# Electrons smaller than protons, but have equivalent charge

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I know that this is a very advanced question, but this was asked in my Chemistry II class today, and the teacher said that he did not know the answer, nor had he ever thought of the question. And so I was curious and wanted to ask this question to someone who knows chemistry and about protons and electrons better than I.

If electrons have a smaller mass than the proton, than how do they have the same charge?

I do know this, that charge is related to the quarks, and that up quarks have +2/3 charge, and down quarks have -1/3 charge. If an electron has -1 charge, than they would have to contain 3 down quarks. The proton has two up quarks and one down quark. Both have 3 total quarks, so why are they different masses? Are down quarks a different mass than up quarks? Is there more than quarks in the protons?

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Electrons aren't made of quarks at all. They are their own fundamental particle.

(In fact, look at the title over your photo box (and mine) "Lepton", which I guess means you haven't made many posts and the forum is comparing you to the most basic particle of the lot ;-) )

A quark is also fundamental as far as we know, so that's the two types: quarks and leptons.

I honestly don't know why electrons have exactly the same size charge as protons. I don't think it even comes out of the standard model of particle physics but I could be wrong. It's obviously not a coincidence.

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I actually just found that out by doing research, that the electrons are not made of quarks. Also, the fact that I am a Lepton on this site does not really apply to the fact that I am a noob on science, I just specialize more in Astrophysics, Nuclear Chemistry/Physics, and Quantum Mechanics, rather than Chemistry. I am also new to this site, which would explain why I am still a Lepton. I still don't know why the electron is way smaller, about 1/1,836 the size of a proton, and still hold the same charge.

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An electron has no size at all, at least according to the Standard Model. It's got ~1/1800 the mass of a proton though, as you said.

No-one knows why electrons and quarks have the mass they do as far as I know. The next lepton up, the muon, has a mass about 212 times the electron, and AFAIK no-one knows why.

Size is no guarantor of charge. Quarks, like leptons, are sizeless. So you've got a group of sizeless particles all with closely related charges (electron -1, up quark +2/3 etc.) and I don't think we've established the reason.

I Googled it and there seems to be some discussion about quantum gravity / complicated supersymmetry theories causing the charge correspondence but I'm ignorant of it.

And I didn't call you a noob ;-)

Edited by JonathanApps
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AFAIK, there is no connection between mass and charge of a particle. They are independent properties.

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Quarks give protons their charge, but what give electrons their charge? That is more of what I want to know, now that I know that electrons are not made of the same thing as protons. Also, something has to be in the electrons, they can't be just particles built out of nothing. Maybe the building blocks for down quarks?

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Also, something has to be in the electrons, they can't be just particles built out of nothing.

Why? Charge isn't a building block, it's a property. This is like saying something is *in* tallness, and all tall things have this "stuff" in them, rather than tallness being a property of something.

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If some particles are fundamental - which the electron seems to be in every experiment up to now - then they are not explained by constituents. This is equivalent to say that they are (or bear, who cares) a set of properties, among others the charge.

Mass and charge are independent up to the self-energy of the electric field, which means a minimum rest mass for a charged particle. Some theories tried to reduce the electron's rest mass to this electric self-energy, I believe they're abandoned.

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Quarks give protons their charge, but what give electrons their charge? That is more of what I want to know, now that I know that electrons are not made of the same thing as protons. Also, something has to be in the electrons, they can't be just particles built out of nothing. Maybe the building blocks for down quarks?

Down quark is decaying to up quark and electron and antineutrino:

$d \rightarrow u + e^- + \bar V_e$

It happens in neutron-rich nucleus, or bare neutron.

$n^0 \rightarrow p^+ + e^- + \bar V_e + 0.782 MeV$

(neutron has half-life ~10 minutes, and mean-life ~15 minutes)

The first isotope that's decaying this mode is Tritium (3rd isotope of Hydrogen, and the first unstable atom):

$T^+ \rightarrow _2^3He + e^- + \bar V_e + 18.6 keV$

(Tritium has half-life 12.32 years)

As you can easily see on the right side there is energy that varies depending on which isotope decayed. It's not constant. It's not even constant for electron and antineutrino. Once electron is accelerated more, other time reverse, and neutrino is taking more energy.

Don't be "fooled" that down quark is "made of" electron and up quark.

In proton-rich nucleus exactly reverse reaction happens:

$u \rightarrow d + e^+ + V_e$

Up quark is decaying to down quark, positron and neutrino.

f.e. Carbon-11 will decay to Boron-11, positron and neutrino:

$_6^{11}C \rightarrow _5^{11}B + e^+ + V_e + 0.960408 MeV$

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Down quark is decaying to up quark and electron and antineutrino:

$d \rightarrow u + e^- + \bar V_e$

It happens in neutron-rich nucleus, or bare neutron.

