#1




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




That's not about halfway to a googol. Halfway to a googol is 5 x 10^{99}.

#3




10^45 is not "about halfway" to 10^100.
Last edited by zombywoof; 06192011 at 11:08 PM.. 
#4




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?

#5




My backofenvelope 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; 06192011 at 11:20 PM.. 
#6




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; 06192011 at 11:26 PM.. 
#7




There is nowhere near 10^{100} protons, neutrons, and electrons in the visible universe. As others have stated, 10^{45} 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^{58} 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^{58} moles of hydrogen. Multiply then by the Avogadro number, 6.02 × 10^{23} to get 9.5 × 10^{81} 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^{82} 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; 06192011 at 11:30 PM.. 
#8




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

#9




Quote:
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. 
#10




Quote:
The number of atomic particles in a trillion universes like our own woujld still fall short of a googol  1.n*10^{94} particles. It would take 100 quadrillion such universes to approach the googol mark. 
#11




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? 
#12




A tad offtopic, 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:

#13




Quote:
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. 
#14




Quote:
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 notdense the universe as a whole is, compared to things like planets. 
#15




But in a logarithmic sense, starting from protonlevel 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 halfway 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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Stringing Words Forum Aspiring writers and authors supporting each other. Goals and resolutions our particular specialty  also sharing commiseration and triumphs. Join today! Last edited by chrisk; 06202011 at 07:45 AM.. 
#16




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. 
#17




Quote:
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. 
#18




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#19




Well, naturally!

#20




Quote:
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The distance between 10^{45} and 10^{100} is enormously greater than any of the "unimaginable" distances that the OP gave. 
#21




You're missing their point.

#22




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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#24




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; 06212011 at 02:29 AM.. 
#25




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 electronpositron 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; 06212011 at 03:04 AM.. 
#26




The other problem is that one can produce an electronpositron pair, interact with and measure one of the pair, and then reannihilate them. That gives you an electron that definitely isn't just a slice of "the one electron".

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