What Does a Coulomb Look Like - What 'Size' is It?

Coulomb, not coulpmb. A Coulomb represents a number of electrons - in fact 6.241509×10¹⁸ electrons. Just as gallons of water per minute could also be defined as a number of water molecules per minute. Have to say that the units of the latter would be rather cumbersome.

Thanks Energyconversion #1

That makes sense. But I assume it has 'size' as well. The radius of an electron (a number of theoretical radii to choose from it seems) but say 2.82 x 10^-15 m means 1 electron has a volume of 93.94 x10^-45 m³ (that seems quite small to me).

So 1 coulomb must be 6.24 x 10¹⁸ larger I guess - and still pretty small.

Yes - rather cumbersome.

An interesting thing is that from an electrochemical viewpoint a coulomb is quite a small unit, it takes around 10⁵ of them (1 faraday) to deposit 1 gm.equivalent of a substance in electrolysis. But from an electrostatic viewpoint, if 2 coulombs are placed 1m apart the force of repulsion is about 9 million tonnes!

It has to do (I think) with mass-energy equivalence, E = m*c². If Maxwell's equations are written using Gaussian units, c is in there.

Actually there is discussions now that an electron may really be a point source charge with actually no volume instead of the previously supposed virtually no volume. All of the techniques used to try and measure the size of these tiny, near zero rest mass (very easy to move) particles that transfer the most common force to the other tangible objects in our macroscopic world all actually say that the measured size is less than the resolution of the experiment. This concept is buried in the Wikipedia article on the electron.

96,485.3399 Coulombs are required to convert one mole of protons to hydrogen (if the system was 100% electrode efficiency), which no system is at this point, however other systems such as plating silver onto a rotating grid do approach unit electron efficiency.

96,485.3399 coulombs = 1 Faraday (F) and will deposit some 107.868 grams silver on a cathode(or very nearly so). In that case it becomes somewhat palpable.

1 Coulomb is equivalent to 0.00112 grams of silver deposited, still a bit hard to weigh on your scales.

"6.0221413e+23 = Avogadro's constant = the number of electrons in a coulomb."

Avogado's number can be used to calculate the number of electrons/charge carriers in a Coulomb, but the answer is not the same number as above.

One Coulomb = 1.036 X Avogrado's number X 10e-5 = 6.241e+18 electrons.

That's right, and Avogadro's number 6*10²³*electron charge 1.6*10^-19C ~ 10⁵C = 1 faraday. IMHO it complicates things to bring Avogadro into number of electrons in 1 coulomb. It's just 1/electron charge ~ 6.25¹⁸.

Avogadro's Number is the number of atoms or molecules in 1 gram-atom or 1 gram-mole of a substance, not the number of electrons in a coulomb.

Like an omb with sunglasses on! And we all know size doesn't matter!

I remember a party in the old college days that we all saw coulombulonimbus clouds floating up in the sky.

Nicely put. A GA vote from me.

I would prefer you used photons rather than protons..it's a question of association when filing in memory for future use. In this case "charge of the light brigade" (photons) as opposed to 6241 quadrillion protons= an indeterminate herd of buffalo, 130 Giraffe and 11 assorted-size turtles sans shells). Don't argue with the math.'....indeterminate' could signify a fraction or multiple of 6241 quadrillion.

I suppose this is a joke? Photons have no electric charge. I don't use quadrillion too often, but it's OK. 6241 quadrillion = 6241*10¹⁵ = 6.241*10¹⁸ electrons per coulomb.

To spades #6. Thanks for the explanation.

But taken a step further, I am trying to picture in my minds eye, what a coulomb looks like, and I can visualize lots of electrons (or proton or whatever) as 'objects' or 'things' similar to imagining air which is invisible to the naked eye.

But these 'things' have 'size' and therefore occupy a 'volume', and being a volume I suppose it could be expressed as a litre or CC or something. I am trying to work out what the volume is - or an approximation to it. I tried myself but the numbers +/- are so large I can't get my head round them. I could be millions out and not realize it.

The experts who are at home in this micro-world might help put things in perspective, but it's no big issue so don't waste any much time on it.

Thanks to all posters. Even the off-topic (which to my mind are not off-topic).

Well stated.

I would only add that a coulomb doesn't necessarily have any volume at all.

It is a measure of charge only, not the electrons, protons or positrons that may produce that charge. It has no physical dimensions.

Agreed!

Well, Spades #28, thanks for that, but trying to 'picture what is flowing, doesn't the charge have to be accompanied by the electrons causing the charge and therefore associated with an appropriate volume to hold the particles.

Albeit that if the electron has no volume itself, I imaging it has a space all to itself in which to exert it's charge, and it is this space that manifests itself as a volume.

Or should I stop trying to imagine a volume, and think more along the lines of the 'smile' of Lewis Carrol's Cheshire Cat - or a bar magnet with only one pole.

Not every attribute of matter occupies a volume of space. The amount and polarity of charge an item has takes no more or less space than that item with no net charge. This is like expecting the car that costs more to buy must be heavier than the cheaper car.

Magnified....not to scale....

If you have a 5 volt supply, 5 Coulombs will fit in here...

Using Wikipedia, which is universally accepted as all-knowing and correct, I find this value for the volume of an electron: 9.4×10^-44 m³.

Assuming my math is correct, I believe it would take a 1 Amp current 54 trillion years to provide enough electrons to fill a volume of 1 cm². Substitute protons for electrons and it would take only 339 million years to fill a volume of 1 cm³. For comparison on the time involved, the age of the Universe is estimated to be between 6,000 and 14 billion years.

