# How do we know the mass of an electron?

Fr0stBite
I've been researching the proof of subatomic particles given the fact that we have never seen them before. It has always been recognized that protons, electrons, and neutrons exist; but I question how we know for certain they exist.

Across my studying I've realized that in 1897, J. J. Thompson used the Cathode Ray Tube experiment to confirm there are substances smaller than atoms. My question throughout researching the Cathode Ray Tube experiment was, "How did he prove the mass of the observed substance?" to verify it is indeed smaller than an atom.

Now I know the experiment consisted of a Cathode (said to have negative charge) and an Anode (said to have a positive charge). For some unknown reasoning to my understanding, like charges oppose each other and opposite charges attract each other. A capacitor (stores charge) in the form of a battery is connected to its correlating charges to the Cathode and Anode. The air between the two have been either vacuumed or replaced with a gas that can be ionized. With a hole in the anode and a fluorescent material against the end of tube, a "Cathode Ray" can be observed.

We know from the experiment the "Cathode Ray" was interfered by a magnet and also an induced electromagnetic force through two plates and another capacitor. By measuring the "Cathode Ray's" change in direction with the increase in voltage, the charge-to-mass ratio can be found. And because of this ratio, the "Cathode Ray" is said to be x1000 smaller than Hydrogen.

In order to have the charge to mass ratio (q/m), you have to know the charge and the mass of the "Cathode Ray." Now what exactly charge is, is still a mystery to me but I understand the force between two charges is calculated through Coulombs Law (1785). The formula is: F = ke q1q2/ r² where F= Force, ke= Coulomb's constant, q1= a charge, q2= another charge, and r²= distance between charges squared.

While dissecting this formula so many questions are raised. Where does Coulombs constant come from? Did he just pulled it out from his arse? I know Coulombs constant is
≈ 9×10∧9 N⋅m∧2⋅C∧−2; But why? I was taught to just use the constant but not "Why?" the constant.

To get the Force (F) we have to know the charges (q1 & q2). In most Coulombs Law problems in academics, the charge is given usually in μC. Where did they get that number from though?

Let's just say Thompson somehow did indeed find the charge. What is the mass? According to KNewton's 2nd Law (Which I have so may questions about) F = m*a which means m = F/a (Axiom of equality allows you to rearrange formulas) where m = mass, F = force, and a = acceleration. How can Thompson know the acceleration that is moving near the speed of light to calculate its mass in order to know it's 1,000 times lighter than hydrogen?

Lastly, How do we accurately know the weight of a hydrogen atom since we cannot isolate a single atom by itself? From my understanding it went like this: We put the same volume of hydrogen to helium and weighed them. Weight times density = mass. Since we know the difference in mass per the same volume of gasses we reduced to the lowest possible point and called this a single hydrogen atom? We know it takes the double volume of hydrogen to equal the mass in helium so that means helium is twice as large as hydrogen. But how do we know for certain that the volume is filled with 100% hydrogen atoms when we cannot physically see them? Perhaps it is natural for a true hydrogen to bond with another atom and we just call this combined atom hydrogen. Regardless, because weighing other substances to hydrogen we know that hydrogen has been the lightest so we gave a single hydrogen atom with the value of 1, as in 1 proton. If we found a substance lighter than hydrogen we would be quick to claim it is subatomic because no element can be smaller than hydrogen. But what if we did the same thing between hydrogen and the new substance and got the same results as between helium and hydrogen? Would we consider the new substance to have one proton and shift all elements down in the periodic table of elements?

Now taking the above from my research I found that we compared the mass of the "Cathode Ray" somehow with the mass of the element hydrogen and found it was 1,000 times smaller.

Why does the air between the electrodes have to be vacuumed?

