Atomic Radii

[steevey]

If I have a helium nucleus, will electrons be closer to it than in a hydrogen nucleus due to the greater amount of positive charge force attracting an individual electron? And if the radii vary, what are the precise radii or at least what is the formula with a given atomic number?

 

Also about hybrid orbitals, how do I figure out their dimensions/radii? I mean there's geometry, but I mean besides that, like how I could figure out the shape and dimensions of a hybrid orbital between two Zinc atoms.

[swansont]

The electrons will be closer on average in He as compared to H. There is no precise value, because there is no classical trajectory.

[steevey]

The electrons will be closer on average in He as compared to H. There is no precise value, because there is no classical trajectory.

 

How come I can say the radius of an S orbital of the first energy level of hydrogen is precisely .529 angstroms in both the Bhor AND wave mechanics model? Not only that, but isn't there something like 0 potential between walls of orbitals, so the only possible place has to be the quantized places they can appear and not what your implying which is because there's no classical trajectory, electrons can appear in energy levels that aren't actually possible like a 2.375834766th energy level? So what if it doesn't have classical trajectory, it still has rules.

Edited May 20, 2011 by steevey

[swansont]

How come I can say the radius of an S orbital of the first energy level of hydrogen is precisely .529 angstroms in both the Bhor AND wave mechanics model?

 

Simple: you can't. Thats the most probable distance in wave mechanics. It's the peak of the distribution function.

[mississippichem]

Also about hybrid orbitals, how do I figure out their dimensions/radii? I mean there's geometry, but I mean besides that, like how I could figure out the shape and dimensions of a hybrid orbital between two Zinc atoms.

 

Well, hybrid orbitals don't really exist. They are an approximation given to freshmen undergrads and high school students that explain molecular geometry in a "pseudo wave mechanics manner". In real life, it's not so easy. Hybrid orbitals do not represent the true electron probability distribution function, but there is some truth to them.

In real life, we have to add atomic atomic orbitals through linear combination, optimize the geometry (usually with computers), check for vibrational overlaps...etc. The process is quite laborious and is something I'm just now getting to where I can wrap my head around.

 

What you want to know is the HOMO (highest occupied molecular orbital), between two zinc atoms. All the other lower energy orbitals contribute 0 to the net bond enthalpy. You're not going to like this answer but it depends on what else is bonded to the zinc atoms. Zn-Zn bridges do exist, but the dimensions of the d-d Zn-Zn bond will be dependent on back donation from other ligands. You can't just have di-zinc that I'm aware of. I'm sure some nerd has made it in the gas phase though.

[John Cuthber]

In order to measure the radius of an atom, it would need to have a surface.

It hasn't. However you can measure the "surface" that encloses most of the electrons most of the time.

On the other hand you can measure the size of atoms that are packed into solids and those values are available.

 

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

[steevey]

Simple: you can't. Thats the most probable distance in wave mechanics. It's the peak of the distribution function.

 

Yeah but thats what I care about. I don't care where the electron is the other 5-10% of the time, I want to know the locations and radii that cause all the interactions.

 

Well, hybrid orbitals don't really exist. They are an approximation given to freshmen undergrads and high school students that explain molecular geometry in a "pseudo wave mechanics manner". In real life, it's not so easy. Hybrid orbitals do not represent the true electron probability distribution function, but there is some truth to them.

In real life, we have to add atomic atomic orbitals through linear combination, optimize the geometry (usually with computers), check for vibrational overlaps...etc. The process is quite laborious and is something I'm just now getting to where I can wrap my head around.

 

What you want to know is the HOMO (highest occupied molecular orbital), between two zinc atoms. All the other lower energy orbitals contribute 0 to the net bond enthalpy. You're not going to like this answer but it depends on what else is bonded to the zinc atoms. Zn-Zn bridges do exist, but the dimensions of the d-d Zn-Zn bond will be dependent on back donation from other ligands. You can't just have di-zinc that I'm aware of. I'm sure some nerd has made it in the gas phase though.

 

SO your saying initial conditions need to be taken into consideration? What if I said a block of zinc at 72 degrees Fahrenheit? What would the orbitals between the zinc atoms look like? Because the electrons in molecules are shared in some way and I've seen hybrid orbitals formed by wave functions in QM...so if you know all the variables, why not hybrid orbitals?

[swansont]

Yeah but thats what I care about. I don't care where the electron is the other 5-10% of the time, I want to know the locations and radii that cause all the interactions.

 

It's a distribution function, and not that sharply peaked. The electron is about half as likely to be found at either 0.5 or 2 Bohr radii as at 1.

[steevey]

It's a distribution function, and not that sharply peaked. The electron is about half as likely to be found at either 0.5 or 2 Bohr radii as at 1.

 

Well I thought I saw from multiple sources that in places such as that first hydrogen radii that thats where the electron is about 90% of the time, hence the reason its the most likely place at that energy level, unless your suggesting that its energy level is always changing from its environment.

[swansont]

Well I thought I saw from multiple sources that in places such as that first hydrogen radii that thats where the electron is about 90% of the time, hence the reason its the most likely place at that energy level, unless your suggesting that its energy level is always changing from its environment.

No, what I'm suggesting is that your source was wrong.

 

http://twinkle_toes_engineering.home.comcast.net/~twinkle_toes_engineering/atoms.htm#Bohr%20hydrogen%20radius

 

Scroll down for the graph of the 1S orbital radial distribution.

[John Cuthber]

They often talk about thinks like the "90% surface" which is the shape that the electron has a 90% probability of being "inside" at any given time.

[steevey]

No, what I'm suggesting is that your source was wrong.

 

http://twinkle_toes_...drogen%20radius

 

Scroll down for the graph of the 1S orbital radial distribution.

 

Perhaps I am misinterpreting it, but I see a lot of specific values, no "limits" or sigmas to establish limits, no infinities, just single number answers for calculations of the radii.

 

and it says electrons actually "move 1/4 as fast" as if to say the electrons are actually in some way accelerating around the nucleus.

 

I get what it should be saying from your view, but I can just look right in my text book where it says "electron's location 90% of the time".

 

It even says "Diameter of typical atom = 300 pm". Doesn't say "from x - y" or "approximately" or anything to suggest the level of uncertainty your suggesting as far as I can see.

 

And if locations really are as unstable as you make them seem, why do specific stable compounds form? And how do they form over and over again in the same ways?

Edited June 7, 2011 by steevey

[swansont]

Scroll down to Real radial distributions. Second graph from where the link takes you, after the x-ray spectrum graph.

[steevey]

Scroll down to Real radial distributions. Second graph from where the link takes you, after the x-ray spectrum graph.

 

Oh yeah, I've seen that graph before, but it still goes to show that there's a radius where its really really most likely, and those are the ones I want to know for different atoms. I guess its more delocalized that I remember.

 

However, doesn't that mean that an electron can posses energy that would cause its own wave destruction? I mean, the graph also shows a non-zero probability of an electron being in between Bhor radii, and I thought an electron could only posses specific values of momentum for a given system.

 

Is there some other function I input into that graph to see all the quantized places an electron appears in, or does and electron really go into a continuum of energy states?

 

Also, is it possible to create a nucleus so massive electrons fall into it? Or does that already happen with large synthetic elements?

Edited June 7, 2011 by steevey