Question

Plutonium-$\mathbf{\text{239}}$ $\mathbf{\left(}{\mathbf{\text{t}}}_{\mathbf{\text{1/2}}}{\mathbf{\text{=2.41×10}}}^{\mathbf{\text{4}}}\mathbf{\text{yr}}\mathbf{\right)}$represents a serious nuclear waste hazard. If seven half-lives are required to reach a tolerable level of radioactivity, how long must ${}^{\mathbf{\text{239}}}\mathbf{\text{Pu}}$be stored?

Short answer

The amount of time that plutonium-$239$ needs to be stored is_{${\text{1.687×10}}^{\text{5}}\text{years}$}

Step-by-step solution

Half-life

The half-life of a radioactive substance indicates the time taken by it to reach the half of its amount. The radioactive decay follows the first order kinetics.

Calculation

- Half-life of plutonium-$239$ is${\text{t}}_{\text{1/2}}{\text{=2.41×10}}^{\text{4}}\text{yr}$

- In order to reach a tolerable level of radioactivity, 7 half-lives are required.

Therefore, the amount of time that plutonium- needs to be stored is

_{$\begin{array}{c}{\text{Time=t}}_{\text{1/2}}\text{×7}\\ {\text{=2.41×10}}^{\text{4}}\text{yr×7}\\ {\text{=1.687×10}}^{\text{5}}\text{yr}\end{array}$}

Hence, the amount of time that plutonium$239$- needs to be stored is${\text{1.687×10}}^{\text{5}}\text{years}$