Question

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

Answer 1

• 7.648 days.

Step-by-step 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:

`A=A_0[(1)/(2)]^n`

From which you get:

`(A)/(A_0)=[(1)/(2)]^n`

Here, you want A/A₀ = 1/4

So, you just must to solve for n:

`(1)/(4)=[(1)/(2)]^n\\ \\ (1)/(2^2)=(1)/(2^n)\\ \\ n=2`

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