The air in some caves contains radon gas, 222Rn which can lead to lung cancer fr

Question

The air in some caves contains radon gas, 222Rn which can lead to lung cancer from a prolonged exposure. In some Irish caves, the air in the cave has an activity per volume of 1.55 × 105 Bq/m3. Suppose that you spend two full days in that cave. Approximately how many 222Rn atoms would enter into and out of your lungs during your two-day stay? Take the half-life of 222Rn to be 3.82 days. You will need to estimate your lung capacity and average breathing rate.

Please explain this as soon as possible, my exam is tomorrow. thank you.

Explanation / Answer

Solution:

Rate constant (k) is

ln [R]t = -(0.18 d-1 ) (2d)

k=0.693 = 0.18 d-1

t ½ = 3.82 d

ln [R]t = -kT

ln [R]t { -(0.18 d-1 ) (2d)}= ln(-0.36)

activity per volume of 1.55 × 105 Bq/m3

1.55 × 105 Bq/m3 ( - 0.36)= -1.02165

1.02165/(1.55 * 10^5 atoms/m^3) = 6.5913 * 10^-6 atoms/litre

Estimated lung capacity of adults is 6litres and tidal volume is 500ml per inspiration

Estimated average breathing rate is 14 inspirations per minute

Volume of air breathed in

If 500 ml = 1 inspiration, 14 inspirations = (14 inspirations * 500 ml) = 7000ml

If 1 hr = 60 minutes, then 2 days = (48 hrs * 60hrs) = 48 hours = 2880minutes

If 7000ml = 1 minute, 2880 minutes = 20160000ml=20160 litres

If 6.5913 * 10^-6 atoms = 1 litre, then 20160 litres = 0.132880608 atoms

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