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

Dec 21, 2016

The answer is $= 0.278 \mu g$

#### Explanation:

We use the following equations

$N \left(t\right) = {N}_{0} {e}^{- \lambda t}$

and $\lambda = \frac{\ln 2}{t} _ \left(\frac{1}{2}\right)$

The half life is ${t}_{\frac{1}{2}} = 3.82$

${N}_{0} = 4.38 \mu g$

$\lambda = \frac{\ln 2}{3.82} = 0.1815 {d}^{- 1}$

$N \left(15.2 d\right) = 4.38 \cdot {e}^{- 0.1815 \cdot 15.2}$

$= 0.278 \mu g$