Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Question

# Scientists think that Earth once had naturally existing plutonium-$239$. Suppose Earth had $10$ trillion tons of $\mathrm{Pu}-239$ when it formed. Given plutonium's half-life of $24,000$ years and Earth's current age of $4.6$ billion years, how much would remain today? Use your answer to explain why plutonium is not found naturally on Earth today.

Solution

Verified
Step 1
1 of 2

The amount of plutonium after a certain time can be calculated using the expression

\begin{align*} \text{new value}&=\text{initial value}\cdot\left(\dfrac12\right)^{\frac{t}{T_\text{half}}}\\ &=10\cdot10^{12}\cdot\left(\dfrac12\right)^{\frac{4.6\cdot10^9}{24,000}}\\ &=3.8385\cdot10^{-57,685}\ \text{tons} \end{align*}

## Recommended textbook solutions 1st EditionISBN: 9780078747687McGraw-Hill Education
1,401 solutions #### Using and Understanding Mathematics: A Quantitative Reasoning Approach

7th EditionISBN: 9780134705187 (3 more)Jeffrey O. Bennett, William L. Briggs
3,437 solutions #### Financial Algebra

1st EditionISBN: 9780538449670Richard Sgroi, Robert Gerver
2,606 solutions #### Financial Algebra: Advanced Algebra with Financial Applications

2nd EditionISBN: 9781337271790Richard Sgroi, Robert Gerver
3,016 solutions