Nuclear Chemistry and RadioactivityhardMCQ SINGLE⭐ Must-Do

One mole of a radioactive nuclide A is placed in a closed vessel and undergoes decay via the reactioNuclear Chemistry and Radioactivity Chemistry Question

Question

One mole of a radioactive nuclide A is placed in a closed vessel and undergoes decay via the reaction: ${}_{Z}^{A}A \rightarrow {}_{Z-4}^{A-8}B + 2{}_{2}^{4}He$. If the half-life of A is $10\text{ days}$, what total volume of Helium gas (in Litres) is collected at NTP after exactly $20\text{ days}$? (Assume ideal behavior, $1\text{ mol gas at NTP} = 22.4\text{ L}$).

Answer: C

💡 Solution & Explanation

20 days = 2 half-lives. Fraction of A remaining = $(1/2)^2 = 1/4$. Fraction decayed = $3/4 = 0.75\text{ moles}$. Reaction stoichiometry shows $1\text{ mol A}$ yields $2\text{ mol He}$. Total He produced = $0.75 \times 2 = 1.5\text{ moles}$. Volume = $1.5 \times 22.4 = 33.6\text{ L}$.

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