Notes:
*Charge - a term used to represent a force between "particles."
*My opinion doesn't matter to Science (and rightfully so... That is why I love it so much), but I do not think particles exist only waves or energy. Thompson was trying to measure a point on the wave and that point is identified as a "particle" called "electron."
*Please forgive me for being all over the place and lack of understanding. My highest degree of education is high school, and even then, I slacked off badly. I aspire to attend university at Georgia Tech. but I must discipline myself to be well-rounded before attending. I am trying hard to grasp these concepts but information is vague in the areas I am seeking detail, so I am turning to the Scientific Community, you guys, for help.
*If you are curious on where I am sourcing, please drop a response for a specific area in which you seek a source.
*Keep in mind Wikipedia is said to be an unreliable source but I disagree at times. If people would just consider that majority of wiki pages have a reference tab which sites the information provided.

Questions I will be asking in the future:
• Can only certain elements be considered potential Cathodes-- and if so, Why?
• Why do we assume all electrons are equal in size with other electrons? Likewise, Why do we assume protons and neutrons are equal in size?
• What makes something fluorescent?
• How did we conclude Hydrogen has only 1 proton?
• Why does air affect the properties of atoms?

• • Delta2 and weirdoguy

Homework Helper
Where does Coulombs constant come from?
It is a constant of proportionality. Once you decide on a unit for charge, a unit for force and a unit for distance, Coulomb's constant is a measurable quantity. The fact of the proportionality is arguably the important bit. The value of the constant is an experimental detail.

It works better if you ask one question at a time and keep those questions focused.

• Lots of questions, and I won't begin to answer all of them. But one suggestion is for you to research the Millikan oil drop experiment. This showed that electric charge comes in discrete units, and measured the charge on a single electron. Since the charge/mass ratio was known, this allowed one to calculate the electron mass. This also allowed one to calculate how many atoms were in a mole of a substance (I'll let you read about how), which allowed one to calculate the mass of an individual atom.

• jtbell, vanhees71 and jbriggs444
Mentor
Then please do not make such broad multi-part questions. Make one question and you will get one reply. I do not feel it is reasonable of you to ask the question in the form that you did and then make this demand of respondents. With a question like you asked some people will respond to one point and some will respond to multiple points, you should be content to accept both. You invited both.

I understand the force between two charges is calculated through Coulombs Law (1785). The formula is: F = ke q1q2/ r² where F= Force, ke= Coulomb's constant, q1= a charge, q2= another charge, and r²= distance between charges squared.

While dissecting this formula so many questions are raised. Where does Coulombs constant come from?
It is experimentally determined. You basically use a known pair of charges separated by a known distance and measure the force. Then you put those known and measured values into Coulomb's law and solve for the constant. Of course, the constant shows up in other equations so you can base experiments off of other principles as well.

Lastly, How do we accurately know the weight of a hydrogen atom since we cannot isolate a single atom by itself? From my understanding it went like this: We put the same volume of hydrogen to helium and weighed them. Weight times density = mass.
High precision measurement of atomic masses typically involve ionizing the atoms, then sending them through a Penning trap which essentially traps them in a strong magnetic field where they rotate in a circular path. The frequency of their rotation is a function of the charge, mass, and field strength. The field strength is known, as is the charge, so we solve for the mass.

http://www-ap.gsi.de/research/posters/isoltrap/

• QuantumQuest, vanhees71, Asymptotic and 1 other person
Fr0stBite
It is a constant of proportionality. Once you decide on a unit for charge, a unit for force and a unit for distance, Coulomb's constant is a measurable quantity. The fact of the proportionality is arguably the important bit. The value of the constant is an experimental detail.

So it was decided that the standard unit for charge is Coulombs, for Force is KNewtons, and for distance is Metres. I understand the concept of units being assigned to a value.

When you say it is, "an experimental detail" what exactly does that mean?

Thank you for your previous response, btw.

Fr0stBite
Then please do not make such broad multi-part questions. Make one question and you will get one reply. I do not feel it is reasonable of you to ask the question in the form that you did and then make this demand of respondents. With a question like you asked some people will respond to one point and some will respond to multiple points, you should be content to accept both. You invited both.

