The uranium isotope ²³⁸U is naturally present at low levels in many soils. One of the nuclei in the decay series of ²³⁸U is the radon isotope ²²²Rn, which decays by emitting a 5.50 MeV alpha particle with t_1/2 = 3.82 days. Radon is a gas, and it tends to seep from soil into basements. The Environmental Protection Agency recommends that homeowners take steps to remove radon, by pumping in fresh air, if the radon activity exceeds 4 pCi per liter of air.

a. How many ²²²Rn atoms are there in 1 m³ of air if the activity is 4 pCi/L?

b. The range of alpha particles in air is ≈3 cm. Suppose we model a person as a 180-cm-tall, 25-cm-diameter cylinder with a mass of 65 kg. Only decays within 3 cm of the cylinder can cause exposure, and only ≈50% of the decays direct the alpha particle toward the person. Determine the dose in mSv per year for a person who spends the entire year in a room where the activity is 4 pCi/L.

c. Does the EPA recommendation seem appropriate? Why?