Do Electrons Orbit the Nucleus Like Planets?

[ΔxΔp≥ћ/2]

Today, I had an argument with my physics teacher about the movement of electrons around the nucleus. I have read way more quantum mechanics than any normal high school student and my teacher is trained as an engineer, not a physicist, but I am not sure if I'm right.

His argument was something like the following:
Electrons move around the nucleus much like planets around the sun. They move in an elliptical orbit. The centrifugal force is what keeps them from crashing into the nucleus.

My response was:
We cannot know the precise position of an electron around the nucleus because of the uncertainty principle (note my name). It is therefore impossible to establish the electron as orbiting (elliptically) the nucleus.

Other thoughts:
If we approach the electron as a wave, I doubt any of his classical stuff makes sense. The centrifugal force thing even seems to be in conflict with the erroneous Rutherford and Bohr models.

I am not too familiar with the following concepts but I believe they also have a role:
The electron cannot fall into the nucleus because of the exclusion principle.
If the electron glued itself to the nucleus, its position would be more or less certain, giving it an enormous momentum.
These classical concepts where an issue after the discovery of the Rutherford model and the only way that an electron would stay out of the nucleus was if it accelerated because it would radiate energy.

Anyways, those are some arguments that come to mind.

Could someone please sort this out for me?

 

[nrqed]

Today, I had an argument with my physics teacher about the movement of electrons around the nucleus. I have read way more quantum mechanics than any normal high school student and my teacher is trained as an engineer, not a physicist, but I am not sure if I'm right.

His argument was something like the following:
Electrons move around the nucleus much like planets around the sun. They move in an elliptical orbit. The centrifugal force is what keeps them from crashing into the nucleus.

He/she is completely wrong!

My response was:
We cannot know the precise position of an electron around the nucleus because of the uncertainty principle (note my name). It is therefore impossible to establish the electron as orbiting (elliptically) the nucleus.

Correct!

Other thoughts:
If we approach the electron as a wave, I doubt any of his classical stuff makes sense. The centrifugal force thing even seems to be in conflict with the erroneous Rutherford and Bohr models.

Exactly

I am not too familiar with the following concepts but I believe they also have a role:
The electron cannot fall into the nucleus because of the exclusion principle.

The electron and nucleus are different types of particles so exclusion principle does not apply here

If the electron glued itself to the nucleus, its position would be more or less certain, giving it an enormous momentum.

correct so it cannot be "glued" there. Same thing prevents white dwarves or neutron stars from collapsing

These classical concepts where an issue after the discovery of the Rutherford model and the only way that an electron would stay out of the nucleus was if it accelerated because it would radiate energy.

This sounds a bit confused. It was that a classical electric charge in an elliptical orbit would necessarily radiate away energy and so a classical nucleus would be unstable.

 

[russ_watters]

Wow, that's painful.

 

[ΔxΔp≥ћ/2]

Feels good to know I'm right.

This sounds a bit confused. It was that a classical electric charge in an elliptical orbit would necessarily radiate away energy and so a classical nucleus would be unstable.

Yeah, that's what I meant, but I'm not a physicist... ...yet.

What kind of scared me though was when my teacher flatly said something along the lines of "No you're wrong." and then to justify himself, "I have a course prepared on nuclear physics/ I teach nuclear physics."

Guess that sometimes happens when engeneers teach physics. Still respect the dude though.

Anyone with a clear, reputable, simple reference that I can print to prove my point to him?

 

[CPL.Luke]

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

simplest case of atomic theory

granted wikipediaisn't the best reference, but any book or set of lecture notes will say the same. do a google search on hydrogen atom to get more info.

also a high school chem book should contain similar information at a simpler level

 

[DaveC426913]

Electrons move around the nucleus much like planets around the sun. They move in an elliptical orbit. The centrifugal force is what keeps them from crashing into the nucleus.

Yep. Dead wrong.

 

[DaveC426913]

Anyone with a clear, reputable, simple reference that I can print to prove my point to him?

