What percentage of the atoms in a sample of plutonium-238 will remain radioactive after 263.1 years

We use the exponential decay formula to solve for the percentage of atoms in a sample of Plutonium-238 will remain radioactive after 263.1 years.

We are given with a half-life of 87.7 years and so, we can get the decay constant:

k = ln 2 / 87.7

k = 0.0079

A/A0 = exp (-kt)

A/A0 = exp (-0.0079 (263.1))

A/A0 = 0.125

or

12.5%