[DanKeitley]

After reading the book 'Quantum: Einstein, Bohr and the Great Debate about the Nature of Reality' (great book btw), I have a question about the angular momentum of electron shells.

In the book it says that electron shells have to have an angular momentum of nh/2pi . I understand that when an electron has an angular momentum of nh/2pi , it doesn't emit radiation and so therefore doesn't crash into the nucleus of the atom but I don't understand why that is.

If anyone could help me out, I would be thankful.

Cheers,
DK

[atsruser]

(Original post by DanKeitley)
After reading the book 'Quantum: Einstein, Bohr and the Great Debate about the Nature of Reality' (great book btw), I have a question about the angular momentum of electron shells.

In the book it says that electron shells have to have an angular momentum of nh/2pi . I understand that when an electron has an angular momentum of nh/2pi , it doesn't emit radiation and so therefore doesn't crash into the nucleus of the atom but I don't understand why that is.

If anyone could help me out, I would be thankful.

Cheers,
DK

Unfortunately there's no real answer to your question. Bohr simply postulated that electrons in allowed orbits would not radiate. This is a very odd thing to do, really, since classical electrodynamics (i.e. the classical theory of moving charges, due to Maxwell et al) predicts that an accelerating charge will radiate energy.

Since electrons were, at that time, considered to be bundles of charge in orbit about a nucleus, that would mean that they would radiate energy, which would mean they would lose KE, and hence move closer to the nucleus, which attracts them due to the Coulomb force. In short, any such atom would collapse in a very short time.

In order to explain why this didn't happen, Bohr made the ad-hoc assumption that radiation didn't take place for electrons in allowed orbits i.e. ones with orbital angular momentum a multiple of h-bar. He gave no theoretical justification for it. It's important to be aware of that: you can't understand it since there's no underlying explanation to be understood.

Modern physics essentially abandons any attempt to make a physical picture of electrons moving around according to Newtonian mechanics and electrodynamics. Instead, we have a purely mathematical description of atomic behaviour, some aspects of which can be given more-or-less plausible "physical" explanations (such as electron "spin", or some aspects of the two-slit experiment for electrons, or conductivity of metals (free electrons floating in a electron "gas")).

[DanKeitley]

Oh right! I suppose that's the abnormality of Quantum physics So could that suggest a weakness in Maxwell's theory? Or is it simply because Bohr made a very large assumption?

[mf2004]

(Original post by DanKeitley)
Oh right! I suppose that's the abnormality of Quantum physics So could that suggest a weakness in Maxwell's theory? Or is it simply because Bohr made a very large assumption?

Quantum Mechanics and Maxwell's theory can be fully unified but that's probably 4th year level undergraduate work (Quantum ElectroDynamics or QED). Bohr's model is not actually even properly quantum mechanical and if I remember correctly he didn't get to the right result for the right reasons, doesn't he assume the ground state has L=1 and that the electrons are point like? In a full quantum mechanical (not QED just QM which would be 2nd year undergrad probably) treatment the electrons are represented by wavefunctions rather than just coordinates and the ground state has L=0 this is much closer to what is actually happening.

[DanKeitley]

(Original post by mf2004)
Quantum Mechanics and Maxwell's theory can be fully unified but that's probably 4th year level undergraduate work (Quantum ElectroDynamics or QED). Bohr's model is not actually even properly quantum mechanical and if I remember correctly he didn't get to the right result for the right reasons, doesn't he assume the ground state has L=1 and that the electrons are point like? In a full quantum mechanical (not QED just QM which would be 2nd year undergrad probably) treatment the electrons are represented by wavefunctions rather than just coordinates and the ground state has L=0 this is much closer to what is actually happening.

Hmmm, sounds interesting! I'd like to look into that Could you expand on the L=0 thing though please?

The wavefunctions are something else that confuses me. I understand that Schrodinger's equation describes the movement of electrons, but I don't understand how you use the equation, how to interpret from it, or how Schrodinger came up with it.

