Physical Dimensions of electron shells

[darkdave3000]

Unfortunately, this is one of those example of let's jump into the middle of the story and see if we can make heads or tails of what has happened so far.

Electrons in an atomic orbital don't actually "interfere" with themselves, at least not in the way you are thinking. They may be in a superposition of states, but these are not the "interference" phenomenon that you are thinking of.

If you are using something to back your claim, it is a clear policy of this forum that you make an explicit reference to that source. Don't just say that you saw something on YouTube, give us the link so that we may verify if (i) it is a legitimate, correct source, (ii) it isn't crackpottery (iii) and that you understood what it said correctly. Otherwise, there's no way to know!

Electron-electron interaction in an atom isn't just a matter of "interference". Besides an added Coulombic interaction between 2 electrons (i.e. an added term in the potential of the Hamiltonian), you also have to satisfy the exclusion principle due to the spin of the individual electrons. It is why we have bonding and antibonding states that depends on how each of the spins align!

You have a lot to learn, but unfortunately, it doesn't appear that you are starting this from the very beginning, the way most of us learn this material. This is why I stated that you're jumping into the middle of the story and thinking that you can make sense out of it.

Zz.

Given enough time and study I can make sense of it, I have to start from somewhere! Starting in the middle of the story is better than starting from scratch. I'll send you the link tomorrow when I am back at work. I am home now. Have a good day!

 

[ZapperZ]

Given enough time and study I can make sense of it, I have to start from somewhere! Starting in the middle of the story is better than starting from scratch.

It isn't. You may think it is "better", but look at just this thread. Every time someone tries to make one step forward, we have to then go 2 or 3 steps back, because we have to explain our explanation. There shouldn't be a reason to explain the geometry of, say, the s-orbital IF you have solved the simple Schrodinger equation.

There is no short-cut.

Zz.

 

[DrClaude]

This answer is some what useful, can you give me a link to such a program that you recommend?

Have a look at GAMESS.

I understand that this is a very complex and dynamic problem to solve, can you help me to understand it discretely?

Lets look first at how it is done for hydrogenic atoms (forgetting about spin to keep it simple):

1. Solve the Schrödinger equation for nucleus + electron in the center-of-mass frame analytically
2. This leads to a series of discrete energy states depending on three quantum numbers, n, l, and m_l
3. Take the electron to be in a single of those states, with a given spatial wave function
4. Taking an arbitrary limit (such as probability = 0.9), plot the absolute value squared of the previous wave function, and call that a visual representation of the wave function

Problem at step #1: analytical solutions exist only when one electron is present. Only numerical solutions are possible, unless big approximations are made. Considering numerical solutions, it is easy to see what the full electronic density is, but considering it electron by electron is problematic, as these solutions are not in terms of the equivalent quantum numbers mentioned in point 2.

One possible solution is to fully neglect electron-electron interaction, which is what I think is done in the video you have posted. I don't see much advantage to this approach from the point of view of individual orbitals, are they are the same as in hydrogen. Also, it leads to an incorrect result, as is plainly seen in the video: when all p orbitals are filled, the resulting electron distribution is necessarily spherical, which is not what is obtained by naively superposing dumbbell drawings of p orbitals.

It is possible to use other approaches, such as the central field approximation, to get better approximations of single-electron orbitals, but I am not sure I see the point of investing much effort in doing that with some rigor.

 

[edguy99]

.. can you have a look at the last question I posted about Helium and hydrongen's 1s shell? Could you be so kind as to compare and contrast to help me? What remains the same and what is different between 1s in hydrogen and in helium.

Great question that remains unanswered. To try and help clarify the question in specific terms:

1. You often see the hydrogen atomic orbitals visualized, but most often without a distance scale. Where would a circle of 53 picometers (Bohr radius) be overlaid on a hydrogen 1s orbital?

2. Has a picture ever been drawn of helium orbitals and where would a circle of 53 picometers be overlaid?

 

[darkdave3000]

Great question that remains unanswered. To try and help clarify the question in specific terms:

View attachment 122812

1. You often see the hydrogen atomic orbitals visualized, but most often without a distance scale. Where would a circle of 53 picometers (Bohr radius) be overlaid on a hydrogen 1s orbital?

2. Has a picture ever been drawn of helium orbitals and where would a circle of 53 picometers be overlaid?

Thanks for understanding where I'm coming from! Surely there has got to be a way to explain this in laymen's terms without studying the Shrodinger equation yet.

 

[Drakkith]

Thanks for understanding where I'm coming from! Surely there has got to be a way to explain this in laymen's terms without studying the Shrodinger equation yet.

There is. It just won't be accurate. So you either choose to be accurate, which requires extremely complex calculations involving quantum mechanics, or you choose to be not accurate and just make some approximations. Either way works just fine depending on what you're going for. The "best bang for your buck" is to probably just model everything as having a single electron, like hydrogen. It's a little bit of work to understand how to use Schrodinger's Equation for a hydrogen atom, but it's far easier than trying to model multi-electron atoms using it.

