# How tall would all the atoms in our body be?

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#### JDPower

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##### How tall would all the atoms in our body be?
« on: 08/08/2012 01:23:57 »
One of those bizarre queries that came to my mind - if you piled up every atom in the body, one on top of the other, how far would it reach (or how high would it be)?

#### CliffordK

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##### Re: How tall would all the atoms in our body be?
« Reply #1 on: 08/08/2012 06:14:11 »
I would imagine there would be several ways to estimate it.

I'm seeing the diameter of a carbon atom (in meters) is about  1.52 × 10-10m ( 0.000 000 000 154 m)

And, here is a calculation for the volume of the human body (in meters), at about 0.07 m3 for a 70 kg person.

Hmmm
So:

$$\frac{0.07 m^3}{(1.52 x 10^{-10} m)^3}$$        gives the approximate number of generic atoms.

[Alternatively, you might choose to calculate the number of moles and atoms in the body using Avagadro's number,  6.02214 ×1023.  You could also estimate for the major constituents, carbon, oxygen, hydrogen, nitrogen, etc.]

To convert that back to meters, multiply that back by the size of a carbon atom.

$$\frac{0.07 m^3}{(1.52 x 10^{-10} m)^3}$$ x $${1.52 x 10^{-10} m$$

And you end up with:
$$\frac{0.07 m^3}{(1.52 x 10^{-10} m)^2}$$  in meters.

And, I came up with about 3 × 1018m  (3,000,000,000,000,000,000 m)
That is bigger than I can count in meters, but it comes out to about three quadrillion km.

A lightyear is about 9.4605284 × 1015 meters

So, you end up with about 300 lightyears.

While it doesn't quite reach across the Milky Way, it would reach a quite a number of stars.
« Last Edit: 08/08/2012 06:20:32 by CliffordK »

#### JDPower

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##### Re: How tall would all the atoms in our body be?
« Reply #2 on: 08/08/2012 15:23:10 »
Wow, that's way more than I thought, I thought it would reach perhaps to a nearby planet, but that far! I'm amazed, thank you for the reply

#### peptidechemist

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##### Re: How tall would all the atoms in our body be?
« Reply #3 on: 08/08/2012 22:41:51 »
Very interesting question.  I took the weight route and came up with 73 light years.  This is lower than the previous estimate, because it takes into account the different weights and sizes of the atoms, especially between Hydrogen and the heavier elements.

I approached this based on the breakdown of the body into the individual elements.  I have attached a table summarizing my calculations.

[attachment=post_tmp_27451_0]

For a 70 kg person I calculated the weight of each element in the body.  Then dividing by the molecular weight of each element you can determine the number of moles of each element in the body.  Multiplying by Avogadro's number (6.022E23 atoms/mole) I calculated the number of atoms for each element.

Next, I multiplied the number of atoms by the atomic radius of each element.  I used the single bond or covalent radius.  This gave me the length of all the atoms lined up in meters, which I then converted to light years.

#### chris

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##### Re: How tall would all the atoms in our body be?
« Reply #4 on: 11/08/2012 21:16:33 »
Wow - fantastic bits of work, thank you both!
I never forget a face, but in your case I'll make an exception - Groucho Marx

#### peptidechemist

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##### Re: How tall would all the atoms in our body be?
« Reply #5 on: 16/08/2012 00:20:19 »
This question made me wonder how long different parts/components would be, so I had to calculate a few more.
Using the compositional data from newbielink:http://en.wikipedia.org/wiki/Composition_of_the_human_body#Composition_by_molecule_type [nonactive] I calculated the following

If you were to line up all the cells in your body they would stretch about 500,000 km which is a little further than the distance between the earth and the moon.

10^13 cells in the human body * 50 um (average size of a human cell) = 500,000,000 meters

If you were to take all the protein in the human body and line it up as a single elongated chain it would stretch about 2.5 light years, or if it formed a single alpha helix it would be roughly 1 light year long.

Humans are roughly 20% protein or around 12 kg on average.
(12,000 g protein) * (The average amino acid is 1 mol / 110 grams) * 6.022*10^23 amino acids / mol =6.57*10^25 amino acids.

The length of an amino acid is roughly 0.36 nm (distance between consecutive alpha carbons), so
6.57*10^25 amino acids * 0.36 nm = 2.4*10^16 meters = 2.5 light years

In an alpha helix each amino acid will increase the length of the helix by about 0.15 nm, so
6.57*10^25 amino acids * 0.15 nm = 9.85*10^15 meters = 1 light year.

If you were to put all of your DNA in a straight line it would be 20-30 billion km long or about 130-200 AU (The AU is the distance between the earth and the sun).

10^13 cells * 2-3 meters of DNA per cell = 20-30 billion km

If you were to line up all of the RNA in your body it would stretch 200-300 billion km, which is 1,300-2,000 AU, or roughly 7-11 light days.

Humans are roughly 0.1% DNA, but about 1% DNA and since DNA and RNA are similar your RNA would stretch 10 times further than your DNA

#### Antemortem

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##### Re: How tall would all the atoms in our body be?
« Reply #6 on: 18/07/2016 07:43:26 »
We tried a more accurate approach considering a 75Kg human body composed (by mass) of:

61.15% Oxygen 16g/mol - diameter 120x10^-12m
23% Carbon 12g/mol - diameter 140x10^-12m
10% Hydrogen 1g/mol - diameter 50x10^-12m
2.6% Nitrogen 14g/mol - diameter 130x10^-12m
1.4% Calcium 40g/mol - diameter 360x10^-12m
1,1% Phosphorus 30g/mol - diameter 200x10^-12m
0.2% Sulfur 32g/mol - diameter 200x10^-12m
0.2% Potassium 39g/mol - diameter 440x10^-12m
0.14% Sodium 22g/mol - diameter 360x10^-12m
0.12% Chlorine 35g/mol - diameter 200x10^-12m

For each element, the distance created by aligning each atom equals:
L=(Na*m*d)/M
Na being the Avogadro constant, m the mass in grams, d the diameter in meters, M in g/mol

So, for a 75kg human being, if we were to line up every single atom, the final distance would equal D=∑L=5.76E17 meters, that is to say roughly 3,850,267 times the distance between the Earth and the Sun, or 61 light years.

So if we stretch out far enough, we can reach beyond the Mensa constellation (Pi, Mensae, 59.4 light years away) to the Capricornius constellation (61.1 light years away).

Hopefully this will actually be useful at some point (if ever the universe becomes one-dimensional...)
« Last Edit: 18/07/2016 07:48:25 by Antemortem »

#### syhprum

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##### Re: How tall would all the atoms in our body be?
« Reply #7 on: 18/07/2016 09:20:23 »
I think the authors deserve a joint unnoble for all these ingenious calculations
syhprum