the half-life of polonium-218 is 3.0 minutes. what percentage of the original sample remains after 4 half-lives?
amount left= (1/2)^4=1/2^4=1/4^2=1/16
The half-life of polonium-218 is 3.0 min. If you start with 16 mg of
polonium-218, how much time must pass for only 1.0 mg to remain?
nohonob
To determine the percentage of the original sample that remains after 4 half-lives, we can use the formula:
Percentage remaining = (100% / 2^n)
where n is the number of half-lives.
In this case, we are given that the half-life of polonium-218 is 3.0 minutes.
To find the number of half-lives in 4 minutes, we divide the total time by the half-life:
Number of half-lives = (Total time) / (Half-life) = (4 minutes) / (3.0 minutes) = 1.33
As we cannot have a fraction of a half-life, we round down to the nearest whole number, which is 1.
Now we substitute this value into the formula:
Percentage remaining = (100% / 2^1) = (100% / 2) = 50%
Therefore, after 4 half-lives, 50% of the original sample remains.