I see what you are saying and I agree. My reasoning behind what I said is just that these are concepts I assume you understand, so it is not a knowledge burden for me to summarize everything in one post. As for your responses though, in order for me to comprehend and grasp concepts I would need to try and understand one at a time little by little.

You are ultimately correct though at an objective viewpoint.

It is experimentally determined. You basically use a known pair of charges separated by a known distance and measure the force. Then you put those known and measured values into Coulomb's law and solve for the constant. Of course, the constant shows up in other equations so you can base experiments off of other principles as well.

"It is experimentally determined." Yes, but how? I take it the continuation of this reply is the how... "Known pair of charges," I thought charges are determined through Coulombs in the units of Coulombs? So how can a person know the amount of charge in order to come up with Coulombs Law without Coulombs Law?

Okay let me digress-- So you come up with the amount of charge between two charges, and you know the force applied to them, and you know the distance between the two charges; How does this create a constant proportion that is applied in order to determine Force in any other two charges?

So let's say for simplicity that the two charges both equal one Coulomb, and the Force applied to them is one KNewton, and the distance between them is 1 Metre; (F = ke q1q2/ r² is Coulombs Law, so ke = r² F / q1 q2 is to find the constant using Colombs Law) That would mean the constant is 1²Metres*1KNewton / 1Coulomb * 1 Coulomb. Is this correct? So Coulombs Constant is an arbitrary variable that was inserted to prove the validity of itself?

"The constant shows up in other equations so you can base experiments off of other principles as well."What is an example of this?

Thanks for all your help in making these things clearer!

Homework Helper
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That would mean the constant is 1²Metres*1KNewton / 1Coulomb * 1 Coulomb. Is this correct? So Coulombs Constant is an arbitrary variable that was inserted to prove the validity of itself?

Physics, unlike maths, can't be proved. You come up with a theory (you "guess", as Feyman put it), then you check whether your guess fits the experimental data.

The idea that the force between two charges is always ##F = \frac{kq_1q_2}{r^2}##, where ##k## is some constant, was originally an inspired guess or an insight or deduced from known experiments. You can't prove this. Coulomb's law is a postulate of classic electromagnetism.

Note that you could always choose units where ##k = 1##, which is what happened for ##F = ma## (in SI units). But, this means that for SI units ##k \ne 1## for Coulomb's law.

You might like to watch Feyman's first "messenger" lecture. In fact, I think they are all worth watching.

• QuantumQuest and vanhees71
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PS This one on "seeking new laws" was actually the one I was thinking about:

• vanhees71
Gold Member
I thought charges are determined through Coulombs in the units of Coulombs? So how can a person know the amount of charge in order to come up with Coulombs Law without Coulombs Law?

You are confusing the notion of measuring with the notion of calibrating.

All you need is a device for comparing the amount of charge on different objects. You could do this with, for example, an electroscope. You need know nothing about coulombs of charge to be able to measure and conclude that one object has, for example, twice as much charge as another object. Later, once you establish a relationship like Coulomb's Law, you define, for example, one unit of charge to be the amount of charge on each of two objects needed to create a force of one Newton when the objects are separated by one metre of distance. Now you are calibrating your measuring device.

Okay let me digress-- So you come up with the amount of charge between two charges, and you know the force applied to them, and you know the distance between the two charges; How does this create a constant proportion that is applied in order to determine Force in any other two charges?

If each of the two objects has a charge of one coulomb, and they are separated by one metre, then the force they exert on each other is about ##9 \times 10^9## Newtons. That number, ##9 \times 10^9 \ \mathrm{\frac{N m^2}{C^2}}##, is your constant of proportionality. If you were to measure force or charge in different units then the constant of proportionality would have a different value.

You can then use this constant of proportionality to determine, for example, what the force would be between any two objects with any amount of charge that are separated by any amount of distance.

