Question: If your a scientist answer this: For each breath that you take, how many of the air molecules would also been breathed by the patron saint of Physics, Sir Isaac Newton (1642-1727)during his life time, the atmosphere is about 8 km high, and the molecules in the air each occupy a space representing a little cubic box about 3.33*10^-9 m along a side, the earths radius is 6..38*10^6. make any reasonable assumptions for any data needed.

Chris Needham answered on 19 Mar 2010:

As a first guess, I’d say not very many.

A quick google, sorry for cheating, leads me to http://www.physicsforums.com/archive/index.php/t-12169.html and this answer.

This is a Fermi type of problem, and you must supply reasonable numbers to get a rough answer! Answers are 3 orders of magnitude apart, so you can even afford to be sloppy! If each breath of Sir Isaac’s (and ours) is about 1 litre = 10-3 m3, and they are 3 seconds apart, then in 1727-1642=85 years, he will have had 85 x 365 x 24 x 3600 /3 = 8.93 x 108 breaths, for a total volume of 8.93 x 105 m3. We will assume that the air mixes well enough that we do not have to worry about air being breathed twice.

The total volume of the atmosphere is 4 Re2 h, where Re is the Earth’s radius, and h is the height of the atmosphere, giving 4.08 x 1018 m3. The fraction of air molecules ever breathed by the patron saint of Physics is thus 8.93 x 105 / 4.08 x 1018 = 2.19 x 10-13. The number of molecules in each breath of ours is the density 1/(3.3 x 10-9)3 = 2.78 x 1025 m-3, multiplied by the volume of each breath, 10-3 m3, or 2.78 x 1022 molecules. Multiplying by the fraction breathed by Newton, each breath of ours has about 6.08 x 109 molecules also breathed by him (D). Since we have about 9 x 108 breaths, each breath of ours has about 7 molecules also breathed by Isaac Newton.