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Can someone help me understand electron shell calculations

Posted: Apr 07, 2010 12:49 pm
by mattthomas
I am trying to get my head around calculating electron shells from a given element and really getting headaches from it :scratch:

For example, I can calculate the electron shells for Ununquadium having an atomic number of 114 by this route
1s2,2s2,2p6,3s2,3p6,4s2,3d10,4p6,5s2,4d10,5p6,6s2,4f14,5d10,6p6,7s2,5f14,6d10,7p2
I'm using shell numbers when I work it out instead of letters as it's more intuitive to me

Which gives me electron shells of
K2
L8
M18
N32
O32
P18
Q4
2,8,18,32,32,18,4

But I run into problems for example I try to work things like Darmstadtium with an atomic number of 110

So I start with
1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s2, 4d10, 5p6, 6s2, 4f14, 5d10, 6p6, 7s2, 5f14, 6d8 (only 8 remaining from 110)

Then I tot them up
K2
L8
M18
N32
O32
P16
Q2

2,8,18,32,32,16,2, but the actual electron configuration is 2, 8, 18, 32, 32, 17, 1... I don't understand why 1 electron is being moved from Q to P

Please anyone who can explain this can you do it as monosyllabic and in crayon if possible, I've killed my brain trying to understand this!

Re: Can someone help me understand electron shell calculatio

Posted: Apr 08, 2010 8:47 am
by Darkchilde
Check where those orbits are. I haven't arrived yet at this point for my Physics course, but had studied something on that before. It has to do with ground states, where each orbit is, if I remember correctly. Check your textbook.

Re: Can someone help me understand electron shell calculatio

Posted: Apr 08, 2010 11:32 am
by Rachel
I don't know how much quantum mechanics you've done so let me know if this doesn't make sense or if I am being greatly patronising!
Keep in mind the two principles you need to work from when trying to work out electron configurations: the principle of least energy (lower energy shells fill up first) and the Pauli Exclusion principle (electrons are fermions so their total wavefunction is antisymmetric --> no two electrons can have the same quantum numbers). You'll also find it useful to remember the shapes of the electron orbits for different values of the quantum number l - i.e., as the orbital angular momentum increases, the orbit becomes more circular. For l=0, i.e. the s electrons, the electron has no orbital angular momentum so its path is like straight lines going through the nucleus and back again - it is more tightly bound than the p electrons because it spends more time close to the nucleus.

I'll start with a simpler example and see if you can work out how it applies to your problem:
Argon has the configuration 1s2 2s2 2p6 3s2 3p6. What's the configuration for potassium, the next element?
Now you'd expect the next electron to go into the 3d shell. However, the 3d electron spends most of its time in a circular orbit outside the inner shell electrons, while an electron in the 4d state will penetrate the inner shell more, so the shielding effect of the inner shell electrons is lessened, so it sees a greater 'effective' nuclear charge - hence it is more tightly bound. More tightly bound electrons have a more negative potential energy - so by the principle of least energy, the more tightly bound energy states will fill up first. So the next element has the configuration 1s2 2s2 2p6 3s2 3p6 4s
Then the next electron will go into the 4s state as well; after this the 3d shell begins to fill.

Does this make sense?

Re: Can someone help me understand electron shell calculatio

Posted: Apr 08, 2010 2:16 pm
by mattthomas
Darkchilde wrote:Check where those orbits are. I haven't arrived yet at this point for my Physics course, but had studied something on that before. It has to do with ground states, where each orbit is, if I remember correctly. Check your textbook.


I have no textbook, I'm just e-learning because I'm intensely interested.

Rachel, that is the level I am at where in my examples you can see I have ordered the shells by energy state
1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s2, 4d10, 5p6, 6s2, 4f14, 5d10, 6p6, 7s2, 5f14, 6d8 (only 8 remaining from 110)

It's just that shell 6 gains an electron from shell 7 which is counter intuitive to how I'm inclined to work this out, is there something about the shape of the orbit that I'm missing which would cause this

It's elements like these where I look at it and just can't seem to work out a reason, but not just these
91 Protactinium 2, 8, 18, 32, 20, 9, 2
105 Dubnium 2, 8, 18, 32, 32, 11, 2
107 Bohrium 2, 8, 18, 32, 32, 13, 2
109 Meitnerium 2, 8, 18, 32, 32, 15, 2
110 Darmstadtium 2, 8, 18, 32, 32, 17, 1

Re: Can someone help me understand electron shell calculatio

Posted: Apr 09, 2010 7:55 am
by Prof. Faust
mattwilson wrote:I am trying to get my head around calculating electron shells from a given element and really getting headaches from it :scratch:

[...]

How are you calculating the orbitals? What equations and assumptions are you using?

Re: Can someone help me understand electron shell calculatio

Posted: Apr 09, 2010 8:10 am
by mattthomas
Prof. Faust wrote:
mattwilson wrote:I am trying to get my head around calculating electron shells from a given element and really getting headaches from it :scratch:

[...]

How are you calculating the orbitals? What equations and assumptions are you using?


Okay I'll take you through my steps
I'll pick Zirconium at random, atomic number 40... I checked and it has 5 shells so I go by this route, and I'll write it out properly as I work it out so you can see where the flaw is on my method.