 

[darkdave3000]

There is. It just won't be accurate. So you either choose to be accurate, which requires extremely complex calculations involving quantum mechanics, or you choose to be not accurate and just make some approximations. Either way works just fine depending on what you're going for. The "best bang for your buck" is to probably just model everything as having a single electron, like hydrogen. It's a little bit of work to understand how to use Schrodinger's Equation for a hydrogen atom, but it's far easier than trying to model multi-electron atoms using it.

I will try and understand the laymen's model first before resorting to more accurate means.

So can some one try and explain to me the laymen's explanation to the shape of the Helium 1s?

Is it a sphere? If not then what exactly? And how big is it? (radius) Can you sketch it?

 

[Drakkith]

I will try and understand the laymen's model first before resorting to more accurate means.

So can some one try and explain to me the laymen's explanation to the shape of the Helium 1s?

Is it a sphere? If not then what exactly? And how big is it? (radius) Can you sketch it?

You can explain things in laymen's terms, but there isn't really a laymen's model. A model inherently implies a lot of math and such that is rarely explained to laymen. Even modeling simple harmonic motion would be beyond what I would call "laymen".

But you yourself can build models of any arbitrary complexity. An extremely basic model could just model each atom as a sphere with a radius equal to the covalent radius for each element.
If you want to get more complicated than that then you're going to have to get into the details of the math. There just isn't a model anywhere close to a "laymen's model" that will give you the shapes of the different orbitals or their sizes. You cannot get the familiar lobes seen in the various subshells without computing wavefunctions, so if you're hoping to do that without quantum equations then you're simply out of luck.

 

[darkdave3000]

You can explain things in laymen's terms, but there isn't really a laymen's model. A model inherently implies a lot of math and such that is rarely explained to laymen. Even modeling simple harmonic motion would be beyond what I would call "laymen".

But you yourself can build models of any arbitrary complexity. An extremely basic model could just model each atom as a sphere with a radius equal to the covalent radius for each element.
If you want to get more complicated than that then you're going to have to get into the details of the math. There just isn't a model anywhere close to a "laymen's model" that will give you the shapes of the different orbitals or their sizes. You cannot get the familiar lobes seen in the various subshells without computing wavefunctions, so if you're hoping to do that without quantum equations then you're simply out of luck.

Once I start getting into the maths it will show that S shells are spheres and P shells are teardrops right?
But I haven't got into the maths yet and I know that P shells are teardrops. So in the same way couldn't you explain what the shape of 1S of helium really is without getting into the maths? Maybe supply me a picture on the next post?

 

[Drakkith]

Once I start getting into the maths it will show that S shells are spheres and P shells are teardrops right?
But I haven't got into the maths yet and I know that P shells are teardrops. So in the same way couldn't you explain what the shape of 1S of helium really is without getting into the maths?

You can explain it, but you can't model it.

Maybe supply me a picture on the next post?

Sorry, computational chemistry is well beyond my skills. I've barely dealt with the Schrodinger equation in one of my classes and even there we kind of just glossed over it.

 

[Khashishi]

When you have one electron, you can imagine the electron in different states which you can label 1s, 2s, 2p, etc. When you have two or more electrons, you can't separate the solution into the sum of single electron states. For example, in helium, the shape of the 1s orbital in a 1s2s state will be different than the shape of the 1s orbital in a 1s2p state. Moreover, the shape will depend on whether the electron spins are aligned or opposite. So there are two 1s2s states: 1s2s [3S1] and 1s2s [1S0]. So it does not make sense to talk about the shape of the 1s orbital by itself, unless you are talking about a helium+1 ion.

Basically, unless you want to spend years of scholarly research on this (by then you will outgrow your teachers), you will have to make some huge approximations. And you can approximately say that the 1s orbital of helium looks like the 1s orbital of hydrogen, but scaled down by slightly less than 2 because of the higher attraction of the nucleus. It's less than 2 because there is some cancellation of the nuclear charge by the other electron.

 

[Drakkith]

My question for the OP is do you know how to go about making even a very basic model of something like this? We can give you equations and modeling methods, but if you don't know how they all fit together then it's all pointless. As an example, while I was taking my first physics class I used my knowledge to make a very simple model of the Earth orbiting the Sun using the equations I learned from my class. I could have gotten those equations from anywhere. I needed to take the class to understand how to use them and when they applied. Knowing how to get the force from the gravitational force equation is useless if you don't know how to find the force vector and how to use the other kinematic equations to make the Earth move correctly. Similarly, giving you the equations used in various approximations is pointless if you have no idea how to use them.

 

[edguy99]

When you have one electron, you can imagine the electron in different states which you can label 1s, 2s, 2p, etc. When you have two or more electrons, you can't separate the solution into the sum of single electron states. For example, in helium, the shape of the 1s orbital in a 1s2s state will be different than the shape of the 1s orbital in a 1s2p state. Moreover, the shape will depend on whether the electron spins are aligned or opposite. So there are two 1s2s states: 1s2s [3S1] and 1s2s [1S0]. So it does not make sense to talk about the shape of the 1s orbital by itself, unless you are talking about a helium+1 ion.

