What causes atomic perpetual motion?

[heartless]

Hello,
Just like in the topic, what causes electrons to move around the nucleus in perpetual motion (they never stop). For now, it's the only question. I'll have some more when I get the answer.

p.s Actually, let me ask another one. A little bit unrelated. What causes electrons to move in a specific path?

Thanks,

 

[mathman]

For question one, there is no such thing as "friction" inside an atom, so the electrons don't lose any energy. (This is a much simplified answer, but it is the essence of what's happening.)

For question two - electrons don't really have paths. They have energy levels. Levels can change only in discrete (quantum) jumps. An atom is NOT like the solar system.

 

[fargoth]

the electron in an atom has "kinetic" energy and "angular moentum", but it doesn't orbit the nucleus, infact its pretty confusing to call these things this way, because the electron is "smudged" around the nucleus (the pattern depends on the angular momentum and kinetic energy - both are discrete).

the electron's minimal energy state - called a ground state is greater then zero, and that's why it can't "stop", in this state there's no angular momentum though.
much like quantum harmonic oscillators (see zero point energy).

hope i didn't confuse you too much... try looking at quantum models of hydrogen in java applets, it might help. (google it up)
and have a look here: http://en.wikipedia.org/wiki/Hydrogen_atom
and in particular the electron's "orbitals": http://en.wikipedia.org/wiki/Image:HAtomOrbitals.png

 

[Danger]

Heartless, it might be helpful if you stop thinking of electrons as solid objects. In my case, at least, it works a lot better to consider them to be little clouds of wave functions that surround the nucleus.

 

[loom91]

Both of these questions stem from some fundamental regrettable defects in our educational system that insists that teaching completely wrong things is supposed to have some educational value. The fact is, electrons don't 'move' in the ordinary sense of the word. They are not little negatively charged spheres moving in elliptical orbits around the nucleus.

At this point, you must abandon all your notions of common sense and what physics 'should' be completely. Any attempt of retaining them will result in disappointment and a feeling that quantum mechanics is 'spooky' (fear not, even then you will be in good company). An electron is represented in quantum mechanics by a 'wavefunction', a function that assigns (at a given instant of time) a complex number to each point in space. This is analogous to representing a system by a point in its phase space in classical mechanics.

According to the Born statistical interpretation, the relevance of this complex scalar field on space is that at any point of space, the square of the modulus of the wavefunction at that point gives the probability of finding the particle at that position upon performing a 'measurement'. This wavefunction changes with time, and its 'dynamics' is governed by a very famous equation known as the Schrödinger equation. This equation is the fundamental pillar of quantum mechanics in the same sense that Newton's second law is the pillar of classical mechanics.

This equation can be used to show that an atom is stable, that is the electrons stay inside the atom. They do not move in a specific path, they do not even move. In quantum mechanics they are just wavefunctions undergoing unitary evolution within their separable Hilbert space and if you accept the Copenhagen interpretation that's all you need to know. The realm of the quantum is even further from common sense than relativity, though the mathematics tend to be a bit easier.

Incidentally, I'm not sure if you understand this, but perpetual motion is the natural state of any particle. The question to ask usually is why is that NOT in perpetual motion. Inertia of motion as derived from Newton's First Law tells us that if no forces are acting on a body then it's possible to find a family of reference frames such that the body undergoes no acceleration (stays in perpetual motion). Hope this helps.

Molu

 

[rcgldr]

If electrons aren't particles, then how can they collide with solids as in the case of high speed accelerators? I was under the impression that there was significant mass (or at least energy) to electrons at very high velocity, as in the case of linear accelerators.

 

[Mk]

If electrons aren't particles, then how can they collide with solids as in the case of high speed accelerators? I was under the impression that there was significant mass (or at least energy) to electrons at very high velocity, as in the case of linear accelerators.

Parteekle-wave duality! An electron is both a particle, and a wave: both a discrete little grain of sand, and an ink smudge or cloud.

Hello,
Just like in the topic, what causes electrons to move around the nucleus in perpetual motion (they never stop). For now, it's the only question. I'll have some more when I get the answer.

I think loom91 said it best! Good job loom!

p.s Actually, let me ask another one. A little bit unrelated. What causes electrons to move in a specific path?

Like mathman said, and Danger (Socraticly ) said, as well as loom91, the electrons don't move in a specific path, they are actually more of a cloud with different energy levels. The different energy levels are the simplification you have seen, as turned into orbits (well, they are called 'orbitals'). In high school chemistry, they grace over truer-visually molecular structure (less than one class period usually), and connect it to why the angles between bonds are how they are. Excess unbonded electrons pile up at the top part and repel the Z and Y atoms away: why they are bent and triangular and dodecahedral instead of just chains.