$n^0 \rightarrow p^+ + e^- + \bar V_e + 0.782 MeV$

(neutron has half-life ~10 minutes, and mean-life ~15 minutes)

The first isotope that's decaying this mode is Tritium (3rd isotope of Hydrogen, and the first unstable atom):

$T^+ \rightarrow _2^3He + e^- + \bar V_e + 18.6 keV$

(Tritium has half-life 12.32 years)

As you can easily see on the right side there is energy that varies depending on which isotope decayed. It's not constant. It's not even constant for electron and antineutrino. Once electron is accelerated more, other time reverse, and neutrino is taking more energy.

Don't be "fooled" that down quark is "made of" electron and up quark.

In proton-rich nucleus exactly reverse reaction happens:

$u \rightarrow d + e^+ + V_e$

Up quark is decaying to down quark, positron and neutrino.

f.e. Carbon-11 will decay to Boron-11, positron and neutrino:

$_6^{11}C \rightarrow _5^{11}B + e^+ + V_e + 0.960408 MeV$

So basically what you are saying is when a down quark decays, it produces an up quark, an electron, and an antineutrino. And when an up quark decays, it produces a down quark, and another electron and antineutrino. So from what we can tell, the up and down quarks must be made of a basic quark that when it decays, it changes form to the opposite quark while releasing some stored energy in the form of electrons and antineutrinos. Is that correct?

If so that would mean that we cannot tell what makes up the quarks at all.

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It's probably more helpful to think of fundamental, sizeless particles as waves or clouds rather than
billiard-ball-like objects, which is what I think you're doing.

An electron or quark in a usual state will be spread over a certain region of space. With an electron,
it's often spread over an atom, a region of size about 10^(-10)m. With a quark, we've only seen them
spread over the interior of a proton / neutron / meson, a region of size about 10^(-15)m.

In fact (and this is Quantum Mechanics here - you'll have to accept it's weird), at least an electron
can be distributed over a much larger volume in some circumstances. You could put it in a box
of size 1 mile x 1 mile x 1 mile and the electron "cloud" would be spread over this 1 mile^3 volume.

But this is not what we mean by "size" in this discussion. Here, "size" means the MINIMUM SIZE
WE CAN GET IT DOWN TO. With an electron or quark THIS IS IN THEORY LIMITLESS.

What this means is that by measuring its position accurately enough, we could in theory reduce that
cloud / wave / whatever you call it down to a size of, say, 10^(-30)m or even smaller. (We can't actually do this
because we don't have accurate enough instruments).

So, in fact, what you'll get from the above if you read it carefully is the following:

***Measurement of a particle to within an accuracy of distance d will reduce the size of its cloud
to that distance.***

If you think about that, it's VERY weird. But that's Quantum Mechanics for you. In general, measuring
some characteristic of a particle will cause it to have a definite value of that characteristic where
before the value was not definite.

Another example is energy. A particle could be in a state where it has 2 energies at once, E1 and E2.
(Yes that's even weirder - it's Quantum Mechanics). If we then measure the energy, it will change
to having a definite energy, either E1 or E2. (Which one we get is as far as we know totally random).

This is getting long so I'll stop there but I hope that gives some idea of what "size" means in
Quantum Mechanics. As many have said, if QM doesn't shock you, you haven't understood it.

Jonathan

Edited by JonathanApps
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It's probably more helpful to think of fundamental, sizeless particles as waves or clouds rather than

billiard-ball-like objects, which is what I think you're doing.

An electron or quark in a usual state will be spread over a certain region of space. With an electron,

it's often spread over an atom, a region of size about 10^(-10)m. With a quark, we've only seen them

spread over the interior of a proton / neutron / meson, a region of size about 10^(-15)m.

In fact (and this is Quantum Mechanics here - you'll have to accept it's weird), at least an electron

can be distributed over a much larger volume in some circumstances. You could put it in a box

of size 1 mile x 1 mile x 1 mile and the electron "cloud" would be spread over this 1 mile^3 volume.

But this is not what we mean by "size" in this discussion. Here, "size" means the MINIMUM SIZE

WE CAN GET IT DOWN TO. With an electron or quark THIS IS IN THEORY LIMITLESS.

