How many protons, neutrons and electrons are there?

[keeganst94]

The difference between the diameter of a carbon atom’s nucleus and the diameter of the known universe is about 40 orders of magnitude. That still leaves about 32 orders of magnitude to sweep under the rug, or about the difference between a carbon atom and the Milky Way. To put it another way, the number of protons, neutrons and electrons in the known universe is much less than one googol. You’ve exceeded that by a margin of unimaginable to the unimaginable power. I knew you could do it, Cecil. Congratulations. --Josef D. Prall, Carrollton, Texas

This is from a person correcting cecil (as if he gets anything wrong). The part I’m talking about is how their are less then a google protons electrons and neutrons in the known universe. I’ve heard a lot of people make the claim, but I don’t see how it could be true, because 1 mol is equal to 6.02214 x10^23 molecules.

So lets take water, which is H20 (HOH if you want to get technical). Hydrogen has (on average) one proton and one electron, for a total of two, plus two more for the other atom, for a total of four. Oxygen has (on average) 8 protons, neutrons and electrons, for a total of 24, and H20 has a total number of 28 particles. This has a mass of 18 grams.

So every 18 grams, or mol, of water has 28 x 6.02214x10^23 parts, which is equal to 1.6861992 x 10^25. Their is about 1377974508000000000000000 grams of water on earth, or 76554139333333333333 mol’s of water. That, times the number of particles in 1 mol gives us about 1.29 x 10^45 particles in the water on earth.

Given that we’re about halfway to a googol particles already, using the number of electrons protons and neutrons in water, I would suggest that the statement above is wrong. This ended up way longer than I expected, but if any of you actually kept reading, am I wrong, and this Joseph Prall is right, or is Joseph Prall full of it?

[Chronos]

That’s not about halfway to a googol. Halfway to a googol is 5 x 10[sup]99[/sup].

[zombywoof]

10^45 is not “about halfway” to 10^100.

[keeganst94]

@zombywoof

10^45 is not “about halfway” to 10^100.

Okay, I may have messed that up. But still, was I right or wrong about there being more than a googol protons neutrons and electrons in the universe?

[Frylock]

@keeganst94

Okay, I may have messed that up. But still, was I right or wrong about there being more than a googol protons neutrons and electrons in the universe?

My back-of-envelope calculations seem to show that a massive overestimation of the number of particles in the universe puts it at something on the order of 1/(10^40)th of a googol.

[zombywoof]

@keeganst94

Okay, I may have messed that up. But still, was I right or wrong about there being more than a googol protons neutrons and electrons in the universe?

I am not a physicist, but FWIW Wikipedia puts the number of atoms in the universe around 10^80 (an infinitesimally small number in comparison to 10^100).

[RadicalPi]

There is nowhere near 10[SUP]100[/SUP] protons, neutrons, and electrons in the visible universe. As others have stated, 10[SUP]45[/SUP] is still 55 orders of magnitude short, which is 15 orders of magnitude (apparently) more than the distance that separates the diameter of a carbon atom from the diameter of the visible universe. 15 orders of magnitude is what separates a meter from a lightyear, more or less.

To give a quick and dirty estimate on the number of protons, neutrons, and electrons in the universe (and physics people, correct me if I’m wrong), take the mass of the universe, 1.59 × 10[SUP]58[/SUP] grams. Given that most of the mass of the universe is hydrogen, divide by the mass of a mole of hydrogen, 1.00794, to get 1.58 × 10[SUP]58[/SUP] moles of hydrogen. Multiply then by the Avogadro number, 6.02 × 10[SUP]23[/SUP] to get 9.5 × 10[SUP]81[/SUP] protons and neutrons. This leaves out all the electrons, but I think it’s a safe guess that we can assume that no more than half of the particles counted thus far are neutrons, which gives us a total of half again as many, that is, 1.49 × 10[SUP]82[/SUP] protons, neutrons, and electrons. In any case, I’d be willing to bet, although not a large amount, that this number is right within say three orders of magnitude.

This is still 17 orders of magnitude away from a googol, which is still really, really, big.

[Chronos]

As an aside, I have actually encountered numbers larger than a googol in a real, non-combinatoric, scientific calculation. The very largest black holes will last for a few thousand googol seconds before evaporating completely.

