From: David Burton
Subject: Jewels, Moles & Avocados (was Re: How much is a joule)
Date: 1995/04/19
newsgroups: sci.electronics
Message-ID: <cPuT4c3w165w@salzo.Cary.NC.US>
references: <3movho$> writes:
> You know, I'm tired of reading these messages. I know that this is probably a
> old thread, hey, I haven't read this group in awhile. But surely, someone mus
> know the exact number of electrons in a joule?

Yes, though (of course) the number of electrons in a jewel depends
upon its size (in carats) and what gemstone it is.  The canonical
gemstone used for counting electrons is the 1 carat diamond, which
contains 6.0167 x 10**22 electrons.  That number is called a jewel.
>                                              I was told in school the other
> day, but have forgotten, but I seem to remember it was a 6 followed by a
> helluvalot of zeros..<G>

Yes, the number of electrons in a standard jewel (a 1 carat diamond)
is 6 followed by a helluvalot of zeros (22 of them).  However,
you're probably thinking of the number of electrons in a *mole*,
rather than a jewel.

Of course, just as a cubit depends upon the size of your arm, the
actual number of electrons in a mole depends upon the species of
mole (there are a lot of species in the family Talpidae), and also
whether it is a baby mole or a full-grown, adult mole.

Fortunately, there is a standard for the weight of a "canonical"
adult mole.  It is actually about 1/20 the weight of an adult North
American Common Mole.  I don't know why it is so small.  Perhaps
the "standard" weight is supposed to be that of a baby shrew mole or
something, or maybe the physicists who came up with the unit didn't
bother to check how big moles really grow.  My guess is that naming
the unit after the rodent was a whimsical choice, and they really
didn't care much whether or not their "standard" rodent was a

Anyhow, the "standard" mole has another problem, besides his small
stature.  He is 100% water!  (That's actually a pretty good
approximation to real moles, a lot closer than the weight, anyhow.)
His composition was chosen for easy analysis.  Anyhow, the standard
mole is a hypothetical 100% H2O critter that contains exactly
avocado's number of electrons (and the same number of protons, of

I'll bet that's the number you are thinking of: "6 followed by a
helluvalot of zeros" (23 of 'em, to be exact).  It is called
avocado's number, which is the number of electrons in a 10 carat
diamond.  Legend has it that it is called avocado's number because
an 18th century Italian scientist (named Amedeo) exclaimed, upon
seeing a 10 carat diamond, "Wow!  That's the size of an avocado!"
He was exaggerating, of course, but nevertheless the term stuck.

For some reason, a mole is now more commonly used than a jewel.
Why use a unit based upon a 10 carat diamond instead of a 1 carat
diamond?  Who knows?  You could ask the same question about
optical wavelength measurements: why are we all using nanometers
these days, instead of angstroms?  (A nanometer is 10 angstroms.)

Anyhow, back to moles.  Unfortunately, as a result of improved
measurement techniques, the original "avocado's number,"
6.0225x10**23, which was believed to be the number of electrons in a
10 carat diamond, is now known to have been slightly high.  There
are actually only 6.0167x10**23 electrons in a 10 carat diamond.
That's very close, of course (less than .01% off).  Unfortunately,
the entire metric weight system is based upon the old value of
avocado's number!

Oops!  Rather than change the whole weight system, it was decided to
stick with the original number, and accept the fact that a 10 carat
diamond doesn't have quite enough electrons in it.  (So we're
getting gypped by almost .01% every time we buy diamond jewelry by
the carat!)

Anyhow, avocado's number is still officially 6.0225x10**23, even
though that is *actually* the number of electrons in a 10.0096 carat
diamond, rather than in a 10 carat diamond.

(It is all the fault of the traces of carbon-14 in the diamond,
actually, which slightly increases the weight, and thereby decreases
the number of molecules per given weight.  Avocado's number is
actually the number of electrons in a hypothetical 10 carat diamond
made entirely of carbon-12.)