That's calculated from the classical electron radius of an electron. The Wikipedia internal link states:

In simple terms, the classical electron radius is roughly the size the electron would need to have for its mass to be completely due to its electrostatic potential energy - not taking quantum mechanics into account. We now know that quantum mechanics, indeed quantum field theory, is needed to understand the behavior of electrons at such short distance scales, thus the classical electron radius is no longer regarded as the actual size of an electron. Still, the classical electron radius is used in modern classical-limit theories involving the electron, such as non-relativistic Thomson scattering and the relativistic Klein-Nishina formula. Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics.

I know, it is really weird to think that a particle could not have any volume but quantum mechanics is really weird.

OK, so I used an overestimated radius. Add a few trillion years to the estimate. And, in the interest in clarity, I ignored leap days and used 365 as the number of days in a year, so we should also shave a some years off the estimate, too.

Not only that, it would take all the superconducting Unobtainium in the known universe to contain that quantity of charge. Your calculation would also violate Heisenberg's Uncertainty limit in the sense that confining the position of each electron that tightly would allow the energy to be completely uncertain, meaning that each electron may have all the energy in the known universe, or a certain approximation of it.

The calculation still does not explain to the OP how many Coulombs would be contained in 1 cm³, and the units you used refer to a "volume of 1 cm²".

Typo on my part. I meant to reduce everything to one cubic centimeter (cm³).

Since I am violating so many limits and principles, that may explain why it would take more than the age of the Universe to accomplish this feat. I thought I was working toward the OP's challenge to visualize a coulomb. I couldn't think of a one coulomb example, so I thought I'd change it slightly. I can visualize a volume of one cm³. If I filled that one cm³ at the rate of one coulomb per second (that is, one ampere), how long would that take? What size is a coulomb? Small enough it would take an unimaginable amount of time to gather enough of them into a small space.

You are telling me that this much charge in this small a volume would be astounding even to people possessing flux capacitors and dilithium crystals. (I'm just an idea man, let the experimental physics guys worry about how to build the lab equipment to demonstrate this idea.) I think it is very interesting this raises the points you make. Would it be possible to find such a dense concentration of charge in a black hole? Or is that singularity essentially volumeless, too?

Also, I understand (and I use the word understand very loosely, perhaps with a definition unique to me) that quantumly speaking, an electron is a point without volume. But then I look at myself and marvel about how much volume I occupy considering I am composed of quantumnesses of zero or infinitesimal volumes.

To Reward #54. In an abstract sense your typo could be right, because if the charge had no size then the volume might well be 1 m², or would it be 1 m¹, or even 1 m⁰. But why stop there, why not 1 m^-1 ....and so on ...1 m^-n

Sorry, I've wandered off into one of my goon moments........

Redfred and others are only trying to help, and here's me appearing to make fun of the answers. Sorry.

But on a serious not, these goon sessions can take you on a lateral thinking journey and get you out of the vertical thinking rut - sometimes

On a completely serious note this is a difficult topic to grasp and accept. We are use to the laws and conditions that make up our macroscopic world, the idea that these rules no longer apply when one gets really, really tiny in scale is disturbing. The idea that the macroscopic rules and concepts are completely meaningless once one gets this tiny seriously disturbs our rational psyche. Particularly when one realizes that our macroscopic world perceptions relies on these quantum interactions to collect into the macroscopic interactions we accept as normal.

Consider this: If you place protons into the spaces of a metal lattice (you may allow them to hold one electron each if you wish), and the lattice interactions are so well-defined that there is virtually no uncertainty in the proton position, then the proton can have complete uncertainity in momentum (meaning: the proton can have whatever energy is necessary or convenient to have). This allows the proton to have sufficient energy to capture an electron, and become a "free", zero momentum neutron (cold neutron), and also for the next proton over to capture this neutron and become a deuteron, and so on, until ⁴H (highly unstable 4 a.m.u. hydrogen) is made, and this emits a β particle to become He), as proposed by Brillouin Energy's reactor they are working on that uses Q pulse compression/rarefaction of the crystal lattice of Nickel metal to achieve their effects. It think this is absolutely brilliant, and very hopeful. By the way, they may be nearer to going commercial than you think. I believe the company literature stated that they will go commercial when the COP reaches a factor of 3 relative to energy input total.

Free electrons have wave-particle duality, just as these do when bound by an atom/ion. ΔzΔp~h/2π (Heisenberg Uncertainty Limit). Note also that by stuffing all these electrons into 1 cm³, one would produce the highest potential (voltage) ever seen, therefore all would leak out in one giant bolt of lightning.

I showed people the equivalent of one coulomb in terms of the amount of silver deposited on an electrode wire, as approximately 1 mg, but that answer was mostly ignored.

I am not a physicist, so this may not be accurate or makes sense.

I recall hearing about some test where a theory regarding where an electron is. The theory said that an electron shows up somewhere, because we think it should be there. Maybe it is tied to the energy we put out and since the electron is such a small particle, we can make it show up where we want it to.

So, if this is correct, then trying to measure the size of X number of electrons could be as easy as willing them into a location or it could be that our minds are not complex enough to control the location of 10^23 electrons.

Or, this could be a completely moot point, because I'm wrong about the theory I stated above???

This is an interesting conversation. May I ask a few questions ?

1. How was it determined that there are 6241 trillion electrons in a caulomb ?

2. Who made this discovery ?

3. In a semiconductor, what is inside of the holes ?

Google Michael Faraday, Lord Kelvin, and Sir Isaac Newton, and Benjamin Franklin. You will begin to understand. You might also was to Google Mr. Avogadro and his number, and it is not 666.

1. How was it determined that there are 6241 trillion electrons in a coulomb?

It wasn't. There are 6241 quadrillion = 6241*10¹⁵ = 6.241*10¹⁸ electrons per coulomb.

Good job in pointing out the distinction between what was done classically, and what was done later to demonstrate the quantum world.