If a radioactive isotope has a half-life of 1 year, how much of the original sample will be left at the end of the 2nd year?

after two half-lives, 1/4 is left

To determine how much of the original sample will be left at the end of the 2nd year, we need to understand the concept of half-life and use the following formula:

Amount remaining = Initial amount × (0.5)^(time elapsed / half-life)

In this case, the half-life of the radioactive isotope is 1 year. So we can substitute the values into the formula:

Amount remaining = Initial amount × (0.5)^(2 / 1)

Simplifying the exponent:

Amount remaining = Initial amount × (0.5)^2

Evaluating the exponent:

Amount remaining = Initial amount × (0.5)^(2)

Squaring the value:

Amount remaining = Initial amount × 0.25

Thus, at the end of the 2nd year, 25% (or 0.25) of the original sample will be left.