# Electrons and protons

Gold Member
Hi,
suppose we have a proton at point A and an electron at point B, at a distance of 1cm , separated by a screen.

If we remove the screen one would expect the particles to meet and clash somewhere near point A, but I read this never happens.

Can you explain why it's so and what exactly happen in reality?, and what is PE and what are final speeds?
Thanks

UltrafastPED
Gold Member
PE is the potential energy; it is the work that would have been required to separate them.

I would expect the electron to be (a) kicked off in some hyperbolic path, or (b) some elliptical path. As energy is bled off the two will become a hydrogen atom in some excited state.

You need very high energies for the electron to "crash" into the proton.

Gold Member
I would expect the electron to be (a) kicked off in some hyperbolic path, or (b) some elliptical path.

You need very high energies for the electron to "crash" into the proton.
As both particles attract each other, why don't they follow a straight line?

What energy is required to make it land on the proton?

UltrafastPED
Gold Member
You are asking me to explain quantum mechanical behavior of sub-atomic particles ... this is how people thought prior to 1910. Look up the Rutherford experiments.

http://en.wikipedia.org/wiki/Positronium

mfb
Mentor
Particle are not like billard balls.
The screen wouldn't work, but let's just assume you put a proton and an electron somewhere in space. If you have a perfect vacuum: They would accelerate towards each other, and probably form a hydrogen atom. It is hard to prepare that, however - electron and proton have to come very close to each other to do that. If one of the particles started with some initial velocity, they will probably orbit each other for a while. Accelerated charges radiate, so the orbit will decay and you end up with a hydrogen atom as well.

Gold Member
They would accelerate towards each other, and probably form a hydrogen atom..
That is what I read, I wounder if you can tell me roughly at what point the electron leaves the straight path toward the proton , and what kind of forces make it deflect, is it magnetic force?

mfb
Mentor
There is no classical "deflection" and the final state has the same symmetry as the initial state.
It is quantum mechanics, classical physics is not appropriate to describe it.

1 person
Gold Member
Thanks!
Do you happen to know a link or an applet where to see how it works?

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Gold Member
You are asking me to explain quantum mechanical behavior of
It is quantum mechanics, classical physics is not appropriate to describe it.

Does that mean that QM is only complicated math and has no explanation of the forces, or that the forces are too complex to explain?

UltrafastPED
Gold Member
It means that classical ideas break down in the quantum world. This has been know since at least 1900 when Planck's law was published.

Thus your "intuition" of what should happen needs to be informed by the physical knowledge of what _does_ happen. For example, when you ionize hydrogen gas the electrons don't fall into the nucleus; you get a hydrogen atom back, and these combine to form hydrogen molecules.

It _is_ possible to drive an electron into a proton with the electron then scattering from the "partons" which make up the proton (now known as quarks), or to even break up the proton. But these require very high energies.

UltrafastPED
Gold Member
BTW, QM is usually solved using energy, and not forces. The forces are converted to potential energy which then appears in the Shroedinger equation.

The same can be done for mechanical problems; these techniques are studied in a course on analytical mechanics where you will learn about Lagrangians and Hamiltonians. The ideas are a few hundred years old now:
http://en.wikipedia.org/wiki/History_of_classical_mechanics

OTOH quantum physics starts about 1900, and quantum mechanics starts in 1924/5:
http://en.wikipedia.org/wiki/History_of_quantum_mechanics

Gold Member
BTW, QM is usually solved using energy, and not forces. ]
Pardon my ignorance, but it's QM [or whatever theory] that should solve problems i.e. to explain reality.

In this instance the problem is why an opposite charge is not attracted in a straight line. Classical Physics has no solution.
If QM has an explanation it doesn't matter if you use energy instead of forces, its process should be explainable in a clear way that makes sense. There must be some energy-force that bends its path, anyway.

Gold Member
I am sorry I'm thick, but I do not see the point.
You can call it reality, or events, or phenomena or random whatever, but you are describing, explaing something-real-imaginary-random-allucination,... else you sut up shop.
QM considers the phenomenon , the issue at hand? Gives a decription-explanation whatever? what is it ?

UltrafastPED
Gold Member
I don't think that I can provide an "explanation" which will satisfy you.

Solving for the hydrogen atom is difficult enough; you will spend several lectures on this in an undergraduate course, or a happy weekend solving it for yourself in a more advanced course:
see http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html

But the problem that you have posed is more difficult. Many problems can be stated, but are difficult to carry out mathematically.

Your original question was "Can you explain why it's so and what exactly happen in reality?" I told you what would happen - what the final possible states of the system are. You also asked for the potential energy (which you can easily calculate for yourself based on the charges on the two particles, and their initial separation).

If you have the potential energy you can estimate the final speeds from PE = sum of their kinetic energies. This requires that you calculate the momenta for each particle: by Newton's third law of motion you expect the momenta to be equal but opposite (for classical objects), so their magnitudes are m_e x V_e = m_p x V_p, and the sum of the kinetic energies at the "collision" is equal to the total potential energy: so two equations with two unknown velocities.

So go ahead and carry out the classical calculations!

But they won't tell you what "actually happens".

Gold Member
But they won't tell you what "actually happens".
Thanks for your efforts, but by that I did not mean anything detailed, just to know the actual path of the particles and the forces(or energies as you call it) that cause that path. And all that before it becomes an H-atom.
As simple as That.

I must conclude that QM has not yet found an explanation for that, and nobody really knows how it works.

ZapperZ
Staff Emeritus
I must conclude that QM has not yet found an explanation for that, and nobody really knows how it works.

And you arrive at this conclusion based on what? A careful study of QM, or simply reading stuff on the web? And you trust that kind of "knowledge"? You know LESS about how QM works that many of the people who responded to you in this thread!

This is now veering on philosophy and personal tastes. If you wish to learn about QM, then please do so. However, if you think that you know more about such subject matter as to make your own conclusion based on superficial knowledge, then this thread will end very soon.

Zz.

Dale
Mentor
2021 Award
I must conclude that QM has not yet found an explanation for that, and nobody really knows how it works.
That is called "jumping to a conclusion". It is a pretty big jump to a pretty bad conclusion.

mfb
Mentor
Thanks for your efforts, but by that I did not mean anything detailed, just to know the actual path of the particles and the forces(or energies as you call it) that cause that path. And all that before it becomes an H-atom.
As simple as That.

I must conclude that QM has not yet found an explanation for that, and nobody really knows how it works.
There is no single, classical "path" the electron follows, in the same way as there is no single position where the electron "is".
You can describe electron and proton with wave-functions, and calculate the evolution of those wave-functions. It is complicated, but it is possible. The result will keep its symmetry all the time, and you end up with radiation and a hydrogen atom, probably in a superposition of multiple states.

I must conclude that QM has not yet found an explanation for that, and nobody really knows how it works.

You should've concluded instead that you don't really understand QM.

Note that there's no need for a deflection because in the lower energy shell the electron doesn't have any angular momentum around the proton. The electron IS NOT orbiting the proton.

.Scott
Homework Helper
Can you explain why it's so and what exactly happen in reality?, and what is PE and what are final speeds?
Thanks
The first problem with you problem is that you are holding both particles steady at a distance of 1cm from each other. In fact, these particles are not precise enough to allow that. Heisenberg Uncertainty will limit how steady these particles can hold their positions. What really happens is that these particles will spread about about the points where you are trying to hold them.

Next you let them go - and they begin falling towards each other. At this point, you need to deal with them - or at least the electron - as waves. If you insist on dealing with the electron as a particle, then bear in mind that this particle is spread over an area and consists of a cloud of virtual particles. These particle fall towards the proton along a variety of trajectories and, in the process, constructively and destructively interfere with other - so much for dealing with them as particles.

At 1cm, the electron will flitter about as a free electron until it looses energy - by emitting a photon and dropping into an an electron orbital about the proton. Once in this orbital, it will no longer make any sense to talk about the position or trajectory of the electron. It will immediately fill up the entire orbital being constrained only by its energy and constructive and destructive interference. It will not collide with the proton because that is a region of destructive interference where there is no chance of finding the electron.

If I've mischaracterized any of this, please corrected me.

UltrafastPED
Gold Member
I've tried to provide factual information which I understand and can support; perhaps my PhD in physics is not up to the task!

Khashishi
The answer depends on how set up the experiment, and how you measure the results. In real experiments, it's very hard to deal with single protons and single electrons.