...X
.../..\
.Z...Y

 

[Farsight]

I like to think of an electron as a place with properties, not a particle. I don't like particles. Little ball bearings, bah. But a place can be nice and fuzzy, with no silly edges or surfaces or pointy bits. So it's got no defined size, or particular point where's it's at. It's very easy to get a rough concept of this. Just try pointing at the USA.

 

[neutrino]

I think the best description of quantum mechanics in layman's terms is from the master himself.

Now we know how the electrons and light behave. But what can I call it? If I say they behave like particles I give the wrong impression; also if I say they behave like waves. They behave in their own inimitable way, which technically could be called a quantum mechanical way. They behave in a way that is like nothing that you have seen before. Your experience with things that you have seen before is incomplete. The behavior of things on a very tiny scale is simply different. An atom does not behave like a weight hanging on a spring and oscillating. Nor does it behave like a miniature representation of the solar system with little planets going around in orbits. Nor does it appear to be somewhat like a cloud or fog of some sort surrounding the nucleus. It behaves like nothing you have seen before.

There is one simplication at least. Electrons behave in this respect in exactly the same way as photons; they are both screwy, but in exactly in the same way….

-
R.P.Feynman

A part of this appears as a short clip in the documentary No Ordinary Genius.

 

[rcgldr]

the electrons don't move in a specific path

They do move in a specific path in accelerators, and as individual instances.

My assumption is no one truly understands the nature of electrons yet.

 

[loom91]

They do move in a specific path in accelerators, and as individual instances.

My assumption is no one truly understands the nature of electrons yet.

I don't know your educational level, but high-school physics/chemistry covers topics such as quantization of dynamical variables, electron orbitals, wave-particle duality, time-independent Schroedinger equation, probability density of the electron in a H atom, linear superposition of wavefunctions, 'shapes' of orbitals etc. Your textbooks may be a good place to get some idea about the topics. Free electrons (electrons that are not bound to a nucleus) are considerably less quantum an are sometimes well-approximated by classical concepts.

But even then, they do not move in a specific path. I'll repeat this in case it is not clear, electrons do NOT move in a specific path UNDER ANY CIRCUMSTANCES, never. This is a misconception you have to correct now. The electron's mass is small enough for the HUP to be non-negligible, and they never ever have a well-defined trajectory in the classical sense. I don't know who teaches you this sort of rubbish. Even in particle accelerators, there's always uncertainty in their position and velocities, though probably less than inside an atom.

And I'm speculating here, but the relativistic speeds in an accelerator will introduce additional complications and we must examine Dirac's equation for the relativistic electron.

It is quite true that no one truly understands the nature of electrons yet, but not in the sense you mean it.

 

[ZapperZ]

Please note that in particle accelerators, the trajectory and description of particle motion is often classical. You are welcome to look at the popular codes that are used to describe such trajectories such as PIC codes and PARMELA.

Does this mean we can treat all electrons in all cases as classical particles? Nope! We have clearly seen why this doesn't work in atomic description, tunneliing motion, etc. However, does that also means we can never, ever use classical description either? Nope! There are plenty of cases where the classical picture of electrons DO WORK, and in fact, is more convenient. Example? Particle accelerators, Drude model, and Boltzmann transport equation.

This doesn't mean that the QM description fails in those cases. Just like in the Newtonian physics case for v << c, at some point, the classical description is more convenient when the right boundary conditions come up, when there's no significant overlap between the particles/electrons, etc.

Zz.

 

[Mk]

They do move in a specific path in accelerators, and as individual instances.

And hey, we're talking about in the ideal atom.

 

[LeonhardEuler]

Hello,
Just like in the topic, what causes electrons to move around the nucleus in perpetual motion (they never stop). For now, it's the only question. I'll have some more when I get the answer.

p.s Actually, let me ask another one. A little bit unrelated. What causes electrons to move in a specific path?

Thanks,

The wavefunction of the electron describes the probability that it is in a particular location. When the electron is bound to the nucleus of an atom and you measure position relative to the nucleus, the probability that an electron is at a given position does not vary with time. So, in a sense, it is not really moving at all. However, if you were to measure its position twice, you would likely find it in different positions each time. You might consider this "motion" in the sense that the particle has changed position. But this still does not show that the electron is moving around the nucleus when you are not measuring it because you must disrupt the wavefunction in order to carry out a measurement. It is best not to think of the electron as having a position before you measure it. It does have an "expected" position, or the average position in a probabalistic sense. This position does not vary with time in this case.

