electron orbits

[someguy]

are there any current theories that explain why electron orbits are the shape that they are?

[swansont]

Are you looking for something beyond the quantum mechanical solutions that have been around for a while?

[someguy]

I'm not sure, do those explain exactly why the orbits on every level are that specific shape for any given orbit? if not, how close do they get or.. what exactly are those quantum mechanical solutions?

[swansont]

You get solutions for the hydrogen atom from QM, by solving the Schroedinger equation. There are a few refinements to that, which require the Dirac equation, but the basic orbital information is there.

[Norman Albers]

I think of electrons as the singularities that the vacuum wants to create. Give them an environment, like a nucleus, or nucleus plus other electrons, or maybe in a crystal, and the get the wave expressions that are manifested. Super-pinball.

[someguy]

hmm i don't completely understand the Schroedinger equations yet. there's prerequisites i don't really have to understand them fully plus my math is really rusty and even in its prime was not really totally sufficient. So i guess for now i'll just have to take your word for it that these adequately explain the shapes of the probability clouds for hydrogen. do you know of equations that explain their shape in density/volume? also do you know roughly how they came to figure that the clouds were this shape?

[swansont]

It pops out of the solution

 

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html

[someguy]

thanks for the link. unfortunately though it's a little beyond me. however if i understand it correctly it is using a different set of geometry to give the answer. it is positing a sphere as reference space. something like the trigonometric circle but 3d. I was thinking of something more along the lines of if say the probability cloud was a sphere then you would have an integral between to set coordinates of M/(4/3 pi r^3) where M would be some relation to r and that way you would have a mathematical formula describing the density and shape of the cloud all the way through, in this case a sphere of density unknown (at least i think that's what it is). if the rate of density can be known then for people that are good at math this should be pretty easy I think. but maybe i'm missing something.

[Klaynos]

It's in spherical polar coordinates because when dealing with things that are spherically symetric that is far far easier to work with.

 

There is a probability density described across the r axis, this is tied up in the wave equation for the electrons...

[Norman Albers]

 

There is a probability density described across the r axis, this is tied up in the wave equation for the electrons...

 

Could you elaborate this for me, Klaynos, I'm not sure why you say "across the r-axis"?

[Klaynos]

Could you elaborate this for me, Klaynos, I'm not sure why you say "across the r-axis"?

 

Well along the r-axis.

 

I'd suggest you read:

 

http://mathworld.wolfram.com/SphericalCoordinates.html

 

Because it's spherically symetric (the 1s shell) then the only changes are happening in r.

[Norman Albers]

Klaynos, in the 1s state, yes, or any excited s-state.

[someguy]

do you know of a non spherical coordinate equation that describes say the probability clouds of electrons for hydrogen? where you could plot density relative to r and also find the total mass of the system. the equation doesn't need to contain the number of electrons in it and whatnot and instead could just be a separate equation for every scenario. or does what you gave already reduce to exactly that if i enter the proper scenario. it doesn't look to me like it does.

[Klaynos]

do you know of a non spherical coordinate equation that describes say the probability clouds of electrons for hydrogen? where you could plot density relative to r and also find the total mass of the system. the equation doesn't need to contain the number of electrons in it and whatnot and instead could just be a separate equation for every scenario. or does what you gave already reduce to exactly that if i enter the proper scenario. it doesn't look to me like it does.

 

The wolfram site I linked to above gives you equations to convert the spherical polars into Cartesian...

 

For hydrogen there is only one electron. This makes the situation far simpler. But for more complicated systems we talk about the individual orbitals, each one needs to be derived separately.

[someguy]

oh oops my bad. ok i'll give it a try. i only ever took calculus II and that was a little while ago so i hope i'll be able to figure it out. but ya i think hydrogen is the way to go because it is simplest for starters like you said and also because of what I was trying to figure out a while ago about the speeds of electrons. remember that thread? grifter had figured that we could approximate the speeds of the electron for hydrogen. but we would be assuming it is moving. which i remember you and grifter were both adamant about the fact that it wasn't.

[Norman Albers]

oh oops my bad. ok i'll give it a try. i only ever took calculus II and that was a little while ago so i hope i'll be able to figure it out. but ya i think hydrogen is the way to go because it is simplest for starters like you said and also because of what I was trying to figure out a while ago about the speeds of electrons. remember that thread? grifter had figured that we could approximate the speeds of the electron for hydrogen. but we would be assuming it is moving. which i remember you and grifter were both adamant about the fact that it wasn't.

Babe, I think you speak understandably. This is a major aspect of quantum theory and I think it is called the Copenhagen interpretation whereby the wavefunction is taken to be useful as a probability density. This is not the only possibly useful perspective. Do our measurements demand that there be a unit of charge in some place?