Start with
1s 2 (40-2=38)
2s 2 (38-2=36)
2p 6 (36-6=30)
3s 2 (30-2=28)
3p 6 (28-6=22)
4s 2 (22-2=20)
3d 10 (20-10=10)
4p 6 (10-6=4)
5s 2 (4-2=2)
4d 2 (2 remaining)

add these up
1 = 1s2 = 2
2 = 2s2+2p6 = 8
3 = 3s2+3p6+3d10 = 18
4 = 4s2+4p6+4d2 = 10
5 = 5s2 = 2

So I end up with 2,8,18,10,2 which I just checked... is right... helllllllp :confused:

Re: Can someone help me understand electron shell calculatio

Posted: Apr 11, 2010 11:35 pm
by Prof. Faust
mattwilson wrote:Okay I'll take you through my steps
I'll pick Zirconium at random, atomic number 40... I checked and it has 5 shells so I go by this route, and I'll write it out properly as I work it out so you can see where the flaw is on my method.

Start with
1s 2 (40-2=38)
2s 2 (38-2=36)
2p 6 (36-6=30)
3s 2 (30-2=28)
3p 6 (28-6=22)
4s 2 (22-2=20)
3d 10 (20-10=10)
4p 6 (10-6=4)
5s 2 (4-2=2)
4d 2 (2 remaining)

add these up
1 = 1s2 = 2
2 = 2s2+2p6 = 8
3 = 3s2+3p6+3d10 = 18
4 = 4s2+4p6+4d2 = 10
5 = 5s2 = 2

So I end up with 2,8,18,10,2 which I just checked... is right... helllllllp :confused:


OK, I think I see what is going on. The electron configuration algorithm is based off of calculating eigenstates of hydrogen's single electron at various excited energy levels. Each orbital corresponds to a different solution of the Scrödinger equation with a different electron energy level in a hydrogen atom. (Hydrogen is used as a model because the equations for more complicated atoms are insoluble, and approximate solutions for atoms that are more complex than helium are scant.) Atomic orbitals, as verified experimentally, are very similar to the shape and size of hydrogen's exited orbitals, so in most cases the model correctly predicts the energy levels of orbitals, and thus the arrangement in which electrons exist at an atom's ground state.

However, in a few cases actual atoms differ so much from the hydrogen model that it makes incorrect energy level predictions (read the whole section on the Aufbau principle for more specifics). Since Darmstadtium is a very heavy atom, with many particles interacting with each other, it is unsurprising that it deviates from the hydrogen model. You just happened to pick an exception to the normal rules by chance.

Re: Can someone help me understand electron shell calculatio

Posted: Apr 12, 2010 7:32 am
by mattthomas
So basically there are elements where you can't accurately figure out the electron shells by calculations, I've been busting my hump over trying to work something out that I can't work out haha... only me.... only me :lol:

This quote summed it up for me "The principle works very well (for the ground states of the atoms) for the first 18 elements, then decreasingly well for the following 100 elements"

Thanks for your time, I appreciate it (no'one on a chemistry forum even answered)

Re: Can someone help me understand electron shell calculatio

Posted: Apr 13, 2010 9:15 pm
by Prof. Faust
mattwilson wrote:So basically there are elements where you can't accurately figure out the electron shells by calculations, I've been busting my hump over trying to work something out that I can't work out haha... only me.... only me :lol:

This quote summed it up for me "The principle works very well (for the ground states of the atoms) for the first 18 elements, then decreasingly well for the following 100 elements"

Thanks for your time, I appreciate it (no'one on a chemistry forum even answered)


That's because most people on a chemistry forum are probably students who were at most only told, "this is an exception so memorize it."

Re: Can someone help me understand electron shell calculatio

Posted: Apr 13, 2010 10:53 pm
by klazmon
mattwilson wrote:So basically there are elements where you can't accurately figure out the electron shells by calculations, I've been busting my hump over trying to work something out that I can't work out haha... only me.... only me :lol:

This quote summed it up for me "The principle works very well (for the ground states of the atoms) for the first 18 elements, then decreasingly well for the following 100 elements"

Thanks for your time, I appreciate it (no'one on a chemistry forum even answered)


I suppose you could calculate it in principle but for accuracy you would have to use the Dirac equation rather than the Schrodinger equation as you can't ignore relativistic effects for these heavy elements. I guess it would take a lot of supercomputer time. The dreaded N body problem.

Re: Can someone help me understand electron shell calculatio

Posted: Apr 15, 2010 9:00 am
by mattthomas
klazmon wrote:
mattwilson wrote:So basically there are elements where you can't accurately figure out the electron shells by calculations, I've been busting my hump over trying to work something out that I can't work out haha... only me.... only me :lol:

This quote summed it up for me "The principle works very well (for the ground states of the atoms) for the first 18 elements, then decreasingly well for the following 100 elements"

Thanks for your time, I appreciate it (no'one on a chemistry forum even answered)


I suppose you could calculate it in principle but for accuracy you would have to use the Dirac equation rather than the Schrodinger equation as you can't ignore relativistic effects for these heavy elements. I guess it would take a lot of supercomputer time. The dreaded N body problem.


I have no real need to, I just wanted to understand why my calculations didn't always work but I'm happy with my progress on the subject :dance: