, $\frac{3}{4}$ of the isotope ${}_{Z}^{A}X$ has disintegrated, i.e., $\frac{3}{4}$g atom of helium has been formed from $\frac{3}{4}$g atom of ${}_{Z}^{A}X$

Volume of 1 g atom of helium = 22400 Ml

Thus, Volume of $\frac{3}{4}$g atom of helium

$= \frac{3}{4} \times 22400mL = 16800mL$