Question

The half-life of radon-222 is 3.82 days. If a sample of gas contains 4.38 μg of radon-222, how much will remain in the ample after 15.2 days?

Answer 1

`0.28 \mu g`

Step-by-step explanation:

We can write the amount of mass of radon-222 left after a time t by using the equation:

`m(t) = m_0 ((1)/(2))^{t/t_(1/2)}`

where

`m_0 = 4.38 \mu g` is the initial mass

t is the time

`t_(1/2) = 3.82 d` is the half-life

Substituting t = 15.2 d in the formula, we find

`m(15.2 d) = (4.38 \mu g) ((1)/(2))^(15.2d/3.82 d)=0.28 \mu g`