We are asked to determine the time it takes for Plutonium-239 to decay to 1 atom given that the half-life for radioactive decay (a first-order process) of plutonium-239 is 24,000 years.

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Recall that ** half-life** is the time needed for the amount of a reactant to decrease by 50% or one-half. The half-life of a first-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{2}}{\mathbf{k}}}$

The half-life for radioactive decay (a first-order process) of plutonium-239 is 24,000 years.

How many years would it take for one mole of this radioactive material to decay so that just one atom remains?

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