You now have enough almost enough information to calculate the
weight of that hypothetical, standardized, 100% H2O rodent, the
"mole."  That poor, soggy creature is defined to contain avocado's
number of electrons (and protons).  Recall that carbon-12 contains
6 electrons, 6 protons, and 6 neutrons per atom.  Oxygen-16 contains
8 electrons, 8 protons, and 8 neutrons per atom.  Hydrogen contains
just one proton and one electron per atom.

So, can you now figure out what the canonical mole weighs?

Okay, I won't keep you guessing.  Here's how you can figure it out
(very closely, anyhow).  Water is H2O, so it contains 10 electrons,
10 protons, and 8 neutrons per molecule (two hydrogens and an
oxygen).  A proton and a neutron weigh (almost exactly) the same,
and an electron weighs almost nothing, so water is 10/(10+8) = 10/18
= 55.55% protons and 44.44% neutrons.  Carbon is only 50% protons
(6 protons and 6 neutrons).  So, one water mole therefore weighs
50/55.55 of what a 10 carat diamond weighs, like 0.9 moles = 9.0
jewels weighing 9.0 carats.  A carat is 1/5 gram, so that means
the "standard" family Talpidae rodent weighs 9/5 = 1.8 grams.
(Actually, a typical adult North American mole weighs more like
1.8 *ounces*, not grams, but don't blame me, I didn't create the

So, now you know: to several digits of precision, a mole has
avocado's number of electrons in 1.8 grams of water, which is the
same number of electrons as a 10 carat diamond.  (Avocado is
sometimes misspelled avogadro - maybe that is avocado in some
other language?)

A related term is the "coulomb," which is yet another (much smaller)
unit of measurement for counting electrons.

You might think that the term coulomb (pronounced like, and derived
from, "cool ohm") has something to do with electrical resistance
("ohms").  It doesn't.  It was defined as the amount by which a one-
carat diamond is undersized.  That is, it was defined as the number
of electrons by which a one-carat diamond is short of having 1/10
avocado's number of electrons.

(Well, as luck would have it, that's not really *quite* right any
more.  That's what it was intended to be, but with ever-more-up-
to-date measurements, the exact number of electrons in a 10 carat
diamond (i.e., what *should* be avocado's number) got corrected
*again*, after the coulomb was defined.  So, a coulomb is really
just a smidgen *over* the actual number of electrons by which
a one-carat diamond is short of having 1/10 avocado's number of
electrons.  To be precise, a coulomb is defined as 6.2418x10**18
electrons, so the difference between a real 1-carat diamond and
a theoretical 1-carat diamond made entirely of carbon-12 is
(6.0225-6.0167)x10**22 electrons / 6.2418x10**18 electrons/coulomb
= 0.93 coulombs.)

Anyhow, the term "cool ohm" was apparently coined from "ice"
(slang for diamonds) and "Mho" (a unit of hardness based on the
diamond; the hardness of a diamond is defined to be 10 Mhos).
So, a one-carat diamond was said to have just "one cool ohm" short
of a full jewel (1/10 mole) of electrons (i.e., just a smidgen).

Okay, so how much smaller is a coulomb than a jewel, or a mole?
A mole is (6.0225x10**23 electrons/mole) / (6.2418x10**18
electrons/coulomb) = 96,487 coulombs/mole.
A jewel is (6.0167x10**22 electrons/jewel) / (6.2418x10**18
electrons/coulomb) = 9639.4 coulombs/jewel.

So, if high-grade diamonds cost $2500/carat, then that one cool
ohm difference between the size of a one-carat diamond and a
diamond containing a full jewel (1/10 mole) of electrons is worth
$2500/9639.4 = about a quarter (actually 25.9 cents).


P.S. - I don't even like avocados!  (Nor moles, for that matter.)
(But I'd be happy to take off your hands any extra 10 carat diamonds
that you might have laying around!)

-Dave Burton

(I'm embarrassed that back then I didn't realize that natural diamonds contain no 14C.)