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.