[Whack-a-Mole]

@Chronos

As an aside, I have actually encountered numbers larger than a googol in a real, non-combinatoric, scientific calculation. The very largest black holes will last for a few thousand googol seconds before evaporating completely.

Well, the “largest number” can never be defined because anything anyone says you can add 1.

For me the largest number is a number used in a calculation and near as I can tell Graham’s Number is the winner.

I think if you wrote it out the universe itself is not big enough to do it (i.e. if every particle in the universe represented a number there are not enough to write out this number).

Maybe you can go with the Clarkkkkson vs. the xkcd Number but I think those don’t really count to my mind.

[Polycarp]

@RadicalPi

There is nowhere near 10[SUP]100[/SUP] protons, neutrons, and electrons in the visible universe. As others have stated, 10[SUP]45[/SUP] is still 55 orders of magnitude short, which is 15 orders of magnitude (apparently) more than the distance that separates the diameter of a carbon atom from the diameter of the visible universe. 15 orders of magnitude is what separates a meter from a lightyear, more or less.

To give a quick and dirty estimate on the number of protons, neutrons, and electrons in the universe (and physics people, correct me if I’m wrong), take the mass of the universe, 1.59 × 10[SUP]58[/SUP] grams. Given that most of the mass of the universe is hydrogen, divide by the mass of a mole of hydrogen, 1.00794, to get 1.58 × 10[SUP]58[/SUP] moles of hydrogen. Multiply then by the Avogadro number, 6.02 × 10[SUP]23[/SUP] to get 9.5 × 10[SUP]81[/SUP] protons and neutrons. This leaves out all the electrons, but I think it’s a safe guess that we can assume that no more than half of the particles counted thus far are neutrons, which gives us a total of half again as many, that is, 1.49 × 10[SUP]82[/SUP] protons, neutrons, and electrons. In any case, I’d be willing to bet, although not a large amount, that this number is right within say three orders of magnitude.

This is still 17 orders of magnitude away from a googol, which is still really, really, big.

Very nice job. I’d add that with cosmic abundances of nuclides being what they are, well over 90% of all known (non-dark matter) atoms are protium (H-1), with proton and electron but no neutron, and over 98% of the remainder is helium-4, with two protons, two neutrons, and two electrons So estimating that “no more than half the particles counted thus far are neutrons” is a gross understatement. In any controlled sample of nucleons, very much less than ten percent will be neutrons, and in a smilar sample of necleons+electrons, the neutron count will be well below 5%. Therefore I’d scale down your 1.4910[sup]82[/sup] to the close order of 1.010[sup]82[/sup].

The number of atomic particles in a trillion universes like our own woujld still fall short of a googol – 1.n*10[sup]94[/sup] particles. It would take 100 quadrillion such universes to approach the googol mark.

[Napier]

I think 10^45 actually is almost halfway to 10^100, in the relevant sense that a logarithmic view of such quantities is more useful. It would be more accurate to say that the log of 10^45 is almost halfway to the log of 10^100, but I can accept the OP as meaning “like reasonable people we are speaking in logarithmic terms, and using scientific notation where the exponent is the part that we are noticing, and in that scheme we are almost halfway to an exponent of 100”.

Or at least I can if I ignore “Their is about 1377974508000000000000000 grams of water on earth, or 76554139333333333333 mol’s of water.” Ouch! Do we start counting digits or what?

[Mijin]

A tad off-topic, but I was wondering whether the number of neutrons in the universe if the entire universe were a neutron star would get us over a googol…

Yep. Way, way more than a googol.

I did the sums in quite a lazy way though. Based on the preceding posts, I assumed that if the density of a neutron star was greater than 10^17 times the average density of the universe, then there would be a googol neutrons.
And in fact the average density of the universe is only 10 ^ -29 grams per cm, versus 5 x 10^11 gcm^-3 for a neutron star.

Meaning that, based on my very crude calculations, I make it there would be 10^123 neutrons in my neutron universe, or 10^23 googols.

By similar logic if the whole universe had the average density of the sun you’d still have 10^9 googols

[septimus]

@Whack-a-Mole

For me the largest number is a number used in a calculation and near as I can tell Graham’s Number is the winner.

Graham’s number is preposterously large. You could take successive logarithms of it a googol times and still have a number too preposterously large to imagine.

