Uranium and radium are found in many rocky soils throughout the world. Both undergo radioactive decay, and one of the products is radon-222, the heaviest noble gas (t1/2 = 3.82 days). Inhalation of this gas contributes to many cases of lung cancer. According to U.S. EPA recommendations, the level of activity in homes should not exceed 4.0 pCi/L of air.
a. What is the safe level of radon-222 in Bq/L of air? (1 Bq = 1 disintegration / 1 s, or 1 dps)
b. A home has a radon-222 measurement of 41.5 pCi/L. The owner vents the basement in such a way that no more radon enters the living area. What is the activity of the radon in the room air (in Bq/L) after 9.5 days?
c. How many more days does it take to reach the EPA recommended level?
a. What is the safe level of radon-222 in Bq/L of air? (1 Bq = 1 disintegration / 1 s, or 1 dps)
b. A home has a radon-222 measurement of 41.5 pCi/L. The owner vents the basement in such a way that no more radon enters the living area. What is the activity of the radon in the room air (in Bq/L) after 9.5 days?
c. How many more days does it take to reach the EPA recommended level?
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a) 1pCi =0.037Bq and 4pCi =0.148Bq
so 4.0pCi/l = 0.148Bq/L
b) formula A=A(0) * 2^(-t/(t1/2))
A= 41.5*(2^(-9.5/3.82))= 41.5*2^-(2.487)=41.5*0.1784=7.402Bq/L
c) to have the level A must be equal to 4
A/A(0) =4/41.5=0.09639=2^(-t/3.82)
you find t/3.82= log base 2 of 41.5/4 =3.75
and t =3.75*3.82=12.9 days
so 4.0pCi/l = 0.148Bq/L
b) formula A=A(0) * 2^(-t/(t1/2))
A= 41.5*(2^(-9.5/3.82))= 41.5*2^-(2.487)=41.5*0.1784=7.402Bq/L
c) to have the level A must be equal to 4
A/A(0) =4/41.5=0.09639=2^(-t/3.82)
you find t/3.82= log base 2 of 41.5/4 =3.75
and t =3.75*3.82=12.9 days