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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