Q24.46 P - Chemistry: Molecular Nature Of Matter And Change

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?

Step-by-Step Solution

Answer

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

Step 1: 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.

 

Step 2: 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 ${\text{1.687×10}}^{\text{5}}\text{years}$