Orbiting electrons

[igosaur]

Do electrons 'actually' orbit the nucleus or is it, as someone has suggested, simply a probability density function?

[Tom Vose]

No they don't orbit the nuclei of atoms. They instead exist as a cloud around the nucleus, due to the wave distribution of probability. So they do not orbit, but exist in all places around the nucleus.

[MolecularEnergy]

The probability of the finding the electron around the nucleus, if you where to deflate the wave function, is found by the density of [math]\int_{\Omega} |\psi|^2=1[/math]. This means that the probability of finding an electron at any one place, is by the absolute square of the wave function.

[iNow]

Indeed. Igosaur, you can find out more by searching for information on the "Bohr model." That was the model which suggested that electrons were like little moons orbiting tiny planets. Interesting intuitively, but not an accurate description. As Tom rightly mentioned, they are more of a "cloud" and better described by probability distributions.

 

 

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

The idea that electrons moved in an orbit-like way inside an atom, was first suggested in 1904. From about 1913 to 1926 the electrons were thought to orbit the atomic nucleus much like the planets around the Sun. Explaining the behavior of the electron "orbits" was one of the driving forces behind the development of quantum mechanics. In quantum mechanics, atomic orbitals are described as wave functions over space, indexed by the n, l, and m quantum numbers of the orbital or by the names as used in electron configurations, as shown on the right. As electrons cannot be described as solid particles (like a planet), a more accurate analogy to the electron would be that of a large and often oddly-shaped atmosphere, the electron, distributed around a relatively tiny planet, which is the atomic nucleus. Because of the difference from classical mechanical orbits, the term "orbit" for electrons in atoms, has been replaced with the term

orbital

.

 

 

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

The Bohr model is a primitive model of the hydrogen atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics, and thus may be considered to be an obsolete scientific theory. However, because of its simplicity, and its correct results for selected systems (see below for application), the Bohr model is still commonly taught to introduce students to quantum mechanics, before moving on to the more accurate but more complex valence shell atom.

[thedarkshade]

That was the model which suggested that electrons were like little moons orbiting tiny planets.

And the condition (IIRC) is that [math]m_ev_er=\frac{h}{2\pi}[/math].

[iNow]

Thanks, TDS (also, good seeing you).

 

What's the r in your equation? It looks like mass of the electron times velocity of the election times radius (?.. didn't think electrons had radius) equals plancks constant over two pi.

 

I just don't know enough about it to know how that equation applies to the question at hand.

[MolecularEnergy]

I could also derive Bohr's energy equation for the orbiting of electrons around the nuclei of atoms, if you wish...?

 

Thanks, TDS (also, good seeing you).

 

What's the r in your equation? It looks like mass of the electron times velocity of the election times radius (?.. didn't think electrons had radius) equals plancks constant over two pi.

 

I just don't know enough about it to know how that equation applies to the question at hand.

 

i do believe, the equation is related to the radius of the energy equation i am willing to derive.

[thedarkshade]

i do believe, the equation is related to the radius of the energy equation i am willing to derive.

Yeah!

I could also derive Bohr's energy equation for the orbiting of electrons around the nuclei of atoms, if you wish...?

There is one thing I don't undersand though. Where does the minus come from when doing the derivation?

[MolecularEnergy]

The minus sign derives from nromalizing the force between a proton and an electron

[thedarkshade]

The minus sign derives from nromalizing the force between a proton and an electron

In english, please?

[MolecularEnergy]

Well, the electron has a negative force, whilst the proton will have a force normalized by a positive force, so the electron is said not to fall into the nucleus.

[swansont]

What's the r in your equation? It looks like mass of the electron times velocity of the election times radius (?.. didn't think electrons had radius) equals plancks constant over two pi.

 

Orbital radius. The left-hand side of the equation is the orbital angular momentum, and the right side is the quantum of angular momentum.

 

There is one thing I don't undersand though. Where does the minus come from when doing the derivation?