This last part is what you learn to do in an introductory physics course. Your questions are about the underlying philosophy, and that may have been left out by your instructor. Or it may be, as is usually the case, that knowing the philosophy is not needed to answer the test questions, so it is ignored.

Staff Emeritus
Where does Coulombs constant come from? Did he just pulled it out from his arse?

So Coulombs Constant is an arbitrary variable that was inserted to prove the validity of itself?

You are coming across as hostile. Given that, by your own admission, you don't know this stuff, maybe you should tone it down a bit.

I can define a unit of charge by a current for a given time. I can go to a laboratory and determine that the force between charges is proportional to each charge and inversely proportional to the square of the distance between them. The constant of proportionality is measured at the same time and the numeric value depends on my units: I get 9 x 109 Nm2 kg m2 A-2 s-4, but I would get a different number if I measured (e.g) time in minutes and length in miles.

• sophiecentaur, QuantumQuest, jim mcnamara and 1 other person
Gold Member
Summary: How is comparing a "Cathode Ray" to Hydrogen prove the mass of an electron?

How did we conclude Hydrogen has only 1 proton?
Research atomic weight and atomic number. Some basic high school physics / chemistry texts might help. It's interesting that deuterium and tritium are two isotopes of hydrogen which have extra neutron(s) so they weigh different amounts, roughly 2 and 3 times as much.

• vanhees71
Mentor
So how can a person know the amount of charge in order to come up with Coulombs Law without Coulombs Law?
Previously you would measure the current as it goes onto a capacitor. Nowadays you would just count electrons.

So you come up with the amount of charge between two charges, and you know the force applied to them, and you know the distance between the two charges; How does this create a constant proportion that is applied in order to determine Force in any other two charges?
Actually, it is a little more than that. What you do is you vary the scenario. You double one charge, and see that the force doubles. You double the other charge and see that the force doubles. You double both charges and see that the force quadruples. You double the distance and see that the force decreases by a factor of four. You test as many different variations of this experiment as possible. Once you have the data then you do statistics to fit the data to the model and find the value of k that minimizes the error for your fit between the data and your model. If you have more than one possible model (which you always do at the beginning) then you compare the models to see which is most accurate.

So Coulombs Constant is an arbitrary variable that was inserted to prove the validity of itself?
Not sure where you are getting a conclusion like that.

What is an example of this?

Thanks for all your help in making these things clearer!
You are welcome! Other equations include the potential energy between two charges and the vacuum permittivity

Fr0stBite
You might like to watch Feyman's first "messenger" lecture. In fact, I think they are all worth watching.

Thank you for making things a little bit clearer. I watched the first video you mentioned and now I'm on to the second. I am soaking it all up like a sponge.

• vanhees71 and PeroK
Gold Member
You are coming across as hostile. Given that, by your own admission, you don't know this stuff, maybe you should tone it down a bit.
I agree totally with this. The OP manages to sound very cross about his not knowing things. The solution to his (it won't be a her) problem is to follow a good course in Physics and then to argue with some of it if and when, having found out enough, he feels the need.
You have to read a book to be able to discuss the plot.

Fr0stBite
You are confusing the notion of measuring with the notion of calibrating.

All you need is a device for comparing the amount of charge on different objects. You could do this with, for example, an electroscope. You need know nothing about coulombs of charge to be able to measure and conclude that one object has, for example, twice as much charge as another object. Later, once you establish a relationship like Coulomb's Law, you define, for example, one unit of charge to be the amount of charge on each of two objects needed to create a force of one Newton when the objects are separated by one metre of distance. Now you are calibrating your measuring device.

If each of the two objects has a charge of one coulomb, and they are separated by one metre, then the force they exert on each other is about ##9 \times 10^9## Newtons. That number, ##9 \times 10^9 \ \mathrm{\frac{N m^2}{C^2}}##, is your constant of proportionality. If you were to measure force or charge in different units then the constant of proportionality would have a different value.