Any help would be much appreciated

Cheers

[mf2004]

For L=0 do you know about angular momentum? If so you should know that in any classical orbit the angular momentum has to be non zero (otherwise the orbiting body crashes into nucleus) in quantum mechanics this isn't the case you can get "orbits", they're not really orbits they're states but think of them as being roughly the same thing in this case, with 0 orbital angular momentum. There's not really an easy way I can think of to explain why, it just comes out of quantum mechanics. http://en.wikipedia.org/wiki/Schr%C3...nd_development is quite nice for how he came up with it. How it works in short: you solve for a wavefunction rather than just a point this wavefunction is not necessarily 0 anywhere and then if you take the modulus squared of this wavefunction that gives you the probability density of the electron.

[DanKeitley]

That's strange, haha. Could you provide a link to find out more about why you can get orbits with an angular momentum of 0?

Also, reading the Schrodinger link, what does it mean by wavenumber? It says that

its spatial frequency, that is proportional to the reciprocal of the wavelength

but I'm struggling to get my head round what that means.

Another thing, why does it confine the wave to one dimension (a circular orbit) if it's a standing wave? After that bit I'm completely out of my depth lol How does it go from to ?!?!?!

the observation that the zero-wavelength limit of optics resembles a mechanical system — the trajectories of light rays become sharp tracks that obey Fermat's principle, an analog of the principle of least action.

I didn't know physicists could speak Klingon so well :P

Thanks for being patient with me, haha

[MeAndBubbles]

(Original post by DanKeitley)
After reading the book 'Quantum: Einstein, Bohr and the Great Debate about the Nature of Reality' (great book btw), I have a question about the angular momentum of electron shells.

In the book it says that electron shells have to have an angular momentum of nh/2pi . I understand that when an electron has an angular momentum of nh/2pi , it doesn't emit radiation and so therefore doesn't crash into the nucleus of the atom but I don't understand why that is.

If anyone could help me out, I would be thankful.

Cheers,
DK

Don't you bring in the other property of electrons called 'instrinsic spin' to explain this, rather than actual real spin in physical space. Because then no 2 fermions can occupy the same place according to Pauli's exclusion principle. So the electron is housed on a certain floor of a tower block of floors.

Because the electron is quantum particle of decribed by Planck's constant time frequency, it can't just arbitrarily loose energy unless it's enough energy for the quantum particle to move to a different energy level, one not occupied by another electron. Remember the electron is a standing wave around the nucleus and has a discrete wavenumber, not continuous energy like classical physics thoughts.

I'm still grappling with it myself, hope this helped.

[DanKeitley]

(Original post by MeAndBubbles)
Don't you bring in the other property of electrons called 'instrinsic spin' to explain this, rather than actual real spin in physical space. Because then no 2 fermions can occupy the same place according to Pauli's exclusion principle. So the electron is housed on a certain floor of a tower block of floors.

Because the electron is quantum particle of decribed by Planck's constant time frequency, it can't just arbitrarily loose energy unless it's enough energy for the quantum particle to move to a different energy level, one not occupied by another electron. Remember the electron is a standing wave around the nucleus and has a discrete wavenumber, not continuous energy like classical physics thoughts.

I'm still grappling with it myself, hope this helped.

Ah ok, I'm getting there. I think to fully understand it all you need understand each part of quantum mechanics in the order it was discovered, to get to grips with how it all fills into place.

I found a good link here that seems to explain part of my question. It says that it doesn't emit radiation because electrons don't agree with the Newton's law of motion (Classical view) and that electrons disappear and reappear in quantum jumps. Since the motion of the electron is not due to angular acceleration, it doesn't emit radiation.

http://answers.yahoo.com/question/in...7012231AAzamEq

However, this asks the question, how come there are discrete electron shells an electron can yield. If in quantum mechanics, accelerating charged particles don't emit radiation, why is there discrete electron shells? I'm sorry if I'm asking questions you guys have already answered

AHHHH I'm getting confused!

[MeAndBubbles]

(Original post by DanKeitley)
Ah ok, I'm getting there. I think to fully understand it all you need understand each part of quantum mechanics in the order it was discovered, to get to grips with how it all fills into place.

