U $$92238$$ is known to undergo radioactive decay to form Pb $$82206$$ by emitting alpha and beta particles. A rock initially contained $$68$$ × $$10$$–$$6g$$ of Pb $$92238$$. If the number of alpha particles that it would emit during its radioactive decay of U $$92238$$ to Pb $$82206$$ in three $$half-lives$$ is Z × $$1018$$, then what is the value of Z ?

Question

U $$92238$$ is known to undergo radioactive decay to form Pb $$82206$$ by emitting alpha and beta particles. A rock initially contained          $$68$$ × $$10$$–$$6g$$ of Pb $$92238$$. If the number of alpha particles that it would emit during its radioactive decay of U $$92238$$ to Pb $$82206$$ in three $$half-lives$$ is Z × $$1018$$, then what is the value of Z ?

Infinity Learn · Accepted Answer

Initial moles of $$U238=68$$×$$10$$−$$6238=x$$ Moles of $$U238$$ decayed in three $$half-lives$$ $$=78xIn$$ decay from $$U238$$ to $$Pb206$$ , each $$U238$$ atom decays and produces $$8$$ α$$-particles$$ and hence, total number of α$$-particles$$ emitted $$out=78x$$×$$8$$×$$NA=7$$×$$68$$×$$10$$−$$6238$$×$$6.022$$×$$1023=1.204$$×$$1018$$

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