Atomic orbitals

The place occupied by electrons: atomic orbitals

Library shelves, as an image of how electrons are arranged in shells and orbitals

The electrons are located around the nucleus in a very organized way, like books in a library, in rows and shelves.
No book may be taking the place of another!
No book can have the same identification label as another!
The same thing happens to the electrons.

Electrons are located in shells that are designated by a number. These would be like the rows of shelves. The greater the number of a layer, the further it is from the nucleus and more "shelves" (orbitals) it has. The orbitals ("shelves") are named with the letters "s", "p", "d" and "f". The "s" shelf holds two electrons, in the "p" there are six, in the "d" ten and in the "f" fourteen.

Orbitals of each shell and number of electrons allowed in each of them.

shell	s	p	d	f
1	2
2	2	6
3	2	6	10
4	2	6	10	14
5	2	6	10	14
6	2	6	(10)	(14)
7	2	(6)	(10)	(14)

Although shells 6 and 7 theoretically support p, d and f orbitals, no atoms have been found in nature that have electrons in them. For this reason they have been indicated in parentheses.

The identification label of the electrons is composed of four numbers (called "quantum numbers"): N, L, M and S.

Number N indicates the shell it is in, from 1 to 7.
Electrons of shell N have different L numbers, from 0 to (N-1).
Electrons with N > 1, having numbers L > 0, bear M numbers going from +L to -L passing through 0
Two electrons having equal N, L and M numbers must have different number S (+½ or -½).

N numbers indicate the shell

L numbers are for the type of orbital

M numbers mark the orbital subtype

S numbers correspond to the electron 'spin'

There are "s" orbitals of only one subtype, three subtypes of "p" orbitals (p_x, p_y, p_z), five of type "d" and seven of type "f ".
(subtypes d y f bear complex shapes that exceed the goal of this course).

There cannot be two electrons in an atom that have the same quantum numbers (Pauli exclusion principle).

Let's take the electrons of the first three shells as an example.
Which are their labels?

N	L	M	S	Orbital where it lays
1	0	0	+½ ó - ½	shell1, orbital s (1s)
2	0	0	+½ ó - ½	shell 2, orbital s (2s)
2	1	-1	+½ ó - ½	shell 2, orbital p_x (2p_x)
2	1	0	+½ ó - ½	shell 2, orbital p_y (2p_y)
2	1	1	+½ ó - ½	shell 2, orbital p_z (2p_z)
3	0	0	+½ ó - ½	shell 3, orbital s (3s)
3	1	-1	+½ ó - ½	shell 3, orbital p_x (3p_x)
3	1	0	+½ ó - ½	shell 3, orbital p_y (3p_y)
3	1	1	+½ ó - ½	shell 3, orbital p_z (3p_z)
3	2	-2	+½ ó - ½	shell 3, orbital d (3d_xy)
3	2	-1	+½ ó - ½	shell 3, orbital d (3d_xz)
3	2	0	+½ ó - ½	shell 3, orbital d (3d_yz)
3	2	1	+½ ó - ½	shell 3, orbital d (3d_x²-y²)
3	2	2	+½ ó - ½	shell 3, orbital d (3d_z²)

In each atomic orbital (subtype) only two electrons fit, each with a different S number (+½ or -½).

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