[knowwhy]

Can you tell me exactly why the first electron shell can only hold a maximum of 2 electrons, why the second shell can only hold 8 and so on?  Why can't the first shell hold 3 electrons?  or 7?  Does anyone have a real answer to this or is it something that just is?

[Jorriss]

It's a 'just is' answer depending on how you detailed you look at it. If you look at it at a high school, general chemistry level, it just is. At a physical chemistry level it's a complicated question and at the most detailed level, who knows?

That was my way of saying, dunno really, it's some quantum stuff.

You could look at this
http://en.wikipedia.org/wiki/Energy_level#Intrinsic_energy_levels

[Khyati]

Its because all the shells are assigned some particular amount of energy & according to that they hold the numbers of

 electron. The first shell K has energy only to hold 2 electrons so it holds 2 electrons. As we move further the energy of

the shells increases & so the numbers of electrons too increases in them. All this energy & other stuffs have been

determined by the observations & experiments conducted by the Scientists in Quantum Physics.

[MrTeo]

It's a matter of quantum numbers: the Pauli exclusion principle tells us that no two electrons can have the same quantum numbers. As there are four of them (n,l,m,m_s) in each orbital we'll only find two of them with different spin quantum numbers (m_s, whose conventional values are +1/2 and -1/2).

Just a brief overview on the meanings of the quantum numbers: n is the so-called "principal quantum number" and tells us the energy level of the electron, the energy of our electron can be roughly exstimated comparing the E=l+n values of different orbitals. l tells us the different "shapes" of the orbitals and its values go from 0 to n-1 (e.g. for n=4 we'll have 0 (s orbitals) 1 (p orbitals) 2 (d orbitals) 3 (f orbitals)). m is the number which provides information about the different directions of the orbitals and goes from -l to +l (e.g. for l=2 (d orbitals) m=-2,-1,0,1,2: five orbitals so 10 electrons in the d-sublevel). The spin quantum number is the orientation of the electron's rotation and it's usually represented with small arrows pointing up or down when we write the Aufbau (or electronic configuration) of the atom.

Now you can easily understand why in the first level we'll only have 2 electrons (n=1, l=0, m=0, m_s=±1/2) while in the second one there are 8 of them (2 in the s-sublevel (the same reasoning I used with n=1) and 6 (n=2, l=1, m=-1,0,+1) in the p-sublevel).
There is also a general rule that tells us the total number of electrons in the first n levels (N=2n²), which you can try to demonstrate as an exercise. Here is a sort of demonstration for all who are interested in it.

For a generic level we can write:



So if we want to find the sum of the electrons in the first N levels we'll have to write:



Using the known relation (easily demonstrated too using induction principle):



we get:

[knowwhy]

It's a 'just is' answer depending on how you detailed you look at it. If you look at it at a high school, general chemistry level, it just is. At a physical chemistry level it's a complicated question and at the most detailed level, who knows?

Your answer is the best because it shows you understood EXACTLY what the question was asking and answered it directly and correctly.

I have been working on this problem for 18 years.  I know EXACTLY WHY there are 2 electrons in the first "shell" and not 3 or 4 or whatever.  It is no longer a matter of 'just is'. 

Since you have shown the most intelligence in answering this question, I would like to ask you:

What is the best application of this knowledge? 
(Should anyone have a worthy answer to this they may email me in the future at knowwhy@deskthing.com)

 

[knowwhy]

Its because all the shells are assigned some particular amount of energy & according to that they hold the numbers of

 electron.

I'm sorry, you failed to answer the question.  Because something is observed to be so, does not address why it is so.

[knowwhy]

It's a matter of quantum numbers: the Pauli exclusion principle tells us that no two electrons can have the same quantum numbers. As there are four of them (n,l,m,m_s) in each orbital we'll only find two of them with different spin quantum numbers (m_s, whose conventional values are +1/2 and -1/2).

I'm sorry, you have failed to address the heart of the question as well. 

[MrTeo]

Bizarre question anyway, and even more bizarre answer... (btw... have you been working 18 years on... electron shells? didn't you get bored?  )

[ardbeg]

the level of detail you want is probably best answered on a quantum physics forum, not a high-school level chemistry forum.

[knowwhy]

Bizarre question anyway, and even more bizarre answer... (btw... have you been working 18 years on... electron shells? didn't you get bored?  )

Not something one can work on everyday, but one day waiting in the airport it struck me.  I rushed home to build model after model of atoms.  Funny enough, I used gumdrops and toothpicks to build the first few dozen models...it was a cheap solution since they don't necessarily sell Atom Model Kits (at least not ones that fit this model).

I was surprised to see how simple, and logical it was.  I had been tinkering with it for years and had wondered if it had been discovered by someone else.  My background is not in chemistry, although it is a hobby to read what I can about chemistry and physics and thought someone might guide me in what to do with this information. 

Again, I know exactly why there are only 2 electrons in the most inner shell, no more-no less, so on and so forth for every other shell.  Almost every single day now when I actually sit down to work out more from the model I begin to see new things...to see why light travels as it does and many other things, very fascinating.

[knowwhy]

the level of detail you want is probably best answered on a quantum physics forum, not a high-school level chemistry forum.

Thank you, but I chose a starting point and this was it.  Obviously, at this point I can take my question to the next level.

[ardbeg]

congratulations, you have reached level 17.  you are now a chemistry ninja.  soon the secret handshake will be revealed to you.

[MrTeo]

Again, I know exactly why there are only 2 electrons in the most inner shell, no more-no less, so on and so forth for every other shell.  Almost every single day now when I actually sit down to work out more from the model I begin to see new things...to see why light travels as it does and many other things, very fascinating.

Amen