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Old 06-19-2011, 11:00 PM
keeganst94 keeganst94 is offline
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How many protons, neutrons and electrons are there?

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?
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  #2  
Old 06-19-2011, 11:03 PM
Chronos Chronos is offline
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That's not about halfway to a googol. Halfway to a googol is 5 x 1099.
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Old 06-19-2011, 11:04 PM
zombywoof zombywoof is offline
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10^45 is not "about halfway" to 10^100.

Last edited by zombywoof; 06-19-2011 at 11:08 PM..
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Old 06-19-2011, 11:13 PM
keeganst94 keeganst94 is offline
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Originally Posted by zombywoof View Post
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?
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Old 06-19-2011, 11:20 PM
Frylock Frylock is online now
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Originally Posted by keeganst94 View Post
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.

Last edited by Frylock; 06-19-2011 at 11:20 PM..
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Old 06-19-2011, 11:24 PM
zombywoof zombywoof is offline
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Originally Posted by keeganst94 View Post
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).

Last edited by zombywoof; 06-19-2011 at 11:26 PM..
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  #7  
Old 06-19-2011, 11:29 PM
RadicalPi RadicalPi is offline
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There is nowhere near 10100 protons, neutrons, and electrons in the visible universe. As others have stated, 1045 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 ◊ 1058 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 ◊ 1058 moles of hydrogen. Multiply then by the Avogadro number, 6.02 ◊ 1023 to get 9.5 ◊ 1081 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 ◊ 1082 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.

Last edited by RadicalPi; 06-19-2011 at 11:30 PM..
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Old 06-20-2011, 01:40 AM
Chronos Chronos is offline
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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.
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Old 06-20-2011, 02:40 AM
Whack-a-Mole Whack-a-Mole is offline
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Originally Posted by Chronos View Post
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.
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Old 06-20-2011, 03:01 AM
Polycarp Polycarp is offline
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Originally Posted by RadicalPi View Post
There is nowhere near 10100 protons, neutrons, and electrons in the visible universe. As others have stated, 1045 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 Iím wrong), take the mass of the universe, 1.59 ◊ 1058 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 ◊ 1058 moles of hydrogen. Multiply then by the Avogadro number, 6.02 ◊ 1023 to get 9.5 ◊ 1081 protons and neutrons. This leaves out all the electrons, but I think itís 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 ◊ 1082 protons, neutrons, and electrons. In any case, Iíd 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 1.49*1082 to the close order of 1.0*1082.

The number of atomic particles in a trillion universes like our own woujld still fall short of a googol -- 1.n*1094 particles. It would take 100 quadrillion such universes to approach the googol mark.
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Old 06-20-2011, 05:56 AM
Napier Napier is offline
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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?
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Old 06-20-2011, 07:17 AM
Mijin Mijin is offline
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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...

SPOILER:

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
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  #13  
Old 06-20-2011, 07:38 AM
septimus septimus is offline
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Originally Posted by Whack-a-Mole View Post
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.
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Old 06-20-2011, 07:41 AM
Quercus Quercus is offline
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Originally Posted by Napier View Post
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.
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Old 06-20-2011, 07:43 AM
chrisk chrisk is online now
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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?
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Last edited by chrisk; 06-20-2011 at 07:45 AM..
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Old 06-20-2011, 11:57 AM
Chronos Chronos is offline
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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.
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Old 06-20-2011, 12:10 PM
Ludovic Ludovic is offline
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Originally Posted by Quercus View Post
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.
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Old 06-20-2011, 12:45 PM
Rain Soaked Rain Soaked is offline
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Originally Posted by Napier View Post
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!
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Old 06-20-2011, 12:50 PM
Polycarp Polycarp is offline
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Trust a poster named Napier to bring up logarithms!
Well, naturally!
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Old 06-20-2011, 02:15 PM
Exapno Mapcase Exapno Mapcase is online now
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Quote:
Originally Posted by Napier View Post
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?
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Originally Posted by Quercus View Post
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.
1045 is half of 2 x 1045. If you double that you get 4 x 1045. Double it again at you're at 8 x 1045. You haven't even gone up one order of magnitude despite three doublings.

The distance between 1045 and 10100 is enormously greater than any of the "unimaginable" distances that the OP gave.
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Old 06-20-2011, 04:02 PM
ZenBeam ZenBeam is offline
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Originally Posted by Exapno Mapcase View Post
1045 is half of 2 x 1045. If you double that you get 4 x 1045. Double it again at you're at 8 x 1045. You haven't even gone up one order of magnitude despite three doublings.
You're missing their point.
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Old 06-20-2011, 04:36 PM
Exapno Mapcase Exapno Mapcase is online now
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I think that the way these posts were made reinforces the OP's mistaken idea that a 45 in a power of ten is somehow halfway to a 100 in a power of ten. Powers of ten do not work that way at all. Moreover, the lack of understanding that this is the case is a common problem. Trying to excuse away that misunderstanding by throwing in logarithms doesn't make it right or lead to the OP - and anybody else reading this thread - understanding where he went wrong.
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Old 06-20-2011, 10:50 PM
RadicalPi RadicalPi is offline
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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 1.49*1082 to the close order of 1.0*1082.
Thanks. That last part was the biggest guess, since I have no idea whatsoever how many neutrons there are. Hence my hedging.
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Old 06-21-2011, 02:28 AM
septimus septimus is offline
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I think OP is not wrong to conclude that an ocean is (logarithmically) "about midway in mass" between an atom and the universe. He just draws the wrong conclusion: the universe is hugely larger than an ocean, but so is an ocean hugely larger than an atom.

Here is a wonderful webpage (primaxstudio.com/stuff/scale_of_universe/index.php) which everyone will want to bookmark. Use the slider at bottom to see different scales.

Last edited by septimus; 06-21-2011 at 02:29 AM..
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Old 06-21-2011, 03:04 AM
Half Man Half Wit Half Man Half Wit is offline
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As an interesting historical nugget, John Wheeler and Richard Feynman toyed around with the idea that the total number of electrons in the universe is -- one. The reason for why this 'works' at all is essentially that one can view a positron as an electron going 'backwards in time', so all the electrons (and positrons) we see are really just the one zipping forward and backward; every annihilation of a positron and an electron, or conversely the photoproduction of an electron-positron pair, would then be just the 'one electron' 'turning around' in its propagation through time. The obvious problem, of course, is that there don't seem to be nearly as many positrons as there are electrons.

Last edited by Half Man Half Wit; 06-21-2011 at 03:04 AM..
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Old 06-21-2011, 11:33 AM
Chronos Chronos is offline
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The other problem is that one can produce an electron-positron pair, interact with and measure one of the pair, and then re-annihilate them. That gives you an electron that definitely isn't just a slice of "the one electron".
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