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

Answer:

$0.28 \mu g$

Explanation:

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

$m(t) = m_0 (\frac{1}{2})^{t/t_{1/2}}$

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

$m(15.2 d) = (4.38 \mu g) (\frac{1}{2})^{15.2d/3.82 d}=0.28 \mu g$