Of much concern to environmentalists is radon-222, which is a radioactive noble gas that c...

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 radium-226 that occurs naturally in rocks and soil in much of the United States. Radon-222, which has a half-life of 3.8 d, decays by alpha decay. Because radon-222 is a gas, it can be inhaled and 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.

a. Write the equation for the decay of Ra-226.

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b. Write the equation for the decay of Rn-222.

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c. If a room contains 24 000 atoms of radon-222, how many atoms of radon-222 remain after 15.2 d?

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d. Suppose a room is 4.0 m wide, 6.0 m long, and 3.0 m high. If the radon level is the maximum allowed (4 pCi/L), how many alpha particles are emitted from Rn-222 in one day? (1 Ci = 3.7 × 1010 disintegrations per second)