.Scott
Homework Helper
I am sorry I'm thick, but I do not see the point.
You can call it reality, or events, or phenomena or random whatever, but you are describing, explaining something-real-imaginary-random-allucination,... else you sut up shop.
QM considers the phenomenon , the issue at hand? Gives a description-explanation whatever? what is it ?
The problem is that you have this notion of electrons and protons that is incorrect. In the macroscopic world, an object traveling from point A to point B will follow a specific path. But is the world of QM, a particle may be emitted from an approximately known source, then detected at another approximately known location, and there is nothing "real" about a path drawn from emitter to detector. So when you ask when does the electron veer from its straight path, the answer is "when it became an electron". There are conditions, for example in a cathode ray tube, when electrons will seem to behave like little bullets. But that is an approximation of their behavior that cannot be used in your example.

Gold Member
You should've concluded instead that you don't really understand QM.
.
Surely I do not know and , of course , do not understand QM.

But the point is that it is a branch of physics, science that studies , describes and explain what we called the world, the universe, phenomena, reality.
Now , whatever interpretation it gives of the world, of the electron (etc) if it is a particle a wave or a poltergeist, does not change the phenomenon we observe of an apple being attracted by the Earth or an electron by a proton, cation.
An electron is attracted by a positive charge roughly by a straigth line ( I hope this is still valid: http://en.wikipedia.org/wiki/Electric_field#Electrostatic_fields) and as Scott confirmed, behave roughly like a bullet in a cathodic tube.
If the positive charge is free, its behaviour is different, even though the electron is exactly the same , be it a particle, a wave or whatever and if it follows a discernible path or not.
I am just asking what makes this behaviour different.
Is it not a legitimate question? If it is did I miss the answer?

I am sorry I wasted your time, I apologize, and stop posting.

ZapperZ
Staff Emeritus
Surely I do not know and , of course , do not understand QM.

But the point is that it is a branch of physics, science that studies , describes and explain what we called the world, the universe, phenomena, reality.
Now , whatever interpretation it gives of the world, of the electron (etc) if it is a particle a wave or a poltergeist, does not change the phenomenon we observe of an apple being attracted by the Earth or an electron by a proton, cation.
An electron is attracted by a positive charge roughly by a straigth line ( I hope this is still valid: http://en.wikipedia.org/wiki/Electric_field#Electrostatic_fields) and as Scott confirmed, behave roughly like a bullet in a cathodic tube.
If the positive charge is free, its behaviour is different, even though the electron is exactly the same , be it a particle, a wave or whatever and if it follows a discernible path or not.
I am just asking what makes this behaviour different.
Is it not a legitimate question? If it is did I miss the answer?

Your question is legitimate. However, note that you ALREADY made your conclusion, all based on a superficial understanding of QM. This is what we do not allow, and this makes this discussion meaningless, because you already made up your mind.

Try to understand the distinction between trying to learn, versus "I'm going draw up my conclusion now even though I know very little about it.". Which one do you think you've done here?

Zz.

UltrafastPED
Gold Member
I built photo-activated electron guns as part of my research; an ultrafast laser was used to generate sub-picosecond electron pulses which I could control so that they had ~1,000 electrons, or ~10,000,000 electrons. I calibrated this process with a precision electrometer and a high quality Faraday cup to capture the electrons.

The electrons were accelerated from ~0.1 eV up to 30,000 eV over a distance of 6 mm; they were then travelling at 1/3 the speed of light. By means of careful design and some novel techniques I was able to "time stamp" the arrival of the electron pulse and a laser heating pulse at a target which contained ultra thin layers of heavy metals (usually gold or platinum); typically these were 10-15 nm thick, or from 25 to 40 atoms thick.

The goal of this research was to track the effects of the laser pulse by means of electron diffraction through the sample ... prior to the arrival of the laser pulse to provide a reference, then at 1 picosecond intervals to develop a "movie" of the diffraction pattern. Each position accumulated 5,000 shots per photographic image to provide averaging, and the length of the movie was 20-30 picoseconds.

Note that a picosecond is one thousandth of a nanosecond; it is the time required for light to travel about 300 microns. The electron pulses were about 300 femtoseconds in duration; a third of a picosecond. The laser pulses were 150 femtoseconds.

Now back to the electrons: the photo-emission of electrons from a metal is a quantum process; Einstein explained this in 1905. Each of the photons in the electron generating path was 4.5 eV, a mid-UV with a wavelength of 260 nanometers. 4.5 eV corresponds to the work function for gold which was used as the photocathode. Note that the light is also treated quantum mechanically: one 4.5 eV photon can dislodge one electron from gold. Most of the photons are absorbed as they pass through the thin metal film, but some eject an electron, but only some travel in the correct direction and are not scattered back into the material.