Basically, unless you want to spend years of scholarly research on this (by then you will outgrow your teachers), you will have to make some huge approximations. And you can approximately say that the 1s orbital of helium looks like the 1s orbital of hydrogen, but scaled down by slightly less than 2 because of the higher attraction of the nucleus. It's less than 2 because there is some cancellation of the nuclear charge by the other electron.

Thank you for the approximation on the Helium 1s² orbital. Information on shapes of orbitals is very hard to find. Like the OP, I am not so much interested in the calculations (although important of course), but am looking for published results to save time (but I am also happy with your approximations). Can you approximate the other 4 you mention? 1s¹2s¹[3S1], 1s¹2s¹[1S0], 1s¹2p¹[3S1], 1s¹2p¹[1S0]

Is there a place where people can look this up?

 

[Khashishi]

I'm really not an expert at this, so I don't know.

 

[darkdave3000]

From a computer scientist point of view I can model any complex/non-trivial 3D shape. Just need the geometry/pixel instructions. For example, if you tell me render a perfect sphere, I can do that. I can also render a porcupine, a pineapple, a cratered moon, it really doesn't matter how complex the shape is, it can be rendered on a computer screen as long as it has 3 dimensions of space and I have a scale to decide how big the 3d model is.

But I don't know how a shrodinger equation works yet and I'm guessing its a lot of work to invest to understand it. So I would like a compromised laymen's 3D instruction on rendering the helium's 1s for 2 elections. So there was a very helpful man in this thread who said 1s should be a sphere 2 times closer to the nucleus for 1 election, I like to know the non ion solution to this for Helium's 2 electrion 1s if possible but a compromised approximation just like the first.

So perhaps with 2 elections interfering with each other will it be like 2 spiked balls with the spikes between each other? Or a spiked ball and a cratered moon overlapping each other?

In fact I don't understand why we were talkinga bout 2s or P shells because Helium has only 2 elections and they both should be occupying the 1s during rest. Am I right or were you talking about excited states?

My question for the OP is do you know how to go about making even a very basic model of something like this? We can give you equations and modeling methods, but if you don't know how they all fit together then it's all pointless. As an example, while I was taking my first physics class I used my knowledge to make a very simple model of the Earth orbiting the Sun using the equations I learned from my class. I could have gotten those equations from anywhere. I needed to take the class to understand how to use them and when they applied. Knowing how to get the force from the gravitational force equation is useless if you don't know how to find the force vector and how to use the other kinematic equations to make the Earth move correctly. Similarly, giving you the equations used in various approximations is pointless if you have no idea how to use them.

 

[Drakkith]

In fact I don't understand why we were talkinga bout 2s or P shells because Helium has only 2 elections and they both should be occupying the 1s during rest. Am I right or were you talking about excited states?

I only brought it up because that's part of what you've been asking about since the beginning of the thread.

 

[Khashishi]

You didn't say you only were interested in the ground state.

 

[edguy99]

I want to model atoms of the periodic table using OpenGL (API for 3D graphics). I was told by a physics teacher one time that this cannot be done because it's not solvable.

Can you guys confirm? Apparently only the shells of the hydrogen atom has been solved meaning that I can only model the lightest atoms but not any other atom?

I want to visualize the S shell P shell etc etc and even use the shrodinger equation to simulate the probability fields of electrons.

Here are a couple of ideas, nothing models everything, but some parts work pretty well and each has its pros and cons.

1/ For electrons that are not bound, consider the energy needed to ionize Hydrogen never exceeds 13.6eVolts. This is the same as the coulomb force at 53 picometers (the Bohr radius). To model this, assume a standard inverse square law of the coulomb force (just like gravity) outside of 53 picometers, but, the proton exerts no force on the electron inside the 53 picometer sphere or shell. You end up with a model like this game. Note for Helium, the ionzation energy for the last electron never exceeds 13.6*4=54.4eVolts, again equivalent to the coulomb force at 53 picometers. To model this correctly for Helium, you also assume the coulomb force outside 53pm and no force inside the shell.

2/ For bound electrons, fill electrons shells made up of multiple orbitals of 2 electrons each. In 3d the Neon atom looks like this (s1, s2 and p2 filled). The filling of these shells in 2d can be modeled like this. Assume again that once a shell is filled, electrons are no longer attracted to points inside the shell, but rather to the shell itself.

3/ For why the shells stay divided up into orbitals, I like this explanation on spherical harmonics and quantum numbers. The only way the s-levels are spherical are if the surface of the sphere is expanding and contracting. Higher S levels are the harmonics of this expanding and contracting rate. For the P levels, we have the "sloshing" of the sphere surface back and forth or in and out at points opposite to each other. This can be done in 3 directions (x, y and z) all at once. Now you have modeled electrons sitting at the proper energy levels.