Chemistry

This problem combines radioactive decay kinetics with stoichiometry—you need to find how many nuclei decay in a given time, then convert that to the mass of helium produced. The key insight is that each alpha particle ($\alpha$) is a helium-4 nucleus, so every decaying atom of $A$ contributes one He atom. Use the decay formula $N(t) = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}$ to find how many atoms have decayed after 20 days, then relate that number to moles of He using Avogadro's number and molar mass.

This problem combines radioactive decay kinetics with stoichiometry—you need to find how many nuclei decay in a given time, then convert that to the mass of helium produced. The key insight is that each alpha particle ($\alpha$) is a helium-4 nucleus, so every decaying atom of $A$ contributes one He atom. Use the decay formula $N(t) = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}$ to find how many atoms have decayed after 20 days, then relate that number to moles of He using Avogadro's number and molar mass.