The half-life of radon-222 is 3.824 days. after what time will one-fourth of a given amount of radon-222 remain?

Explanation:

Half-life is the time for a sample reduce its amount to the half.

The radioactie isotopes, such as radon-222, have constant half-life times.

The amount that remains after a number, n, of half-lives may be calcualted by the following exponential decay equation:

From which you get:

Here, you want A/A₀ = 1/4

So, you just must to solve for n:

Then, two half-lives will have passed, which equals to 2×3.824 days = 7.648 days.