Question

A certain radioisotope ${}^A{Q}_{Z}X$($T_{50}=$ 10 days) decays to give ${}_{Z-2}^{A-4}Y$. If one g atom od ${}_Z^{A}X$ is kept in a sealed vessel, how much He will accumulate in 20 days at STP?

• A. 16.8L
• B. 16.4L
• C. 18.8L
• D. None of these

Answer 1

Answer: (A)

16.8L

${}_z^{A}X{⟶}_{Z-3}^{A-4}Y{+}_2^{4}He$
$t_{50}=10$ days.
$\therefore y=\frac{t}{t_{50}}=\frac{20}{10}=2$
$X$ left after 20 days
$C=C_0{\left(\frac{1}{2}\right)}^y=\frac{1}{4}g$ atom
$\therefore$ Helium formed = amount of $X$ decomposed
$=1-\frac{1}{4}=\frac{3}{4}mol$
$\therefore$ Volume at STP $=\frac{3}{4}\times 22.4L$
$=16.8$ L.