There's also the view of "over what extent is the charge confined" which is important in certain interactions, and not quite the same as measuring the actual location of the electron. And such experiments put a seriously small upper limit on the size of the electron, and that's assuming all experimental error is actually an artifact of the electron having a size.

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So basically what you are saying is when a down quark decays, it produces an up quark, an electron, and an anti-neutrino.

Correct.

And when an up quark decays, it produces a down quark, and another electron and antineutrino.

No.

It produces down-quark, positron and neutrino.

Positron is anti-particle of electron (opposite positive charge).

Neutrino is anti-particle of anti-neutrino (or vice versa).

This happens *exclusively* in proton-rich nucleus.

If particle and anti-particle meet together, they annihilate. Which for positron and electron means that 2 or more gamma photons will be created in their place.

Edited by Sensei
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-So basically what you are saying is when a down quark decays, it produces an up quark, an electron, and an anti-neutrino.

Correct.

-And when an up quark decays, it produces a down quark, and another electron and antineutrino.

No.

It produces down-quark, positron and neutrino.

Positron is anti-particle of electron (opposite positive charge).

Neutrino is anti-particle of anti-neutrino (or vice versa).

This happens *exclusively* in proton-rich nucleus.

If particle and anti-particle meet together, they annihilate. Which for positron and electron means that 2 or more gamma photons will be created in their place.

I understand now, thank you for your help.

An electron or quark in a usual state will be spread over a certain region of space. With an electron,

it's often spread over an atom, a region of size about 10^(-10)m. With a quark, we've only seen them

spread over the interior of a proton / neutron / meson, a region of size about 10^(-15)m.

In fact (and this is Quantum Mechanics here - you'll have to accept it's weird), at least an electron

can be distributed over a much larger volume in some circumstances. You could put it in a box

of size 1 mile x 1 mile x 1 mile and the electron "cloud" would be spread over this 1 mile^3 volume.

But this is not what we mean by "size" in this discussion. Here, "size" means the MINIMUM SIZE

WE CAN GET IT DOWN TO. With an electron or quark THIS IS IN THEORY LIMITLESS.

What this means is that by measuring its position accurately enough, we could in theory reduce that

cloud / wave / whatever you call it down to a size of, say, 10^(-30)m or even smaller. (We can't actually do this

because we don't have accurate enough instruments).

So, in fact, what you'll get from the above if you read it carefully is the following:

***Measurement of a particle to within an accuracy of distance d will reduce the size of its cloud

to that distance.***

I understand Quantum Mechanics pretty well and understand what you are saying, but I am not necessarily referring to the electron cloud, as I know that can be limitless in size, I was wondering about the size of the electron itself, which I understand that it is not a definite size, but I know that it cannot be massively large.

It's probably more helpful to think of fundamental, sizeless particles as waves or clouds rather than

billiard-ball-like objects, which is what I think you're doing.

No, I understand that an electron is a cloud-like object.

Another thing that may tie into this is the fact that energy combined with energy yields matter, and matter split apart yields energy. So therefore, if matter is composed of energy, energy must exist as some form of matter, and probably be the constructor of electrons and positrons. I would assume that it would exist as strings as stated in the String Theory which would allow them to also exist as a wave of energy, while being matter. Does anyone understand what I am saying and is this a possibility, or is there evidence that would contradict this? Yes I do know that this is a different matter, but it can help in my understanding of the Atomic Theory better.

If particle and anti-particle meet together, they annihilate. Which for positron and electron means that 2 or more gamma photons will be created in their place.

I understand this very well, as I have done quite a bit of research on anti-matter and believe in the future of antimatter used to create energy for the earth's energy demands.

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Hi

Well, in your OP you claim that 'electron' is lighter than 'proton'. Right, but it doesn't make your topic sentence correct. No one can claim electrons are smaller than protons.

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No one can claim electrons are smaller than protons.

Of course anybody can claim that. But have to prove it in experiment.. And it's different story.

You should have open mind for any new experimental evidence that might come up in the future.

Edited by Sensei
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Hi

Well, in your OP you claim that 'electron' is lighter than 'proton'. Right, but it doesn't make your topic sentence correct. No one can claim electrons are smaller than protons.

I could claim that electrons are smaller than protons. For this reason - that protons are "composite" objects. Each proton is made of a Down-quark, and a pair of Up-quarks. That's three components.

Whereas, an electron isn't "composite". It has only one component - itself.

Now, it seems to me, that even if the components are "point-like", an object with only one such component (such as an electron), is bound to be smaller than an object with three of them (such as a proton).

After all, when we talk of of "point-like" components , surely we don't mean they have zero-dimensions. If they had, they'd have no physical existence. We mean they're just very small, like a "."

