After two half-lives, what fraction of the initial activity of a radioisotope remains?

After two half-lives of a radioisotope, the fraction of the initial activity that remains can be determined by understanding what a half-life represents. A half-life is the time it takes for half of the radioactive substance to decay. Therefore, after one half-life, 50% of the original activity remains.

When you reach the second half-life, you take this remaining amount (50%) and again reduce it by half. This results in 25% of the original activity still being present. In fractional terms, this is expressed as 1/4 of the initial activity.

The process can be illustrated as follows:

• Initially, you start with a fraction of 1 (100%).

• After the first half-life, the fraction remaining is 1/2.

• After the second half-life, the remaining fraction from the first half-life (1/2) is halved again, leading to 1/4.

This clearly shows that after two half-lives, 1/4 of the initial activity remains. Thus, the correct fraction of the initial activity of a radioisotope that remains after two half-lives is accurately represented by option A.