1. Electron Atomic Orbitals
Modern Atomic Theory
Electron Atomic Orbitals

2. Part I: Quantum Mechanical Model
The Bohr model’s prediction of electron energies and locations was limited in accuracy to the Hydrogen atom.
Scientists DeBroglie and Schrödinger proposed that the electrons is acting as a wave as well as a particle.
Schrödinger developed an equation which predicts the location of an electron based upon probabilities.
Electrons in this model are located in Orbitals not orbits, despite sounding similar, they are vastly different.

3. The location of the electron is given by four numbers called Quantum Numbers
These quantum numbers act like your street address that give you homes location.
Zip code
State
City
Street
Number
Suite

4. Quantum Numbers [n, l, ml, ms]
n is the principle energy level. Limited to integers starting at 1. [n = 1, 2, 3….]
l is the orbital quantum number. Its values are limited to all integer values up to n-1.
ml is the magnetic quantum number. Its values are limited to integers from -l to +l.
ms is the electron spin designation. It is either +½ for spin up or -½ for spin down.

5. Shapes of Orbitals
The shape of the orbital is given by the second and third quantum numbers.
Instead of using a number for the second quantum number, l, a letter designation is used.
0 is s (sharp)
1 is p (principle)
2 is d (diffuse)
3 is f (fundamental)
4 is g
and so on down the alphabet

6. The third quantum number ml, determines the number of possible orientations of the orbital based on the second quantum number.
If l = 0 then ml can only be 0 and there is only one orientation of the orbital.
If l = 1 then ml can be [-1, 0, +1] and there are three orientations of a “p” orbital.
If l = 2 then ml can be [-2, -1, 0, +1, +2] so there are five orientations for a “d” orbital.
If l = 3 then ml can be [-3, -2, -1, 0, +1, +2, +3] so there are seven orientations for a “f” orbital.

7. s Orbitals [l = 0] The s orbital is spherically shaped.
There is only one possible orientation for the s orbital.
Each energy level has an s orbital and they get concentrically larger.
Two electrons fill each s orbital

8. p Orbital [l = 1] The p orbital is “dumbbell” shaped.
There are three possible orientations for the p orbital.
Each energy level n=2 and beyond has a p orbital and they get concentrically larger.
Two electrons fill each orientation of the p orbital for a total of 6 electrons per energy level.

9. p Orbitals – three orientations

10. d Orbital [l = 2] The d orbitals are uniquely shaped.
There are five possible orientations for the d orbital.
Each energy level n=3 and beyond has a d orbital and they get concentrically larger.
Two electrons fill each orientation of the d orbital for a total of 10 electrons per energy level.

11. d Orbitals

12. f Orbital [l = 3] The f orbitals are uniquely shaped.
There are seven possible orientations for the f orbital.
Each energy level n=4 and beyond has an f orbital and they get concentrically larger.
Two electrons fill each orientation of the f orbital for a total of 14 electrons per energy level.

13. f Orbitals

14. The location of electrons is a superposition of all of the individual orbitals.