If so, then an electron which is just . is clearly smaller than a proton, which is ...

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Is it possible that the string theory is tied into this at all? Could the components of electrons, positrons, and neutrinos possibly be strings of energy? I would think this could be so because if energy is combined it produces matter and antimatter, so therefore, energy must be some form of matter that can be a wave at the same time, so I would assume they could be a string. Could this be possible?

I only ask these questions because I think of them in my chemistry class and my chemistry teacher can't answer them, and I am trying to simply connect the dots to get the answers to the questions I think of.

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Hi Dekan,

Of course you claim, but no proof. What do we know about the exact size of protons and electrons? Even quarks? Do they indeed have the so-called exact size? Is it even right to address 'em bigger or lesser? Points, waves or tiny bunches of energy?

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Hi Dekan,

Of course you claim, but no proof. What do we know about the exact size of protons and electrons?

We have the result of experiments.

The proton's charge radius is about 0.877 fm; there's some controversy about this because muonic hydrogen experiments give ~5% smaller results than normal hydrogen with very high precision

electrons are at least a thousand times smaller, with r < 10-18 m; that's an upper bound limited by experiment, not a lower bound — the result is consistent with zero

http://gabrielse.physics.harvard.edu/gabrielse/overviews/ElectronSubstructure/ElectronSubstructure.html

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So,

We have the result of experiments.

The proton's charge radius is about 0.877 fm; there's some controversy about this because muonic hydrogen experiments give ~5% smaller results than normal hydrogen with very high precision

electrons are at least a thousand times smaller, with r < 10-18 m; that's an upper bound limited by experiment, not a lower bound — the result is consistent with zero

http://gabrielse.physics.harvard.edu/gabrielse/overviews/ElectronSubstructure/ElectronSubstructure.html

So the proton is experimentally shown to be bigger than the electron?

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So,

So the proton is experimentally shown to be bigger than the electron?

If by size you mean the charge radius, yes.

As has been explained earlier, though, "size" is not well-defined in QM — there are a number of ways one might interpret it, and context matters.

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So,

We have the result of experiments.

The proton's charge radius is about 0.877 fm; there's some controversy about this because muonic hydrogen experiments give ~5% smaller results than normal hydrogen with very high precision

electrons are at least a thousand times smaller, with r < 10-18 m; that's an upper bound limited by experiment, not a lower bound — the result is consistent with zero

http://gabrielse.physics.harvard.edu/gabrielse/overviews/ElectronSubstructure/ElectronSubstructure.html

So the proton is experimentally shown to be bigger than the electron?

If by size you mean the charge radius, yes.

As has been explained earlier, though, "size" is not well-defined in QM — there are a number of ways one might interpret it, and context matters.

So therefore, what you are saying is that the electron's physical radius is not known, and as far as we know, they can be huge or minuscule. We can only determine how big the charge stretches around the electron, and that appears to be about 1,836 times smaller than that of a proton. Am I correct?

I think that most of my questions that I have asked are answered, but still, I don't see what makes up electrons and quarks, but I believe that the answer to that is unknown at this time, as it appears that nothing can give me a definite answer on this.

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So therefore, what you are saying is that the electron's physical radius is not known, and as far as we know, they can be huge or minuscule. We can only determine how big the charge stretches around the electron, and that appears to be about 1,836 times smaller than that of a proton. Am I correct?

Since the predominant method of interaction with the electron is electrostatically, where its charge is the important "size" factor, at least for such interactions. I don't know what is meant by a "physical" radius; I don't know that it has meaning. The electron is not a little billiard ball.

The EDM experiment I linked to tells us the electron is not actually sampling the field over a large area. Not knowing where it is is not the same thing as saying it's big.

The factor if 1836 is the mass ratio, not the charge radius ratio. The electron's charge radius is much likely significantly smaller than the upper bound given by experiment.

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Since the predominant method of interaction with the electron is electrostatically, where its charge is the important "size" factor, at least for such interactions. I don't know what is meant by a "physical" radius; I don't know that it has meaning. The electron is not a little billiard ball.

The EDM experiment I linked to tells us the electron is not actually sampling the field over a large area. Not knowing where it is is not the same thing as saying it's big.

The factor if 1836 is the mass ratio, not the charge radius ratio. The electron's charge radius is much likely significantly smaller than the upper bound given by experiment.

By physical radius, I mean it's physical size, which would probably be best to measure in mass. So therefore, the electron has about 1/1836 mass of a proton, not it's charge radius. Correct?

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