How about you just show him a couple of diagrams of http://en.wikipedia.org/wiki/Atomic_orbital" and ask him to identify the ellliptical orbit for you?

Or ask him to explain why a water molecule is bent? No classical explanation does this. Orbitals do with ease.

 

[cks]

I'm not sure whether the conditions below justify what your teacher said. Actually, I don't know what is your teacher thinking. It's inappropriate to think of an electron as a body revolves around the nucleus same as planet moving around the Sun and says its path is deterministic. But, I think it's appropritate to say that the centripetal force balances the electric potential. CORRECT ME IF I AM WRONG! Your answer to your teacher sayings sounds like your teacher is asking a question where you answer other things. What you said regarding uncertainty principle is correct, but he's saying other thing.

Let's do a semiclassical way of approaching hydrogen atom.

T=\frac{1}{2}m v^2-\frac{e^2}{ r}

Well, you should have no question about this, the total energy is the sum of kinetic and potential energy.

\frac{m v^2}{r}=\frac{e^2}{r^2}

Well, it's saying the centripetal force is equal to the electric force! surprise

m vr=n\hbar

The third equation expresses the quantization condition, introduced empirically by Bohr in order to explain the existence of discrete energy levels. he postulated that only circular orbits satisfying this condition are possible trajectories for the electron.

E_n=-\frac{1}{n^2}E_1

r_n=n^2a_0

Where E_1 and a_0 are ground state energy and Bohr radius.

 

[ZapperZ]

I'm not sure whether the conditions below justify what your teacher said. Actually, I don't know what is your teacher thinking. It's inappropriate to think of an electron as a body revolves around the nucleus same as planet moving around the Sun and says its path is deterministic. But, I think it's appropritate to say that the centripetal force balances the electric potential. CORRECT ME IF I AM WRONG!

Er.. you are wrong.

The centripetal force IS the "electric force"!

"Centripetal force" is a GENERIC term given to a cental force. ANY force can be a centripetal force. Gravity is the centripetal force in planetary motion. The Lorentz force is the centripetal force when a charged particle is moving in a magnetic field. In the case of a charge being pulled in due to coulombic force, then the electric field IS the centripetal force.

Think about it, if what you claim is true (" ...centripetal force balances the electric potential..."), then what is your NET force? Zero! They balance out, as you claim. Then why would it move in a circular path in the first place? That would violate Newton's first law, wouldn't it?

Zz.

 

[cks]

I just think it's inappropriate to put the analogy of revolving around the sun is same as electron revolving around the nucleus. His argument that says centripetal force acts and balanced by electric potential is correct to some sense.

 

[cks]

Ok, I see, I admitted I didn't use the word centripetal force correctly. I agreed with what you said that centripetal force is indeed electric force. How about centrifugal force balanced by electric force.

 

[ZapperZ]

Ok, I see, then I maybe used the wrong words, how about centrifugal force balanced by electric force.

Er.. invoking a fictitious force doesn't make it any better. There is no "centrifugral force" unless you intend to sit in the electron's reference frame. I thought this whole issue here is that there is no such ability at tracking an electron's path when we solve for the atom's orbital?

Why are we making this more complicated than it is? Write down the free-body diagram of a body in a simple circular motion, and that's that.

Zz.

 

[Parlyne]

I'm not sure whether the conditions below justify what your teacher said. Actually, I don't know what is your teacher thinking. It's inappropriate to think of an electron as a body revolves around the nucleus same as planet moving around the Sun and says its path is deterministic. But, I think it's appropritate to say that the centripetal force balances the electric potential. CORRECT ME IF I AM WRONG! Your answer to your teacher sayings sounds like your teacher is asking a question where you answer other things. What you said regarding uncertainty principle is correct, but he's saying other thing.

Let's do a semiclassical way of approaching hydrogen atom.

T=\frac{1}{2}m v^2-\frac{e^2}{ r}

Well, you should have no question about this, the total energy is the sum of kinetic and potential energy.