The electron bunch is emitted over the time period corresponding to the laser pulse; the laser light was focused to a broad area of about 200 microns in diameter (this was by design, and was measured by means of optical diffraction from a ruled target); a tighter focus damaged the thin metal film; if the film was thicker, fewer electrons were emitted; everything is a tradeoff.

Now the electrons started out almost stationary, and were collected as a "flat pancake" about 200 microns in diameter. As you would expect the electron pancake began to expand due to Coulomb repulsion between the electrons, especially in the direction of highest density: the thickness. However the pulse was also being accelerated through the electron gun by a very strong electric field of 30,000 volts over a distance of 6 millimeters; this is a field strength of 5,000,000 volts per meter. Very quickly the electrons were travelling at 1/3 the speed of light, and only had to travel an additional centimeter to strike the target.

This Coulomb expansion is increased the electron pulse duration from ~100 femtoseconds up to about 300 femtoseconds for pulses with 10,000 electrons; it would be shorter with fewer electrons, or longer with more electrons. This even makes sense for classical reasoning about charged particles! No quantum mechanical reasoning here.

Now the electrons pass through the ultrathin metal film; for the diffraction each electron acts as a wave with an extremely short wave length (much less than an angstrom; a few picometers). This is a quantum mechanical effect - often referred to as the wave-particle duality. After the diffraction the electrons continue on and strike a detector: each electron makes a single hit which is multiplied via a microchannel plate which amplifies each electron into 10,000 electrons which are in turn light up a phosphor screen - this image is recorded by a scientific grade CCD camera.

So each electron has been generated via a quantum mechanical entity: the photon, in a process which is quantum mechanical. It is then accelerated via classical electrical fields to relativistic speeds. Then the electrons act as waves - the quantum mechanical wave-particle duality - and then continue on as though they are classical particles which finally strike individual locations (very much as particles), etc.

I should note that the data which was collected shows the existance of phonons, which are a quantum mechanical version of sound. Phonons of different wavelengths traveled along various crystal axes - something that was unexpected; I was able to document this, though it had not been predicted.

So there you have it: electrons act sometimes as particles, sometimes as waves, and are able to shift back and for between the two modes - actually they exhibit both properties simultaneously.

But you will spend a few years studying before all of this becomes everyday work for you. Along the way you must drop your preconceptions about "what really happens". Good luck with your journey!

1 person
mfb
Mentor
An electron is attracted by a positive charge roughly by a straigth line ( I hope this is still valid: http://en.wikipedia.org/wiki/Electric_field#Electrostatic_fields) and as Scott confirmed, behave roughly like a bullet in a cathodic tube.
That "roughly" really depends on the setup, and it is the question how relevant quantum-mechanical effects are. They can be neglected in a cathode tube (they are still there, but you don't care about them), as there are strong and large electromagnetic fields and the electrons are fast. They cannot be neglected in your setup.

Gold Member
Very quickly the electrons were travelling at 1/3 the speed of light... for the diffraction each electron acts as a wave with an extremely short wave length (much less than an angstrom).
Thanks, ultrafast, for your efforts and patience, and congrats for your amazing competence!
Now if you are willing to clarify other aspects of the electron:
the wave lenghth λ is h/mv[c/3], at c/3 is supposed to be roughly cm x 7/10^10, is it possible to actually measure it in reality, in what way?,
... and, what is the wave amplitude at that speed?, what is it when the speed is 1cm/sec?, is there a formula to calculate it ?

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UltrafastPED
Gold Member
The wave amplitude is the "probability amplitude"; at each point in space it has a complex value, psi such that |psi|^2 is the probability of detecting the electron there. The probability amplitudes are subject to constrictive and destructive interference.

You can calculate this "wave function" by writing the Hamiltonian for the experimental setup, transform it to quantum operators, then solve the Schroedinger equation for psi: H |psi> = E |psi>

Where H is the Hamiltonian operator and E is an energy eigenvalue. The Schroedinger equation is an eigenvalue equation over a complex function space.

if you know linear algebra, differential equations, and Fourier series you can work out the answers to simple problems; otherwise you must use numerical techniques and a computer.

Gold Member
Do you know the value of the amplitude of the wave at c/3?
Is it possible to detect and measure with instruments the length and the amplitude of the wave of an electron?
Is that wave electromagnetic like light?

UltrafastPED