a radioactive sample has a half-life of 4.0 min. what fraction of the simple is lefts after 20min?
20 min = 5 half-lives
so, you will have (1/2)^5 = 1/32 of the original amount
To determine the fraction of the sample that remains after a certain time, we need to use the concept of half-life.
The half-life of a radioactive substance is the time it takes for half of the sample to decay. In this case, the half-life is 4.0 minutes, which means that after 4.0 minutes, only half of the sample will remain.
To find the fraction of the sample that remains after a given time, we can divide the elapsed time by the half-life:
Fraction remaining = (Elapsed time) / (Half-life)
In this case, the elapsed time is 20 minutes and the half-life is 4.0 minutes. Plugging these values into the formula, we get:
Fraction remaining = 20 min / 4.0 min
Simplifying this expression gives:
Fraction remaining = 5
Therefore, after 20 minutes, there is 1/5 or 0.2 (20%) of the initial radioactive sample remaining.