Chapter 24, Problem 82A

Interpretation Introduction

Interpretation:

The nuclear waste generated today that will remain in 1000 years needs to be determined.

Concept introduction:

Half-life: Itis thetime required for one-half of a radioisotope’s nuclei to decay into its products.

Answer to Problem 82A

97.2% of nuclear waste generated today will remain in 1000 years.

Explanation of Solution

Given information, half-life ( ${\text{t}}_{\frac{\text{1}}{\text{2}}}$ ) of plutonium-239 is 24000 years.

T is 1000 years.

First,

$\begin{array}{c}\text{n=}\frac{\text{t}}{{\text{t}}_{\frac{\text{1}}{\text{2}}}}\text{where, n is the number of half-lives occurred over the period of time}\text{.}\\ \text{n}=\frac{1000}{24000}\\ \text{n}=0.04167\end{array}$

Relation between initial amount, remaining amount is

$\begin{array}{c}\frac{\text{N}}{{\text{N}}_{\text{0}}}={\left(\frac{1}{2}\right)}^n\\ \frac{\text{N}}{{\text{N}}_{\text{0}}}={\left(\frac{1}{2}\right)}^{0.04167}\\ \frac{\text{N}}{{\text{N}}_{\text{0}}}=0.9715\\ \frac{\text{N}}{{\text{N}}_{\text{0}}}=97.2\%\end{array}$

Conclusion

Use the relation between initial amount, final amount and time passed.