\frac{m v^2}{r}=\frac{e^2}{r^2}

Well, it's saying the centripetal force is equal to the electric force! surprise

m vr=n\hbar

The third equation expresses the quantization condition, introduced empirically by Bohr in order to explain the existence of discrete energy levels. he postulated that only circular orbits satisfying this condition are possible trajectories for the electron.

E_n=-\frac{1}{n^2}E_1

r_n=n^2a_0

Where E_1 and a_0 are ground state energy and Bohr radius.

This line of reasoning fails once you try to explain why there can be multiple angular momentum states corresponding to each energy level. In a sense you can trace the problem to the assumption of circular orbits.

The fact that this model leads to correct prediction for the energy levels, however, suggests that, mingled in with the oversimplifications, there must be some bit of good physical intuition. In this case, it can be found in a physical justification for the introduction of the Bohr quantization condition. If you start by assuming that the electron has wave properties and will interfere with itself if it's orbit is not an integral number of wavelengths, you can actually derive that condition. And, as it happens, this is essentially an over-simplified version of what you're doing when you solve the Schroedinger equation for the hydrogen atom.

 

[Crosson]

Teacher's who want to use Bohr's semi-classical model of the hydrogen atom as a teaching tool should at least be clear that this was "thought at one time to be a complete description, but it has its shortcomings, and has since been replaced by quantum mechanics...but the mathematics for that is very difficult, so we are going to work with Bohr's model".

 

[strangerep]

Today, I had an argument with my physics teacher about the movement of electrons around the nucleus. [...]

His argument was something like the following:
Electrons move around the nucleus much like planets around the sun. They move in an
elliptical orbit. The centrifugal force is what keeps them from crashing into the nucleus.

That's incorrect, as others have already said. Electromagnetic radiation from the
accelerating electron would make it lose energy and spiral inwards.

But perhaps the best thing to do (to maintain a constructive teacher/student relationship)
is to point your teacher at this forum and get him to say what he was really thinking (in
case there was some misunderstanding about the debate). I'm sure the heavy-hitters
around here will quickly set things straight.

 

[blechman]

I have taught physics at all levels, from high school tutorials to graduate courses. Let me say that as a physics teacher and researcher, I am deeply disturbed by this post. When a student asks for justification, and the teacher's response is to pull rank ("I teach physics, you don't, so shut up!"), that is criminal! If any teachers are reading this: if your students ask questions that you can't answer, then be honest - admit that you don't know the answer and encourage them to find out, as DpDx>hbar/2 (who I'll refer to as HUP) did. HUP: I cannot praise you enough! I truly feel very sorry for your colleagues who aren't as inquisitive as you are, and I very much hope that they turn out alright. As a active member of APS, I truly worry for them. Keep up the great work - don't trust anyone!

Especially me!

 

[Count Iblis]

Teacher's who want to use Bohr's semi-classical model of the hydrogen atom as a teaching tool should at least be clear that this was "thought at one time to be a complete description, but it has its shortcomings, and has since been replaced by quantum mechanics...but the mathematics for that is very difficult, so we are going to work with Bohr's model".

I thought that Bohr-Sommerfeld theory led to an extremely awkward formalism and that quantum mechanics is much simpler.

 

[Parlyne]

I thought that Bohr-Sommerfeld theory led to an extremely awkward formalism and that quantum mechanics is much simpler.

The simple Bohr model (with circular orbits) can be derived with a couple of simple physical assumptions and algebra. The full quantum version requires one to solve a non-linear partial differential equation (which can, in this particular case, be done analytically). I think there's really no question that the Bohr model is simpler. It's also quite wrong.

 

[Hans de Vries]

His argument was something like the following:
Electrons move around the nucleus much like planets around the sun. They move in an elliptical orbit.

Apparently one can still win a Nobel prize with such a picture...

proof:

http://www.nobel-prize.org/EN/Peace/images/iaea.jpg



Regards, Hans.

 

[Count Iblis]

The simple Bohr model (with circular orbits) can be derived with a couple of simple physical assumptions and algebra. The full quantum version requires one to solve a non-linear partial differential equation (which can, in this particular case, be done analytically). I think there's really no question that the Bohr model is simpler. It's also quite wrong.

