Physics / Maths Question

Quote:

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The average breath inhales 0.5L of air. Assume all air particles have the same mass as an argon atom, 5*10^-26. The atmosphere is roughly 1% argon atoms.

1) How argon atoms does a person inhale with each breath? The density of air is 1.2 kg m^-3 (Note: there are 1000L in a m^3)

2) Estimate how many argon atoms passed through a person's lungs during their lifetime. The same atom was never breathed twice. He averaged 14 breaths per minute for the duration of his life - 85 years.

3) Estimate the total number of particles in the Earth's atmosphere. Do this by nothing that the surface air pressure of 10^5 Nm^-2 supports the weight of the atmosphere. Aussme that g does not vary over the height of the atmosphere. The radius of the Earth is 6.4*10^6m

4) Assume that the argon atoms the person in 2) breathed are now completely mixed throughout the Earth's atmosphere. Estimate how many of these you breathe in with each breath.

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I have done some parts of it, but want to know what you guys get. I think i've mucked up some of the conversions

oh come on,

someone please help :p

Here's what I think:

1) 4.8*10²⁶ argon atoms per breath

2) 3.0*10³⁵ argon atoms in his life

Now I just need to know how to work out how many atoms there are in the atmosphere and I can have a crack at the third part :o

1.2Kgm^-3 = 0.0012KgL^-1
0.0012KgL^-1 x 0.5L = 0.0006Kg
0.0006Kg / 5x10^-26 = 1.2x10²² atoms in one breath.

1.2x10²² * 14 * 60 * 60 * 24 * 365 * 85 = 4.5x10³² atoms in his life.

P = F/A --> F = AP = 10⁵Nm^-2 * 4pi * 6.4x10¹²m² = 8.05x10¹⁸N
F = ma --> m = F/g = 8.05x10¹⁸N / 9.8ms^-2 = 8.2x10¹⁷Kg
8.2x10¹⁷Kg / 5x10^-26 = 1.6x10⁴³ particles in atmosphere

You can't do the last part because you haven't told us how thick the atmosphere is, although you could work it out using the densities given but I can't be fagged.

Thanks,

Could you tell me what I did wrong for part 1 then:

1.2kg / 5*10^-26 = 2.4*10²⁵ = atoms per m³

2.4*10²⁵ / 100 = 2.4*10²³ = argon atoms per m³

breath size = 5*10^-4

2.4*10²³ / 5*10^-4 = 4.8*10²⁶ argon atoms per breath.

?

2.4*10²³ * 5*10^-4 = argon atoms per breath

I divided instead of mutiplying :/


BTW: you forgot to divide by 100 for the 1% argon atoms..