# Plutonium has a half-life of 23105 years. What percentage of a sample of Plutonium has decayed after 10000 years?

Lewis Harvey 2021-05-03 Answered
Plutonium has a half-life of 23105 years. What percentage of a sample of Plutonium has decayed after 10000 years?

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## Expert Answer

Theodore Schwartz
Answered 2021-05-04 Author has 16465 answers

Plutonium has a half-life of 23,105 years. What percentage of a sample of Plutonium has decayed after 10,000 years?
Use the half-life formula:
$$\displaystyle{N}={N}{0}\frac{{\left(\frac{{1}}{{2}}\right)}^{{t}}}{{t}}{h}{a}{l}{f}-{l}{\quad\text{if}\quad}{e}$$
Substitute t=10,000 years and thalf-life $$=23,105t$$:
$$N=N0(1/2)^{10000/23105}$$
$$N \sim 0.74N0$$
This means that 74% of the sample remained. Hence, 26% of the sample of Plutonium decayed.

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