Yes, but Bohr and Sommerfeld attempted to generalize the result for the hydrogen atom to general systems to obtain a general theory. What they came up with was much more complicated than Quantum Mechanics, http://en.wikipedia.org/wiki/Bohr_model#Refinements".

The Bohr-Sommerfeld model proved to be extremely difficult and unwieldy when its mathematical treatment was further fleshed out. In particular, the application of traditional perturbation theory from classical planetary mechanics led to further confusions and difficulties. In the end, the model was abandoned in favour of the full quantum mechanical treatment of the hydrogen atom, in 1925, using Schrödinger's wave mechanics. The current model of the atom, called the atomic orbitals model, could not have been formulated, however, without the groundwork laid down by the Bohr atom.

However, this is not to say that the Bohr model was without its successes. Calculations based on the Bohr-Sommerfeld model were able to accurately explain a number of more complex atomic spectral effects. For example, up to first-order perturbation, the Bohr model and quantum mechanics make the same predictions for the spectral line splitting in the Stark effect. At higher-order perturbations, however, the Bohr model and quantum mechanics differ, and measurements of the Stark effect under high field strengths helped confirm the correctness of quantum mechanics over the Bohr model. The prevailing theory behind this difference lies in the shapes of the orbitals of the electrons, which vary in shape according to the energy state of the electron.

The Bohr-Sommerfeld quantization conditions lead to questions in modern mathematics. Consistent semiclassical quantization condition requires a certain type of structure on the phase space, which places topological limitations on the types of symplectic manifolds which can be quantized. In particular, the symplectic form should be the curvature form of a connection of a Hermitian line bundle, which is called a prequantization.

 

[ΔxΔp≥ћ/2]

Well, I've been busy the last few days (don't do physics 3 and 2 at the same time kids). Anyway, I talked to my physics teacher the day after my first post and he was quite willing to accept my reasoning seeing as I researched it at length(I have yet to put together some proof). So thanks to nrqed for his rapid and clear response.

It seems that he had familiarised himself with the Bohr model as is shown in his textbooks. If the so-called nuclear physics class was offered at my high school, the students would do calculations based on that model, that I understand are easy enough to carry out, if not mostly (completely) wrong physically.

As for what’s criminal IMOHO, is that trough physics 1, 2, and 3, we do almost exclusively mechanics. I don't know if its like that elsewhere in the world, but it's a great way to get inquisitive young minds interested in physics (sarcasm). None of modern (after prehistory :-)) theory is touched: no relativity, no quantum mechanics, no thermodynamics, no electricity/magnetism (ph 4), no particle physics, no optics... ...nothing. I think that it is a problem that should be addressed if we expect to have a new generation of physicists. Students end up thinking that Newton is God and that all physicist do is push stuff and watch it move. I am the only person seriously considering a career in physics in my graduating class.

…well that’s my rant for the day.

 

[nrqed]

Well, I've been busy the last few days (don't do physics 3 and 2 at the same time kids). Anyway, I talked to my physics teacher the day after my first post and he was quite willing to accept my reasoning seeing as I researched it at length(I have yet to put together some proof). So thanks to nrqed for his rapid and clear response.

thanks for the update. And you are very welcome!

It seems that he had familiarised himself with the Bohr model as is shown in his textbooks. If the so-called nuclear physics class was offered at my high school, the students would do calculations based on that model, that I understand are easy enough to carry out, if not mostly (completely) wrong physically.

What bothers me a bit is that you said tha he teaches nuclear physics?
At what level? I am a bit shocked that someone would teach nuclear physics without a proper understanding of the most basic concepts of atomic physics.

 

[ΔxΔp≥ћ/2]

I don't really understand why he would have a nuclear physics class prepared that is not offered (most schools in my area don't even offer as many physics classes as we have available), seems to me that this stuff is standardised by the school district (province?). Not to mention that nuclear physics is usually a 3rd or 4th year class in university.

