How Does Radon-222 Impact Indoor Air Quality?

[figureskater]

Radioactivity of Radon 222!

Homework Statement

Uranium is naturally present in rock and soil. At one step in its series of radioactive decays, Uranium 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, Rn-222 can be a serious pollutant, accumulating to reach much higher activities in enclosed spaces, sometimes reaching 4.00 pCi/L. If the radon radioactivity exceeds 4.00 pCi/L, the U.S. Environmental Protection Agency suggests taking action to reduce it such as by reducing infiltration of air from the ground.
(a) Convert the activity 4.00 pCi/L to units of becquerels per cubic meter.
148 Bq/m3

(b) How many Rn-222 atoms are in 1 m3 of air displaying this activity?
7.05e7 atoms/m3

(c) What fraction of the mass of the air does the radon constitute?

Homework Equations

The Attempt at a Solution

volume fraction= #of atoms/ # of air molecules
# of air molecules = density of air x volume / average molecular weight of air, this answer then multiplied by avogadro's number (6.0221415e23)

=(0.00122521)(1m^3)/28.96 g/mol *6.0221415e23
=2.55e25

=7.05e7/2.55e25
=2.76e-18

To which I got a comment that my response was within 10% of the correct answer. Not sure if I missed something or did not convert units somewhere..

Please help! its due TONIGHT by midnight thanks!

 

[da_nang]

First off, try putting the entire calculation into one equation. Standard procedure should always be to solve the problem symbolically with calculations in the end unless the problem is long/tedious enough to justify calculations in the middle of the solving process. But in that case you should save the value so you don't lose data that could make an answer round down instead of up. In other words, don't use rounded numbers in your calculations.

Secondly, you might also be using the wrong density for air. As its density is temperature and pressure dependent, perhaps using the air density in STP conditions would give the correct answer.

Using the STP density for air with the other value from B I got an answer within 10% of yours.