Chapter 6, Problem 12CI

Of much concern to environmentalists is radon-222, which is a radioactive noble gas that can seep from the ground into basements of homes and buildings. Radon-222 is a product of the decay of radiurn-226 that occurs naturally in rocks and soil in much of the United States. Radon-222, which has a half-life of 3.8 days, decays by emitting an alpha particle. Radon-222, which is a gas, can be inhaled into the lungs where it is strongly associated with lung cancer. Radon levels in a home can be measured with a home radon-detection kit. Environmental agencies have set the maximum level of radon-222 in a home at 4 picocuries per liter (pCi/L) of air. (5.2, 5.3, 5.4)

a. Write the balanced nuclear equation for the decay of Ra-226.
b. Write the balanced nuclear equation for the decay of Rn-222.
C. If a room contains 24 000 atoms of radon-222, how many atoms of radon- 222 remain after 15.2 days?
d. Suppose a room has a volume of 72 000 L ( $7.2\times {10}^4$ L). It the radon level is the maximum allowed (4 pCi/L) how many alpha particles are emitted from Rn-222 in 1 day? ( $\text{1 Ci = 3}.7\times {10}^{10}$ disintegrations/s)