Graham’s number G arises in a Ramsay Number problem, whose solution (N*) is unknown but satisfies
13 <= N* <= G
Thus the number for which G was constructed as a bound may in fact be a very small number, preposterously smaller than G.

[Quercus]

@Napier

I think 10^45 actually is almost halfway to 10^100, in the relevant sense that a logarithmic view of such quantities is more useful. It would be more accurate to say that the log of 10^45 is almost halfway to the log of 10^100, but I can accept the OP as meaning “like reasonable people we are speaking in logarithmic terms, and using scientific notation where the exponent is the part that we are noticing, and in that scheme we are almost halfway to an exponent of 100”.

I agree: the OP is reasonable in saying 10^45 is almost halfway to a googol. We’re talking about orders of magnitude.

But of course, since we’re talking orders of magnitude, being halfway doesn’t mean it’s easy to get the rest of the way, and so it doesn’t mean that there are anywhere close to a googol protons in the universe. I think this is a little lesson in just how small atoms really are, compared to things like planets, and how not-dense the universe as a whole is, compared to things like planets.

[chrisk]

But in a logarithmic sense, starting from proton-level particles and getting up to planet Earth level scale, I certainly don’t have much of a problem with the idea that we’ve already come about half-way to universal scale, or maybe a little bit more. Does anybody here feel that the macroscopic is so many orders of ten above us than the microscopic is below us?

[Chronos]

What does what we feel have to do with anything? Just run the numbers.

And my mention of black hole ages was because it was a number that came up in a scientific context, not a purely mathematical one. Scientific numbers that large are a genuine rarity.

[Ludovic]

@Quercus

I think this is a little lesson in just how small atoms really are, compared to things like planets, and how not-dense the universe as a whole is, compared to things like planets.

Plus, how large a galaxy is, compared to the size of the universe. If a galaxy (plus the empty spaces around it) were a marble, the observable universe would probably be not much bigger than a baseball stadium. Still enough to fit billions in, but nothing compared to the other scales.

This first hit me when I realized how wide the Andromeda is in our sky (we only see the core of it visibly AFAIK.) If the Andromeda is large enough to see in detail with the naked eye (if it were bright enough), and it is millions of light years away, and the univese is only billions of light year big, then the observable universe is tiny compared to the leaps we take from galaxy to stars, and from stars to atoms.

[Rain_Soaked]

@Napier

I think 10^45 actually is almost halfway to 10^100, in the relevant sense that a logarithmic view of such quantities is more useful. It would be more accurate to say that the log of 10^45 is almost halfway to the log of 10^100, but I can accept the OP as meaning “like reasonable people we are speaking in logarithmic terms, and using scientific notation where the exponent is the part that we are noticing, and in that scheme we are almost halfway to an exponent of 100”.

Trust a poster named Napier to bring up logarithms!

[Polycarp]

@Rain_Soaked

Trust a poster named Napier to bring up logarithms!

Well, naturally!

[Exapno_Mapcase]

@Napier

I think 10^45 actually is almost halfway to 10^100, in the relevant sense that a logarithmic view of such quantities is more useful. It would be more accurate to say that the log of 10^45 is almost halfway to the log of 10^100, but I can accept the OP as meaning “like reasonable people we are speaking in logarithmic terms, and using scientific notation where the exponent is the part that we are noticing, and in that scheme we are almost halfway to an exponent of 100”.

Or at least I can if I ignore “Their is about 1377974508000000000000000 grams of water on earth, or 76554139333333333333 mol’s of water.” Ouch! Do we start counting digits or what?

@Quercus

I agree: the OP is reasonable in saying 10^45 is almost halfway to a googol. We’re talking about orders of magnitude.

But of course, since we’re talking orders of magnitude, being halfway doesn’t mean it’s easy to get the rest of the way, and so it doesn’t mean that there are anywhere close to a googol protons in the universe. I think this is a little lesson in just how small atoms really are, compared to things like planets, and how not-dense the universe as a whole is, compared to things like planets.

10[sup]45[/sup] is half of 2 x 10[sup]45[/sup]. If you double that you get 4 x 10[sup]45[/sup]. Double it again at you’re at 8 x 10[sup]45[/sup]. You haven’t even gone up one order of magnitude despite three doublings.

The distance between 10[sup]45[/sup] and 10[sup]100[/sup] is enormously greater than any of the “unimaginable” distances that the OP gave.