Burning questions of a Saturday morning.

So there I was lying in bed this morning, still half-asleep, when I got to pondering the fact that I, like the atoms that compose me, am made up of 99.99% empty space. I then idly contemplated the fact that most of this mass was in the nuclei of my atoms, at which point I was seized by a burning desire to find out how much all the electrons in all the atoms of my body put together weighed.

I know that last I checked, I had a mass of approximately 60 kg (my weight is left as an exercise for the reader), and a little searching on the 'net produced a table with the percent-by-mass composition of an average person. Starting with the first entry in the list, I have around $61.35\text{%}\cdot 60\ \text{kg} = 36.81\ \text{kg}$ of oxygen in me. That's 36,810 grams of oxygen. A mole of oxygen being 16.00 grams, that's almost exactly 2,300 moles of oxygen in me.

(A mole, in chemistry, is simply a very large number $-\ 6.022\times10^{23}$, to be exact. The conversion between grams and moles is pretty easy; if you have an amount of a substance equal in grams to the atomic weight of one atom (or molecule) of that substance, you have one mole of that substance, i.e., $6.022\times10^{23}$ atoms (or molecules) of the substance. Since the atomic weight of oxygen is 16.00 atomic mass units, one mole of oxygen is 16.00 grams of oxygen. One more of oxygen at $0^\circ$C and normal atmospheric pressure would occupy about 22.4 liters, or just under 6 gallons.)

Now, each oxygen atom comes with 8 electrons in tow, $8$ electrons $\times$ $2,300$ moles $\times$ $6.022\times10^{23}=1.11\times10^{28}$ electrons.

That...is a very large number. (11.1 billion billion billion).

And that's just the first element on the list! (Although, by virtue of its nature, it is likely to provide the largest number of electrons.) Next up is carbon, which, at 22.83%, comprises 13.70 kg of me. Dividing by 12.00 grams per mole, and multiplying by 6 electrons to each carbon atom, we arrive at $3.09\times10^{27}$ electrons from carbon, a factor of 10 less than from oxygen (not surprisingly).

Since the procedure is relatively boring, and quite simple, I will spare you further talk and simply list the amounts in the table below:

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oxygen        36.81 kg  $1.11\times10^{28}$ electrons

carbon        13.70 kg  $3.09\times10^{27}$ electrons

hydrogen      6.00 kg   $3.57\times10^{27}$ electrons

nitrogen      1.54 kg   $4.64\times10^{26}$ electrons

calcium       0.86 kg   $2.58\times10^{26}$ electrons

phosphorus    670 g     $1.94\times10^{26}$ electrons

potassium     120 g     $3.51\times10^{25}$ electrons

sulfur        120 g     $3.61\times10^{25}$ electrons

sodium        84 g      $2.42\times10^{25}$ electrons

chlorine      84 g      $2.43\times10^{25}$ electrons

magnesium     18 g      $5.35\times10^{24}$ electrons

iron          6.0 g     $1.68\times10^{24}$ electrons

fluorine      2.4 g     $6.85\times10^{23}$ electrons

zinc          1.8 g     $5.00\times10^{23}$ electrons

silicon       0.60 g    $1.80\times10^{23}$ electrons

rubidium      0.60 g    $1.56\times10^{23}$ electrons

strontium     0.30 g    $7.84\times10^{22}$ electrons

bromine       0.24 g    $6.33\times10^{22}$ electrons

lead          0.12 g    $2.86\times10^{22}$ electrons

copper        0.06 g    $1.65\times10^{22}$ electrons

aluminum      60 mg     $1.74\times10^{22}$ electrons

cadmium       60 mg     $1.54\times10^{22}$ electrons

cerium        60 mg     $1.50\times10^{22}$ electrons

barium        18 mg     $4.42\times10^{21}$ electrons

iodine        18 mg     $4.53\times10^{21}$ electrons

tin           18 mg     $4.57\times10^{21}$ electrons

titanium      18 mg     $4.98\times10^{21}$ electrons

boron         18 mg     $5.01\times10^{21}$ electrons

nickel        12 mg     $3.45\times10^{21}$ electrons

selenium      12 mg     $3.11\times10^{21}$ electrons

chromium      12 mg     $3.34\times10^{21}$ electrons

manganese     12 mg     $3.29\times10^{21}$ electrons

arsenic       6.0 mg    $1.59\times10^{21}$ electrons

lithium       6.0 mg    $1.56\times10^{21}$ electrons

cesium        5.4 mg    $1.35\times10^{21}$ electrons

mercury       5.4 mg    $1.30\times10^{21}$ electrons

germanium     4.2 mg    $1.11\times10^{21}$ electrons

molybdenum    4.2 mg    $1.10\times10^{21}$ electrons

cobalt        2.4 mg    $6.62\times10^{20}$ electrons

antimony      1.8 mg    $4.54\times10^{20}$ electrons

silver        1.8 mg    $4.72\times10^{20}$ electrons

niobium       1.2 mg    $3.19\times10^{20}$ electrons

zirconium     0.60 mg   $1.58\times10^{20}$ electrons

lanthanum     0.60 mg   $1.48\times10^{20}$ electrons

gallium       0.60 mg   $1.61\times10^{20}$ electrons

tellurium     0.60 mg   $1.47\times10^{20}$ electrons

yttrium       0.54 mg   $1.42\times10^{20}$ electrons

bismuth       0.42 mg   $1.00\times10^{20}$ electrons

thallium      0.42 mg   $1.00\times10^{20}$ electrons

indium        0.36 mg   $9.25\times10^{19}$ electrons

gold          0.18 mg   $4.35\times10^{19}$ electrons

scandium      0.18 mg   $5.06\times10^{19}$ electrons

tantalum      0.18 mg   $4.37\times10^{19}$ electrons

vanadium      0.12 mg   $3.26\times10^{19}$ electrons

thorium       0.060 mg  $1.40\times10^{19}$ electrons

uranium       60 μg     $1.40\times10^{19}$ electrons

samarium      42 μg     $1.04\times10^{19}$ electrons

beryllium     30 μg     $8.02\times10^{18}$ electrons

tungsten      18 μg     $4.36\times10^{18}$ electrons

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(if you're wondering about the units, conveniently, 0.06 g = 60 mg and 0.06 mg = 60 μg)

If you add all those electrons up, you come up with a total of $1.88\times10^{28}$ electrons. That's a lot of electrons -- 18.8 billion billion billion, to be exact. But how much mass do they have? And how much do they weigh?

Finding the mass is easy. The mass of an electron is $9.11\times10^{-31}$ kg so $1.88\times10^{28}$ of them together have a mass of 17.1 grams, which has a weight of approximately 1/25 of a pound.

Wow. All the electrons in my body make up a measly 0.0000029% of my mass. Everything else is concentrated in the nuclei of my atoms. Wild, huh?