You can then use this constant of proportionality to determine, for example, what the force would be between any two objects with any amount of charge that are separated by any amount of distance.

This last part is what you learn to do in an introductory physics course. Your questions are about the underlying philosophy, and that may have been left out by your instructor. Or it may be, as is usually the case, that knowing the philosophy is not needed to answer the test questions, so it is ignored.

I love the way you have explained everything. It took me time to understand what is being said but I think I grasp it now. The only part I'm stumped on is ## \ \mathrm{\frac{N m^2}{C^2}}##. Where does this tie in with ##9 \times 10^9##?

I get k being the name for the proportionality much like speed is the name for the proportion d/t.

Yes much of my academics has been, "Here are a set of rules. Use them because they work. No need to question them." I gain interest by understanding the how in things not just following a set of equations just because.

My final question would be, in Coulombs Law, why does distance need to be squared?

Fr0stBite
You are coming across as hostile. Given that, by your own admission, you don't know this stuff, maybe you should tone it down a bit.

Apologies if you took my posts as hostile. None was intended. I was using humor in the sentence you quoted me on. It is very difficult to express emotion through text so please be advised that the only emotion I am intending in any of my posts is the emotion of interest. It is difficult for me to be politically correct as it is not very realistic in nature. Nonetheless, I will try harder from now on to be concise through text.

• Tom.G
Fr0stBite
Research atomic weight and atomic number.
I do understand the difference it is just the question of how do we calculate atomic weight accurately and how can we say that isotopes have the same number of protons but just different number of neutrons? The only reason we know Hellium has two protons is because it takes 2 times the amount of Hydrogen to equal same amount of Hellium. So all elements use Hydrogen as the base and one proton.

Fr0stBite
I agree totally with this. The OP manages to sound very cross about his not knowing things. The solution to his (it won't be a her) problem is to follow a good course in Physics and then to argue with some of it if and when, having found out enough, he feels the need.
You have to read a book to be able to discuss the plot.

You also have to question the book as you read it in order to understand the plot. Otherwise you will be a reader but not a learner and say, "I just read this entire book now what was it about?" WHy read if you do not analyze what you are reading?

Aren't all breakthroughs in Physics the ability to question vice argue the normality of things? I mean Albert Einstein found a slight gap in KNewton's Law of Gravity because he opposed propositions. We found the Earth wasn't flat because we questioned the notion. You are viewing my post at the wrong angle. I can saying you are viewing it wrong because I am the one that wrote it, so technically I know the point I was seeking and it isn't the one you are suggesting.

I could discuss "to his (it won't be a her) problem," but because I also do not want to take your words out of context and lead into an off subject I will leave this as is.

I truly do value all input though, so thank you!

Mentor
Use them because they work.
This is the core of the scientific method.
My final question would be, in Coulombs Law, why does distance need to be squared?
Because it works. Experimentally, when we double the distance we measure a four-fold decrease in the force. When we triple the distance we get a nine-fold reduction in force.

Gold Member
The only part I'm stumped on is Nm2C2 Nm2C2 \ \mathrm{\frac{N m^2}{C^2}}.
I don't see how that can be true. If you are stumped by the units that appear in the constant of proportionality, then I don't see how you could have had much practice using Coulomb's Law.

Fr0stBite
I don't see how that can be true. If you are stumped by the units that appear in the constant of proportionality, then I don't see how you could have had much practice using Coulomb's Law.

So the constant's units are in ##\ \mathrm{\frac{N m^2}{C^2}}##? Those are the units of k and the number of those units are ##9 \ 10^9##?

Kind of like the unit of s in ##s ={\frac{d}{r}} ## could be in ##\ \mathrm{\frac{m}{s}}## (where m= meters and s=seconds), and you could have ##9 \times 10^9## of the unit ##\ \mathrm{\frac{m}{s}}##?

