The half-life of plutonium-238 is 87.7 years. What percentage of the atoms in a sample of plutonium-238 will remain radioactive after 263.1 years? % What percentage of the atoms in the same sample of plutonium-238 will have changed to another isotope after 263.1 years?

The answer is 12.5 and then 87.5

(263.1 years) x (half-life / 87.7 years) = 3 half-lifes

In 3 half-lifes, (1/2 x 1/2 x 1/2) = 1/8 of the atoms in a sample remain unchanged.

That's 12.5% that remain unchanged.

The other 87.5% of the atoms in the sample have decayed, and changed to either other isotopes of plutonium or into atoms of other elements.