Given a sample of 8 g of a radioisotope with a half-life of 10 years, how long will it take for approximately 1 g of the isotope to remain?

To determine how long it will take for approximately 1 g of a radioisotope, starting from an initial 8 g, to remain, we begin by applying the concept of half-lives. The half-life of a substance is the time required for half of the radioactive atoms in a sample to decay.

Starting with 8 g of the radioisotope, after one half-life of 10 years, the amount remaining would be half of 8 g, which is 4 g. After a second half-life (20 years total), the sample would further reduce to half of 4 g, leaving 2 g remaining. A third half-life (30 years total) would reduce the sample to half of 2 g, resulting in 1 g remaining.

Thus, it takes three half-lives, or 30 years, for the amount of the radioisotope to decay from 8 g to approximately 1 g. This reasoning helps verify that the answer of 30 years aligns with the decay process described by the concept of half-lives.