Sorry if you are having to be repetitive. I know this is super basic but I want to make sure all my 't's are crossed and my 'i's are dotted.

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Fr0stBite
This is the core of the scientific method.
Because it works. Experimentally, when we double the distance we measure a four-fold decrease in the force. When we triple the distance we get a nine-fold reduction in force.

I see now, thank you. Through measurements we observed that the force is decreased the amount of distance squared.

Fr0stBite
This is the core of the scientific method.
Also, without going too far off topic, weight used to be understood as mass until we realized that we also need to factor gravity into the mix. Could this be applied to Coulombs Law. Like is it possible for the need to factor in something we currently are not doing? I guess what I am getting at, how would we find those things that need to be factored?

Gold Member
do understand the difference it is just the question of how do we calculate atomic weight accurately and how can we say that isotopes have the same number of protons but just different number of neutrons?
Calculate? Theses things are measured to great accuracy. The unit charge is measured (Millikan Oil drop was the first measurement there have been many others using different methods since). One method of measuring atomic weight is using a mass spectrometer. One ionizes single atoms and passes them at a known energy through an analyzing magnet. Different isotopes have different masses. All these things have been measured over the years repeatedly. Nuclear masses don't follow exact integral numbers of proton and neutron mass because of the binding energy. This is all basic nuclear physics.

• diogenesNY and Dale
Gold Member
Also, without going too far off topic, weight used to be understood as mass until we realized that we also need to factor gravity into the mix.

There was never any realization that it had been misunderstood!

The way weight is defined legally matches the way scientists and engineers define mass. It's a matter of semantics.

Mentor
Like is it possible for the need to factor in something we currently are not doing? I guess what I am getting at, how would we find those things that need to be factored?
Certainly it is possible, this is part of science. To find such things we would need to do ever more precise experiments to test the laws and find something that didn’t fit.

This has already happened with Coulomb’s law. It was eventually discovered to be wrong if the charges are moving. There was also found to be forces due to magnetic fields when the charges were moving. Eventually, this led to the unification of electromagnetism in Maxwell’s equations.

Then Maxwell’s equations were found to be inaccurate at very low amplitudes and incomplete in describing how electromagnetism interacts with matter. So quantum electrodynamics was developed. Today there is no known EM phenomenon that QED does not describe.

Question for you: given the known inaccuracies in Coulomb’s law and Maxwell’s equations why are they still taught? Shouldn’t we just learn QED?

• sophiecentaur
Gold Member
Without reading from the beginning, you are very unlikely to be in a position to "analyse". You are demonstrating this, all along by the questions you are asking. The topic is too big to take it all on board without a lot of plain learning. When we learn enough we can start to make connections which can generate the answers that you keep seeking. A barrage of questions from you will not get you there, I'm afraid. You ask about elementary bits of Science history; stuff which you would know about if you took it a a suitable pace.

• phinds
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Aren't all breakthroughs in Physics the ability to question vice argue the normality of things? I mean Albert Einstein ...

There are two things here. 1) You need go focus on what's important for you, in terms of achieving what you want to achieve. 2) You need to choose your battles, as it were.

It's good to question what you're learning and looking at it from different angles helps you understand it better. But, in 2019, there is a vast body of physics that has been gone over so many times that it's as solid as you're going to get.

Ironically, this will become more important when you come to Einstein's theory of SR (Special Relativity). Then you may have a strong urge to reject it and retreat back to comfort of Newtonian physics. You can look through the threads on here (or take my word for it!), that there are many who will never accept it.

The biggest risk is rejecting things because you don't quite understand them yet, That's a bigger risk than accepting some stuff on trust for the time being.

Also, learning university level physics or maths is partly an attempt to change yourself. If you do go on to learn SR and QM (Quantum Mechanics), then this will radically change you and the way you think.

What is almost impossible is that, at this stage in your education, you will change physics!

PS there's no "K" in Newton, by the way!

• Vanadium 50, Ibix and Paul Colby
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