I found a good link here that seems to explain part of my question. It says that it doesn't emit radiation because electrons don't agree with the Newton's law of motion (Classical view) and that electrons disappear and reappear in quantum jumps. Since the motion of the electron is not due to angular acceleration, it doesn't emit radiation.

http://answers.yahoo.com/question/in...7012231AAzamEq

However, this asks the question, how come there are discrete electron shells an electron can yield. If in quantum mechanics, accelerating charged particles don't emit radiation, why is there discrete electron shells? I'm sorry if I'm asking questions you guys have already answered

AHHHH I'm getting confused!

Well, they're discrete particles of energy that are released from atoms in the form of photons. This got Albert Einstein the nobel prize. When a collision takes place with the electron, the particle must have enough energy to move it to the next higher orbital (or lower?) shell. A more intense, more energetic beam will not do this if the particles are not energetic enough.

If you're asking why the electrons are located in orbitals? The big why questions are not always answerable in science. Plus it's well know quantum physics is difficult to picture or explain intuitively. Do you do QM at A level? It would be possible to explain it in terms of potential energy, with the electron being in a potential energy well.

[suneilr]

(Original post by DanKeitley)
However, this asks the question, how come there are discrete electron shells an electron can yield. If in quantum mechanics, accelerating charged particles don't emit radiation, why is there discrete electron shells? I'm sorry if I'm asking questions you guys have already answered

The discrete shells come about naturally when you solve the Schrodinger Equation for atoms. The solutions are characterised by discrete labels representing the different shells.

The electron isn't orbiting the nucleus like a classical model. It's difficult to talk about motion and acceleration in quantum mechanics because it's impossible to know the exact location and momentum of a particle simultaneously.

[DanKeitley]

(Original post by MeAndBubbles)
Do you do QM at A level? It would be possible to explain it in terms of potential energy, with the electron being in a potential energy well.

I'm going into 6th form in September, but I'll look into it

(Original post by suneilr)
The discrete shells come about naturally when you solve the Schrodinger Equation for atoms. The solutions are characterised by discrete labels representing the different shells.

It seems as though, understanding Schrodinger's equation is fundamental to answering a lot of my questions. Does anyone know any good links/books that describe how it works etc. ?

So how is it that particles like electrons don't follow classical physics? ...and at what point do you start to convert from classical to quantum physics?

It seems as though a lot of this is based on assumptions (but I guess it's probably not), the fact that you cannot observe the position and momentum simultaneously sparks the idea that the particle is quantum jumping and isn't following classical physics. Personally, I struggle to think in the same way as the Copenhagen interpretation, that what your not observing doesn't exist. I don't mean to start the philosophical debate but how much of that is based on science and not assumptions?

Probably confusing myself here.

[suneilr]

(Original post by DanKeitley)
It seems as though, understanding Schrodinger's equation is fundamental to answering a lot of my questions. Does anyone know any good links/books that describe how it works etc. ?

I don't know if there's any way to easily understand it without studying the maths.

So how is it that particles like electrons don't follow classical physics? ...and at what point do you start to convert from classical to quantum physics?

Everything is quantum mechanical, but the quantum effects for large objects are normally negligible. The results of quantum measurements are probabilistic, but for macroscopic objects the probability distributions tends to the classical results.

It seems as though a lot of this is based on assumptions (but I guess it's probably not), the fact that you cannot observe the position and momentum simultaneously sparks the idea that the particle is quantum jumping and isn't following classical physics. Personally, I struggle to think in the same way as the Copenhagen interpretation, that what your not observing doesn't exist. I don't mean to start the philosophical debate but how much of that is based on science and not assumptions?

It's to do with the Heisenberg Uncertainty Principle. Position and momentum are conjugate variables which means that there is some bound on how well you measure the position and momentum. A similar classical result is the Fourier transform. If you have a small spread in one Fourier variable, the other variable will necessarily have a larger spread.

[mf2004]

(Original post by DanKeitley)
It seems as though, understanding Schrodinger's equation is fundamental to answering a lot of my questions. Does anyone know any good links/books that describe how it works etc. ?

So how is it that particles like electrons don't follow classical physics? ...and at what point do you start to convert from classical to quantum physics?

It seems as though a lot of this is based on assumptions (but I guess it's probably not), the fact that you cannot observe the position and momentum simultaneously sparks the idea that the particle is quantum jumping and isn't following classical physics. Personally, I struggle to think in the same way as the Copenhagen interpretation, that what your not observing doesn't exist. I don't mean to start the philosophical debate but how much of that is based on science and not assumptions?

