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According to Wikipedia, the composition (by atomic percent) of the human body is:

  • 62% hydrogen
  • 24% oxygen
  • 12% carbon
  • 1% nitrogen
  • etc.

Question: What is our volumetric composition*?

*I get this is a tricky question since the volume of the electron clouds fluctuate depending on neighboring atoms, but I wonder if we can get a course approximation.

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  • $\begingroup$ This has the potential to be a fun Fermi estimate sort of exercise, but I'm not sure if it would be considered on topic here. $\endgroup$
    – Sean
    Sep 2, 2015 at 0:43
  • $\begingroup$ Hey Sean, why do you think it's OT? As a geneticist, I'm interested to know if my intuition about how electron clouds look is correct. If there is any other effect that governs atomic radii in large macromolecules which I didn't take into account, I'd like to know. $\endgroup$
    – crypdick
    Sep 2, 2015 at 3:15
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    $\begingroup$ The real problem is that all that stuff is organized in a myriad of different complex molecules.. maybe it is easier to scale down the question to the basic kind of cells that compose "animals" similar to us. But if you just want rough estimates, you answer should be fine. $\endgroup$
    – Quillo
    Nov 17, 2020 at 14:05

1 Answer 1

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OP here, this is my best guess. I'm interested if anyone has a better answer.

I use the covalent radii listed on Wikipedia. As an approximation, I assume all carbon are $sp^3$ hybridized, and I interpolate oxygen's radius. In picometers:

  • Hydrogen radius = 32
  • Oxygen radius = 60
  • Carbon radius = 76

Therefore, using $V = 4/3 \pi r^3$,

  • $V_{Hydrogen} = 4/3 \pi * 32^3 = 137258 $
  • $V_{Oxygen} = 4/3 \pi * 60^3 = 904779$
  • $V_{Carbon} = 4/3 \pi * 76^3 = 1838778$

Multiplied by their relative abundance:

  • Hydrogen: $ 137258 * .62 = 85099$
  • Oxygen: $ 904779 * .24 = 217146$
  • Carbon: $ 1838778 * .12 = 220653$

Seems like C leads by just a bit!

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