Answer:
[tex]0.28 \mu g[/tex]
Explanation:
We can write the amount of mass of radon-222 left after a time t by using the equation:
[tex]m(t) = m_0 (\frac{1}{2})^{t/t_{1/2}}[/tex]
where
[tex]m_0 = 4.38 \mu g[/tex] is the initial mass
t is the time
[tex]t_{1/2} = 3.82 d[/tex] is the half-life
Substituting t = 15.2 d in the formula, we find
[tex]m(15.2 d) = (4.38 \mu g) (\frac{1}{2})^{15.2d/3.82 d}=0.28 \mu g[/tex]