Yes understanding the Schrodinger equation is key but there is more to it as well. There are good books but if You've just finished your GCSEs you most likely do not have the grounding in maths or physics to follow what is happening. The wikipedia article is quite good.

If you take the limit where stuff is "big" then classical mechanics is recovered from quantum mechanics. Quantum mechanics is always obeyed it's just that classical mechanics is much easier to work with and is a very good approximation on the scale of humans.

Quantum mechanics is incredibly well tested experimentally.

I'd recommend reading this: http://en.wikipedia.org/wiki/Quantum_mechanics its mathematical content is really low and it might be able to clear some things up but don't expect to have a full understanding of what is going on.

[DanKeitley]

(Original post by suneilr)
Everything is quantum mechanical, but the quantum effects for large objects are normally negligible. The results of quantum measurements are probabilistic, but for macroscopic objects the probability distributions tends to the classical results.

Ah ok, but it doesn't work the other way right? i.e. Classical can't describe quantum

(Original post by suneilr)
It's to do with the Heisenberg Uncertainty Principle. Position and momentum are conjugate variables which means that there is some bound on how well you measure the position and momentum. A similar classical result is the Fourier transform. If you have a small spread in one Fourier variable, the other variable will necessarily have a larger spread.

Yeah I'm sort of familiar with Heisenberg's Uncertainty Principle, although I can't remember how the position of a particle changes when you measure its momentum. I remember that measuring the position with an electron microscope will give it extra momentum, but I can't remember what affects the measurement the other way round?

(Original post by mf2004)
Yes understanding the Schrodinger equation is key but there is more to it as well. There are good books but if You've just finished your GCSEs you most likely do not have the grounding in maths or physics to follow what is happening. The wikipedia article is quite good.

Do you know what areas of Maths are required to gain an understanding of the equation? As you can probably tell already, I have quite a bit of time off :P

(Original post by mf2004)
I'd recommend reading this: http://en.wikipedia.org/wiki/Quantum_mechanics its mathematical content is really low and it might be able to clear some things up but don't expect to have a full understanding of what is going on.

Ah, thank you. I'll take a look

By the way, refering back to the Copenhagen Interpretation, am I right in saying that it suggests that an electron doesn't exist if its not being observed? I'm not sure I quite follow that way of thinking philosophically. The Copenhagen interpretation seems to argue that if a tree falls in a forest and no-one hears/sees it fall, it doesn't really happen. This seems quite an assumption. The fact that I have never been, or seen pictures of Slovakia, doesn't mean it doesn't exist, does it?

Probably confusing myself here, lol.

[ben-smith]

(Original post by DanKeitley)
Ah ok, but it doesn't work the other way right? i.e. Classical can't describe quantum

There are formulations of classical mechanics which are almost identical to their quantum counterparts. The hamilton jacobi equation in classical physics is uncanny.

[mf2004]

Ok so maths wise ideally: A level Maths+Further Maths + some partial differential equations + some basic linear algebra. (Doubtful you'll get through all of this before you start college in September)

Generally speaking I'd recommend wikipedia.
http://en.wikipedia.org/wiki/Copenhagen_interpretation

And then just wiki surf (clic the link of anything you are not 100% sure of what it says)

[DanKeitley]

(Original post by ben-smith)
There are formulations of classical mechanics which are almost identical to their quantum counterparts. The hamilton jacobi equation in classical physics is uncanny.

Oh right, so they're interchangeable?

(Original post by mf2004)
Ok so maths wise ideally: A level Maths+Further Maths + some partial differential equations + some basic linear algebra. (Doubtful you'll get through all of this before you start college in September)

Ok, I think you're right but I'll do some digging Hopefully when I fully understand the equation, a lot of my questions will be answered.

If anyone finds/knows any good links/books etc, please let me know :P

Cheers

[ben-smith]

(Original post by DanKeitley)
Oh right, so they're interchangeable?

Only after some brief modifications (see first canonical quantisation).

[...mo...]

Whats quantum mechanics?