# About basic atomic theory

#### Rajan_1993

Joined Dec 24, 2014
6
Q 1).
can anyone tell me why there are two electrons in inner most shell ('K' shell) from nucleus (I know the formula 2n^2 , but why only 2 electrons,why not 4 or 5 or many) ?

#### #12

Joined Nov 30, 2010
18,223
The facts you state are true, but the answer is probably in the Physics forum or the General Science forum. The first shell is considered, "filled" with 2 electrons if the atom is not hydrogen. The "why" is unknown to me.

#### studiot

Joined Nov 9, 2007
4,998
Since you are asking about shells I assume you understand simple maths.

Mathematicians start counting from zero (not 1), or even sometimes - infinity. Keep that in mind.

Now the simplest form of the equations (using only one dimension, x) that govern electrons have a solution

$$Energy = A\sin \left( {n\pi x} \right)*f(t)$$

Where f(t) is some function of time and n is an integer, starting at zero as noted above.

n is known as the principal quantum number.

The integer values of n correspond to the electron shells.

Of course, n = 0 is not very interesting since the whole expression is zero and means no shells and no electrons.
So we often miss out the 0 by convention and start with n = 1,2,3............

So that gives us the shells themselves, (do you know why we need the n to be an integer?)

Of course the real world has three dimensions and is otherwise more complicated.

So it turns out that to solve the full versions of the quantum equations we need more quantum numbers.
So the subsidiary quantum number is introduced, usually given the symbol l.

As before we start counting at zero so l = 0,1,2,3, .....and can go up to (n-1)

We also find there are two more quantum numbers, the magnetic quantum number, m which runs from -l (-l+1).......-1, 0, +1.........(l-1), l

and the spin quantum number s which can only take one of two values, +1/2 or -1/2, but can never be zero.

Any electron in an atom has a unique set of quantum numbers, no two electrons in an atom have the same four quantum numbers.
This is known as the Pauli exclusion principle.

So let us see the effect.

The lowest useful number for n = 1.
The lowest number for l = 0
The lowest number for m = 0 (since a negative number simply means the magnetic moment arrow) pointing the other way, but the lowest magnitude for the magnetic moment is 0 as it is a vector)

Which leaves s, which has two values.

So the lowest energy shell, ie the first shell has room for only 2 electrons.

By playing with the possible combination of values of the four quantum numbers we can generate all the possible arrangements in and within the shells.

Atoms with electrons in shells where the magnetic number is not zero exhibit magnetic properties.

#### Rajan_1993

Joined Dec 24, 2014
6
Thanks "studiot" for your explanation.

#### BR-549

Joined Sep 22, 2013
4,938
Atoms don't always have 2 electrons in the first shell. There are many atoms that have 8 electrons in the first shell.

H2 and He have 2.

Li has 3. Be has 4. B has 5. C has 6 and N has 7 and O has 8 electrons in the first shell.

F has a He nucleus and a 7(N) nuclear outer shell. The outer shell needs 8.........that's why it is so reactive.

A Ne atom has a the first shell of He with a O shell around it. This is why Ne and all noble elements are stable.

Electron shell theory is used to explain the relationships of the periodic table.

There is no proof of this theory and it breaks all electrical law.

Electric law is the only law we can prove.

#### studiot

Joined Nov 9, 2007
4,998
BR-549
Atoms don't always have 2 electrons in the first shell. There are many atoms that have 8 electrons in the first shell.
Maybe on Counter-Earth, Gor or in Flash Gordon's Universe.

But in our universe the first shell is complete with a Helium core of 2 electrons.
The first is often called the K shell (try Google).

Do you know what a shell is?
You may wish to know that the number of electrons per full shell is $$2{n^2}$$
and the number of orbitals per shell is $${n^2}$$

Where n is the shell number.

So we have for the first 5 shells

Shell number|Shell letter|Number of Orbitals|Electrons in full shell
1|K|1|1
2|L|4|8
3|M|9|18
4|N|16|32
5|O|25|50

Further shell theory only applies to individual atoms. It does not apply to polyatomic molecules and in particular to diatomic molecules like the hydrogen molecule.

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