 

[rcgldr]

level of education - high school

Old man here, graduated high school back in 1970, only one semester of physics, and it was mostly mechanical. College degree in computer science, took calculus, differential equations, and linear algebra, but only one year of physics. So I rely on web sites and forums like this one to improve my education. In my work my main math speciaty is Reed-Solomon (Galios) type finite field math as used for error correction codes, I've done some curve fitting and data compression work as well.

specific path in accelerators

Ok, near specific path. The acclerators are programmed in advance to toggle polarity to accelerate electrons that have entered the proper timing window to be accelerated. The speeds are very close to c at SLAC.

Feynman Double Slit

Has anyone come up with a good explantion while electrons can be fired one at a time at a double slit and end up with an interference pattern as if multiple electrons with wavelike properties were fired at the same time? This is going beyond the wavelike properties of light. Is there any reason to believe that the difference could be due to the fired electron interacting with the electrons that compose the double slit?

 

[loom91]

Old man here, graduated high school back in 1970, only one semester of physics, and it was mostly mechanical. College degree in computer science, took calculus, differential equations, and linear algebra, but only one year of physics. So I rely on web sites and forums like this one to improve my education. In my work my main math speciaty is Reed-Solomon (Galios) type finite field math as used for error correction codes, I've done some curve fitting and data compression work as well.

Heh, for some unknown reason I was sure you were a high-school student :D Sorry.

You mean you can choose how much you study a subject in High School? We don't get to do that till we are out of school and in college. Once we choose 4 subjects to study at 11th and 12th Grade, we have to study the whole syllabus of all the subjects. So everyone who takes Physics and Chemistry as subjects has to study the basics of Quantum mechanics (there's a little in both subjects, though more in Chemistry), but there's remarkably little wave mechanics.

Just the theory of time-independent Schrödinger equation and other basic quantum phenomena such as quantization and HUP in 11th Grade, and linear superposition and radial probability densities in 12th Grade. But everyone has to study this minimum, we can't read more of Math by reading less of Physics. We probably won't be able to do that even in College here, our curriculum are not very flexible.

Ok, near specific path. The acclerators are programmed in advance to toggle polarity to accelerate electrons that have entered the proper timing window to be accelerated. The speeds are very close to c at SLAC.

As I said, the electrons are more classical when free. We would also have to examine Dirac's equation (which is the most elegant and beautiful theory in Physics I've seen, though I've not seen much yet) at velocities close to c, though I'm not sure whether that would make the electron more better or worse approximated by classical models.

Has anyone come up with a good explantion while electrons can be fired one at a time at a double slit and end up with an interference pattern as if multiple electrons with wavelike properties were fired at the same time? This is going beyond the wavelike properties of light. Is there any reason to believe that the difference could be due to the fired electron interacting with the electrons that compose the double slit?

I believe the likes of Louis De Broglie and Erwin Schroedinger came up with very good explanations in the first quarter of the last century. As far as I know, firing one electron does not give rise to interference patterns, it gives rise to only one dot as would be expected of a particle. Only when many are fired do their combined impression form interference patterns, leading us to believe that the electron has the characteristics of a matter wave.

I don't think the theory you advance is plausible. It's considered a much more fundamental phenomena rather than experimental errors as you suggest. No physicist worth his salt would claim the wave-particle duality to be false after a century of evidence to support it.

 

[rcgldr]

You mean you can choose how much you study a subject in High School?

It was common in private high schools, but I only had one semester in private junior high school, when my parents got divorced and ended back in public schools in west Los Angeles. Although it was rare in the late 1960's to have majors in public high shools in California, my high school was part of a group of high schools that did have majors, and longer breaks between pairs of classes so that kids could get bussed to a school that specialized in a particular subject. I just happened to be at the school that had physics, calculus (there were only 11 students out of 2500+ in that first calculus class), and a small computer (IBM 1130). I ended up more interested in programming than math, but kept my math major. As mentioned, I graduated during summer 1970. I consider myself lucky to have ended up at this high school.

firing one electron does not give rise to interference patterns

I meant firing one electron at a time, not just one. The issue is that you end up with interference (like) patterns, even though the electrons are fired one a time, so that they do not interfere with each other.

So inspite of the fact that the fired electrons do not interact, you end up with an interference patttern similar (or the same?) as if they were interacting as wave interference. I've seen a few web sites that state that there isn't a good explanation for this, but these may be out dated.

 

[ZapperZ]

This is now degenerating into a double-slit type of a discussion. Please read this thread, for example:

https://www.physicsforums.com/showthread.php?t=108424

There are many others. In all of these discussion, please note that the interference effects that we know and love is NOT due to one particle "interfering" with another. In the standard CI formulation, it is the SAME particle interfering with itself [I dislike that pedestrian description but that's what I'll go with].

Zz.

 

[rcgldr]

Sorry, didn't mean to stray off-topic, only mentioned the double slit issue to show that electrons behave "wierdly".

