1. The QMM
Model
Mr. Matthew Totaro
Legacy High School
Honors Chemistry

2. The Bohr Model for Hydrogen

3. Problems with the Bohr Model
The Bohr model could only predict the emission spectrum for hydrogen.
The Bohr model failed to predict the emission spectra for all of the other elements.
The Bohr model did not take into account the fact that electrons repel each other, thus causing shifts in the lines in their spectra.

4. The Quantum-Mechanical Model of the Atom
Erwin Schrödinger applied the mathematics of probability and the ideas of quantizing energy to the physics equations that describe waves, resulting in an equation that predicts the probability of finding an electron with a particular amount of energy at a particular location in the atom.
Erwin Schrodinger

5. The Quantum-Mechanical Model of the Atom: the Schrodinger Equation

6. Probability Maps and Orbital Shape

7. The Quantum-Mechanical Model: Orbitals
The result is a map of regions in the atom that have a particular probability for finding the electron.
An orbital is a region where we have a very high probability of finding the electron when it has a particular amount of energy.
Generally set at 90 or 95%.

8. Orbits vs. Orbitals Pathways vs. Probability

9. The Quantum-Mechanical Model: Quantum Numbers
The Principal Quantum Number, n, specifies the main energy level for the orbital.
The number of electrons on each principal quantum number still follows the 2n2 rule.

10. The Quantum-Mechanical Model
Each principal energy level (shell) has one or more sublevels (subshells).
The number of sublevels = the principal quantum number.
The quantum number that designates the sublevel is often given a letter.
s, p, d, f.
Each kind of sublevel has orbitals with a particular shape.
The shape represents the probability map.
90% probability of finding electron in that region.

11. s Orbitals

12. p Orbitals

13. d Orbitals

14. f Orbitals

15. Many Electron Atoms

16. Shells and Subshells

17. The Number of Sublevels on an Energy Level
The number of orbitals on an energy level can be calculated by the n2 rule.
n = the principal energy level number.
1st energy level = (1)2 = 1 orbital
2nd energy level = (2)2 = 4 orbitals
3rd energy level = (3)2 = 9 orbitals

18. Sublevels and Orbitals
The sublevels of a principal shell have slightly different energies.
The sublevels in a shell of H all have the same energy, but for multielectron atoms the subshells have different energies.
s < p < d < f.
Each sublevel contains one or more orbitals.
s sublevels have 1 orbital.
p sublevels have 3 orbitals.
d sublevels have 5 orbitals.
f sublevels have 7 orbitals.

19. Electron Configurations
The distribution of electrons into the various energy levels and sublevels in an atom in its ground state is called its electron configuration.
Each energy level and sublevel has a maximum number of electrons it can hold (1 orbital = 2 e-).
s = 2, p = 6, d = 10, f = 14.
We place electrons in the energy shells and sublevels in order of energy, from low energy up.
Aufbau principle

20. 6s 6p 6d 7s 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d
Energy 2s 2p 1s

21. Practice —Write an electron configuration for Potassium (K)

22. Filling an Orbital with Electrons
Each orbital may have a maximum of 2 electrons with opposite spins.
Pauli Exclusion principle.
Electrons spin on an axis.
Generating their own magnetic field.
When two electrons are in the same orbital, they must have opposite spins.
So their magnetic fields will cancel.

23. Electron Spin

24. Orbital Diagrams
We often represent an orbital as a square and the electrons in that orbital as arrows.
The direction of the arrow represents the spin of the electron.
Unoccupied
orbital
Orbital with
1 electron
Orbital with
2 electrons

25. Filling an Orbital with Electrons
When filling orbitals that have the same energy, place one electron in each before completing pairs and they must have the same spin.
Hund’s rule.

26. Practice —Write an Orbital Diagram for Potassium (K)