# Problem: 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?

###### FREE Expert Solution

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:

$\overline{){{\mathbf{t}}}_{\mathbf{1}}{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{2}}{\mathbf{k}}}$

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###### Problem Details

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?