Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 01/02/2017 18:25:16
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How can we make a "guestimate" of this - please show your working!
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I cheated.
http://education.jlab.org/qa/mathatom_04.html (http://education.jlab.org/qa/mathatom_04.html)
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Given than most of the atoms in our body are hydrogen, followed by oxygen and carbon, I will estimate the average atomic mass of a human at 5 grams per mole. For a person weighing in at 75 kg, that would amount to (75000/5) 15000 moles of atoms, or about 9x1027 atoms. How did I do?
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To show working for a couple of steps that chiralSPO glossed over:
1) To work out the average atomic mass of an atom in the human body, we can take the atomic ratios from the link above, and say:
almost 2/3 is hydrogen, 1/4 is oxygen, and about 1/10 is carbon. These three atoms add up to 99% of the total!
Element Percentage Atomic Mass
Hydrogen 66% 1
Oxygen 25% 16
Carbon 10% 12
Weighted Average: 1 x 0.66 + 16 x 0.25 + 12 x 0.1 = 5.8 atomic mass units = 5.8 grams per mole (after correcting for the fact that the percentages add to 101%!)
(ChiralSPO calculated 5 grams per mole).
2) To convert 15000 moles to atoms, multiply by Avogadro's Number (https://en.wikipedia.org/wiki/Avogadro_constant) (6.022140857×1023 mol−1).
15000 x 6 x 1023 = 9 x 1027
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Phew. That's pretty close to what I said on the radio and how I calculated it. Thank you. Nice question too I thought...