He prepared the class from textbooks. I think he followed some kind of model. I do not see how this class would be fit for a high school at all though.

 

[Bork]

I think you are mostly correct. The electron is like a fuzz cloud extending to infinity, but mostly concentrated in a region near the nucleus. It is most definitely not a billiard ball in shape or behaviour, but it does have some similar properties, and in this sense your teacher would be partially correct. When you solve the Schrödinger equation for the hydrogen atom and allow the electron to have orbital angular momentum, the math looks almost analogous to solving for elliptical orbits in Newton's theory, with some extra wrenches thrown in of course. Also, electrons don't radiate at the ground state energy, but at higher energies they do radiate and it gets close to classically predicted levels as you get up to the very high energy orbits.

 

[vanesch]

What bothers me a bit is that you said tha he teaches nuclear physics?
At what level? I am a bit shocked that someone would teach nuclear physics without a proper understanding of the most basic concepts of atomic physics.

Maybe it is more "elementary nuclear engineering", which is in fact really basic. You know, composition of the nucleus, mass defect (E = mc^2 oooh... ) energy balance in reactions, elastic collisions (neutrons on nucleus such as ping pong ball on soccer ball), some elementary nuclear model (radius as a function of N and Z)... fission reactions, moderators, diffusion equation etc...

You can do that without one single word of actual quantum mechanics (except maybe the concept of "excited state").

 

[blechman]

As for what’s criminal IMOHO, is that trough physics 1, 2, and 3, we do almost exclusively mechanics. I don't know if its like that elsewhere in the world, but it's a great way to get inquisitive young minds interested in physics (sarcasm). None of modern (after prehistory :-)) theory is touched: no relativity, no quantum mechanics, no thermodynamics, no electricity/magnetism (ph 4), no particle physics, no optics... ...nothing. I think that it is a problem that should be addressed if we expect to have a new generation of physicists. Students end up thinking that Newton is God and that all physicist do is push stuff and watch it move. I am the only person seriously considering a career in physics in my graduating class.

I have two comments on this:

1. I remember being in High School, thinking that there can be nothing more worthless than banging balls together and studying Newton's laws of motion. When are we going to get to Black Holes?! How boring! Unfortunately, all of modern physics builds on the "prehistoric" kind! I have done research on all sorts of "modern physics", and I'm sorry to say that a solid understanding of Newton has proved vital to my success. I know it seems like a drag, but if you're serious about doing physics, you have to have a first-name relationship with Sir Isaac. Don't worry, before you know it, you'll be getting deep into cool stuff. You've just got to be patient.

In the meantime, let me encourage you to keep doing what you seem to be doing - read pop-science books, get a subscription to "Scientific American" or "Physics Today" and ask questions on the forum and elsewhere. That'll help keep your interest up.

2. Unfortunately, for better or for worse, as you have discovered, many high school physics teachers do not have a solid background in physics. This is a serious problem, one that the APS and the AAPT have been struggling with for years. I don't know of a good solution (and it isn't really appropriate for this thread anyway - there are other forums for this kind of thing). But it is sad that many teachers cannot teach such "advanced" subjects, even if they wanted to, simply because they do not understand it themselves.

Also: most modern physics subjects require a certain mathematical sophistication that is not expected in high school students (such as vector calculus, group theory, etc); even E&M and thermo (which are not what I'd call "modern physics") involves a higher level of math than bouncing balls. It's not generally appropriate to teach a semester course on optics or nuclear physics at the high school level - you've just got to wait for university. Or if you are lucky enough to have a wonderful teacher, maybe you can arrange a reading course with him or her. But you can't expect that everywhere.

 

[Bork]

In my final year of high school physics, I didn't get along well with the teacher. He was from more of an engineering background, and didn't seem too interested in the more theoretical aspects of what I was studying. While sometimes he was willing to go into a more detailed theoretical or philosophical discussion of the concepts, most of the time he simply brushed off my concerns and shrugged his shoulders, basically telling me either to accept the answer as is or to find the answers myself from someone else.