 

Which minus sign? The force is attractive, so there will be a negative sign there. The potential energy is likewise negative; we define zero to be when the particles are infinitely far apart.

Edited December 21, 2008 by swansont
multiple post merged

[MolecularEnergy]

He means this part:

 

[math]-k \frac{e^2}{r}[/math]

 

I think???

[thedarkshade]

Which minus sign? The force is attractive, so there will be a negative sign there. The potential energy is likewise negative; we define zero to be when the particles are infinitely far apart.

Clear enough! Thanks

[pioneer]

Say we were to stop time by taking a high speed photo, would the electron still be everywhere? Say we used high speed video and then looked at the video, frame by frame, would the electron look the same in all the frames? I would guess if we studied frame to frame it looks like an orbit. One would see the path of maximum probability as it orbits about the nucleus. It might look like a fuzzy bright core orbiting it we plotted probability as brightness versus position. If we use real time, it looks like time lapse photography and sort of blurs together and doesn't look like an orbit.

 

Hiesenberg showed the uncertainty of an electron, but his uncertainty results weren't off an atomic diameter. It was a little fuzzy ball, instead of a point electron that had been assumed. We can't know position and momentum, but we can know one or the other. This would show up in stopped motion as a particular position.

Edited December 21, 2008 by pioneer

[swansont]

Say we were to stop time by taking a high speed photo, would the electron still be everywhere? Say we used high speed video and then looked at the video, frame by frame, would the electron look the same in all the frames? I would guess if we studied frame to frame it looks like an orbit. One would see the path of maximum probability as it orbits about the nucleus. It might look like a fuzzy bright core orbiting it we plotted probability as brightness versus position. If we use real time, it looks like time lapse photography and sort of blurs together and doesn't look like an orbit.

 

You still wouldn't see an orbit.

 

Hiesenberg showed the uncertainty of an electron, but his uncertainty results weren't off an atomic diameter. It was a little fuzzy ball, instead of a point electron that had been assumed. We can't know position and momentum, but we can know one or the other. This would show up in stopped motion as a particular position.

 

Show me the calculation. What is the uncertainty of the momentum in a Bohr orbit? What is the momentum?

[Severian]

One should not be using the Bohr model to discuss atoms, since it is wrong! We should instead use the Schrodinger Equation. (One of my pet hates is introducing atomic physics to undergraduates via the Bohr model.)

[swansont]

One should not be using the Bohr model to discuss atoms, since it is wrong! We should instead use the Schrodinger Equation. (One of my pet hates is introducing atomic physics to undergraduates via the Bohr model.)

 

That's what the calculation should show. pioneer's claim implies that the atom really does behave like the Bohr model. I'm requesting that he substantiate the claim with a calculation, without which it's really just a WAG.

[Royston]

(One of my pet hates is introducing atomic physics to undergraduates via the Bohr model.)

 

The reasoning with the course I recently finished, was to show how the Schrodinger equation imrpoved upon the Bohr model (a lesson in critical thinking I guess). However, it still devoted an entire chapter on the Bohr model, which seemed like a waste of time to me, especially as it kept pointing out it was wrong. It really should of just cut to the chase, and spent more time on the Schrodinger equation, because, frustratingly it glossed over a lot of the details...albeit the details will be covered in later courses.

 

a WAG.

 

A wobbly Arctic giraffe ?

[Severian]

The reasoning with the course I recently finished, was to show how the Schrodinger equation imrpoved upon the Bohr model (a lesson in critical thinking I guess). However, it still devoted an entire chapter on the Bohr model, which seemed like a waste of time to me, especially as it kept pointing out it was wrong. It really should of just cut to the chase, and spent more time on the Schrodinger equation, because, frustratingly it glossed over a lot of the details...albeit the details will be covered in later courses.

 

Maybe you should switch to a proper university

[Royston]

Maybe you should switch to a proper university

 

I would do, but I hear most the tutors are too preoccupied with research to teach properly.

[swansont]

 

A wobbly Arctic giraffe ?

 

Wild-Assed-Guess (as opposed to a domestic or feral one)