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.