Now in retrospect, I can actually appreciate his perspective a bit more. I thought I was at a level where I could understand the concepts in full detail, and that it would only be a few extra steps beyond what we had done in class. I had taught myself some calculus a year ahead of schedule, on my own time, thinking that oughtta suffice. Wrong! Once I got to university, it actually turned out to be a lot trickier than I had thought to apply calculus to problems and to properly describe the ideas we had been skimming over in high school. I had no idea how vast the subject of calculus actually was, and that it's still in development even today. You need to understand and have a good background in topics like differential equations, vector calculus, linear algebra, etc. etc. Even then when you've done introductory courses in these topics, you'll find out that's all basic material compared to what goes on at the grad level (you'd think mathematicians ought to have discovered a thing or 2 in the last 300 years since Newton, right?).

There's a lot of subtle material which is hidden away from sight when you study physics in high school, but trust me, if you thought you were done with clanking balls, springs, spinning tops and the like, think again. You've only just gotten started, because in university you're going to be torturing these concepts to death before they allow you to even taste the forbidden fruit of QM. And then after you've had your first nibble, they'll send you back to the basics to torture them even more. It would have made our mutual relationship a lot better if only my high school teacher had just pointed this simple fact out, rather than just saying we know it's true because some genius said so.

 

[Count Iblis]

When I was in high school I studied from university textbooks. It is not difficult at all. In high school they teach you almost nothing. They let you do the same type of problems over and over again. You can teach all of the high school math to a ten year old primary school student in about two years time.

When I was 16 I had mastered most of calculus, complex function theory (e.g. contour integration), discrete maths (e.g. solving combinatorial problems using generating functions). At university I learned linear algebra, but I could easily have learned that in high school too.


Primary and high school education is simply abominable as far as physics and math education is concerned

 

[blechman]

When I was 16 I had mastered most of calculus, complex function theory (e.g. contour integration), discrete maths (e.g. solving combinatorial problems using generating functions). At university I learned linear algebra, but I could easily have learned that in high school too.


Primary and high school education is simply abominable as far as physics and math education is concerned

You're the exception, not the rule, My Count! Most people in high school are not as motivated as you were, nor are they interested or even able to comprehend such subjects as complex analysis and group theory. You have to have a certain knack for these things, and there's a reason why it's not taught until you get to a more advanced level. It wouldn't be fair to the majority of students who would never benefit from such advanced concepts and would just be left in the dust. After all, sooner or later these young people are going to be voting for government members who will or will not vote to support research (or they'll become one of those people), and it's important to make sure they understand the basics of science. That's the real point of primary/secondary science and math education.

In a perfect world, there would be a special class for people like you who can leave other students behind. But there are only so many resources, money, and time! Instead, you just have to hang on and wait to pay x thousand dollars a year at a university to learn these things properly.

 

[ΔxΔp≥ћ/2]

I do agree on the importance of the physics that I learn in high school. I just think that it would not be difficult to expose us to other stuff. For example, we are never told that Newton’s law of gravitation has been replaced with general relativity, but his law still yields good results.

We often learn isolated and impractical cases in mechanics, I don't think it would be bad to talk about other types of physics if we omitted some of the math.

I taught myself special relativity. It is an amazing and surprising theory that any high school student can grasp. They can do most of the math and even the Minkowski diagrams.

At my high school we have wonderful textbooks with optics, particle physics, special relativity, EM and the beginning of QM in them, but we do not use them at all (and they are shiny new and did I mention wonderful?). I've read some of one and it is really top notch.

We do some elementary calculus in my physics 3 class (I don't think my teacher really knows how it works though)... ...we are only scheduled to learn the stuff next semester in math class (and we won't even be doing integrals... ...that's another story).

In general, I think that a lot of science (math, physics especially) does not teach us the history behind the theory (I thought about it and Newton and Cavendish are the only scientists ever mentioned in my physics class.). This would make the science much more accessible to students.

Unfortunately, we rarely if ever get to see what careers are possible in science.