You inhale about 0.5 liter of air in each breath and breath once in every five seconds. Air has about 1% argon. Mass of each air particle can be assumed to be nearly `5 xx 10^(-26) kg`. Atmosphere can be assumed to be around 20 km thick having a uniform density of `1.2 kg m^(-3)`. Radius of the earth is `R = 6.4 xx 10^(6) m`. Assume that when a person breathes, half of the argon atoms in each breath have never been in that person’s lungs before. Argon atoms remain in atmosphere for long-long time without reacting with any other substance. Given : one year `= 3.2 xx 10^(7)s`
(a) Estimate the number of argon atoms that passed through Newton’s lungs in his 84 years of life.
(b) Estimate the total number of argon atoms in the Earth’s atmosphere.
(c) Assume that the argon atoms breathed by Newton is now mixed uniformly through the atmosphere, estimate the number of argon atoms in each of your breath that were once in Newton’s lungs.

Answer

(a) `3.2 xx 10^(28)`
(b) `2.5 xx 10^(42)`
(c) `1.5 xx 10^(6)`