 

[ZapperZ]

But why pick on electrons? Photons, neutrons, protons, buckyballs, etc... all show the identical behavior.

Zz.

 

[rcgldr]

why pick on electrons

I thought that electron "perpetual" movement was the original subject of this thread. Again, the double slit thing was just a tangent on the unusual behavior of electrons, but without the intention of implying it was just electrons.

I'll try to avoid this type of off-tangent discussion if it's an issue with the forums here. It's hard for me to determine what is and isn't allowed to seemingly related topics.

 

[Astronuc]

Interesting discussion on the behavior of electrons (and other particles) in the subatomic realm.

high-school physics/chemistry covers topics such as quantization of dynamical variables, electron orbitals, wave-particle duality, time-independent Schroedinger equation, probability density of the electron in a H atom, linear superposition of wavefunctions, 'shapes' of orbitals etc.

I don't believe that is generally the case. It certainly wasn't 30+ years ago, and I have yet to meet a high school student who understands these concepts, let alone 1st year university students. However, there are those who learn it themselves. Most of the advanced students are only learning about the derivative and differential and integral calculus by the time they graduate from high school, so I can't see where Schrödinger's equation (a PDE) would be introduced, but perhaps in an exceptionally advanced program.

Somewhat back on topic - I think part of the problem is that electron (particle) behavior does not have a 'classical' analog that we observe in the macroscopic world. Most of what is taught through high school is based on classical mechanics, and if one is fortunate, there is some exposure to quantum mechanics along the lines of what loom91 describes.

Trying to understand wave-particle duality and putting aside 'classical' preconceptions are necessary in understanding QM.

The electron in an atom is subject to a very different potential than a 'free' electron in an accelerator, and the single/double slit (diffraction) behavior is yet again somewhat different. We haven't touched on electron optics yet (which is related to accelerator behavior).

Clearly people involved in this discussion have widely varying backgrounds. How to bring all this to a common coherent understanding?

Recommendation(s) for good textbook(s)?

 

[loom91]

I thought that electron "perpetual" movement was the original subject of this thread. Again, the double slit thing was just a tangent on the unusual behavior of electrons, but without the intention of implying it was just electrons.

I'll try to avoid this type of off-tangent discussion if it's an issue with the forums here. It's hard for me to determine what is and isn't allowed to seemingly related topics.

Don't lose sleep over it, I'm sure evryone here are nice people.

Anyway, you talk about your major, but it was my understanding that major refers to the main focus of a graduation/Bachellors study, the course you take to earn your graduate degree in college. By high-school I mean the previous stage, 11th and 12th Grade probably in the American and Indian education systems. You could take majors at that level?

Anyway, I hope you've got your answer. An electron moves differently based on whether it's inside the atom/molecule or outside, a free electron being less uncertain. A ground state electron inside an atom, being a stationery solution to the SE, has 0 linear momentum and therefore does not move. Perpetual motion problem solved!

Molu

 

[loom91]

Interesting discussion on the behavior of electrons (and other particles) in the subatomic realm.

I don't believe that is generally the case. It certainly wasn't 30+ years ago, and I have yet to meet a high school student who understands these concepts, let alone 1st year university students. However, there are those who learn it themselves. Most of the advanced students are only learning about the derivative and differential and integral calculus by the time they graduate from high school, so I can't see where Schrödinger's equation (a PDE) would be introduced, but perhaps in an exceptionally advanced program.

Not exceptionally advanced, it's the national curriculum in India. From what I've heard, the Indian curriculum on Science subjects is on average 2 years ahead of its American counterpart. For example while books like Halliday and Resnick and Morrison and Boyd would be used as 1st/2nd year graduation textbooks in USA, in India they are used at high-school (11+12 grade) level.

About the SE being a PDE, you have struck home at a curious characteristic of our educational system. We study all other subjects at a much higher level than Math. For example, we start learning Calculus only late in the 11th grade and cover upto 2nd order ODE by the end of 12th. But our Physics and Chemistry syllabus starts using calculus from the second chapter, since it would be ridiculous to teach mechanics without calculus. For that reason our Physics teacher has to teach calculus himself without waiting for the math teacher.

At many places, particularly Gravitation, the integrations we do are much closer to Exterior Calculus than Leibinz's one, definitely not anything we are taught in our math class. In Statistics we also have partial derivatives without learning about them in our math class. But keep in mind that we don't have to *solve* the TISE, only *see* it. Though the radial probability density of an electron in the H atom is calculated from the SE, the solution is just given as a statement without derivation.

Clearly people involved in this discussion have widely varying backgrounds. How to bring all this to a common coherent understanding?

Recommendation(s) for good textbook(s)?

Griffiths is probably an accessible treatment, and I hear Dirac and Feynman are also good.