Indoor air pollution. Uranium is naturally present in rock and soil. At one step
ID: 1391087 • Letter: I
Question
Indoor air pollution. Uranium is naturally present in rock and soil. At one step in its series of radioactive decays, 238U produces the chemically inert gas radon-222, with a half-life of 3.82 days. The radon seeps out of the ground to mix into the atmosphere, typically making open air radioactive with activity 0.3 pCi/L. In homes, 222Rn can be a serious pollutant, accumulating to reach much higher activities in enclosed spaces. If the radon activity exceeds 4 pCi/L, the Environmental Protection Agency suggests taking action to reduce it, such as by reducing infiltration of air from the ground.
(a) Suppose that the activity is actually 5.7 pCi/L. Convert this to units of becquerel per cubic meter.
210 Bq/m3 was correct
(b) How many 222Rn atoms are in one cubic meter of air displaying this activity?
10^8 was correct
(c) What fraction of the mass of the air does the radon constitute?
4*10^-18 was incorrect
Explanation / Answer
Here ,
a)
1 Curie = 3.7 *10^10 Bq
Now , 5.7 pCI/l = 5.7 *10^-12 * 3.7 *10^10 * 10^3
= 210 Bq/m^3
b)
Here , as N*ln(2)/half life = 210
N * ln(2)/(3.83 * 24 * 3600) = 210
N = 1.007 *10^8
c)
Now, as the denity of air = 1.19 Kg/m^2
fraction of mass of Rn = 0.222 * 1.007 *10^8 /(1.19 * 6.022 *10^23)
fraction of mass of Rn = 3.12 *10^-17