1. Historical Overview of Quantum Mechanical Discoveries
James Cedric Maxwell (1865) proposed that light consist of a series of electromagnetic waves. Classical Physics was based on Newton’s laws of motions for particles and Maxwell’s laws of electromagnetic waves.
Max Planck (1900) proposed that light consist of energy (E=nhγ) where n is an integer and h is a constant (h=6.626 x 10-34). This demonstated that light can only have discrete values of energy and helped explain the ultraviolet catastrophe of Blackbody Radiation.
Albert Einstein (1905) proposed that light consist of packets of energy called photons and used it to explain the Photoelectric Effect.

2. Historical Overview of Quantum Mechanical Discoveries
Niels Bohr (1913) proposed a model of the Hydrogen atom consistent with the emission spectrum of Hydrogen.
Louis De Brogie (1924) proposed that matter has wavelike behavior (λ=h/p) where p is the linear momentum of the particle and h is a Planck’s constant (h=6.626 x 10-34).
Wolfgang Pauli (1925) proposed that electrons have spin characteristics and can be paired in an orbit only when their spins are in opposite directions.
Erwin Schrodinger (1926) postulated an equation (Hψ=Eψ) that allowed for the calculation of the probability distribution of an electrons over a molecule.

3. Historical Overview of Quantum Mechanical Discoveries
Werner Heisenberg (1927) proposed the Heisenberg uncertainty principle which states that it is not possible to find exact solutions to the position and momentum (Δp Δx = h/4π). Thus Δp is the uncertainty in linear momentum and Δx is the uncertainty in the position.
Max Born (1926) proposed solutions to the Schrodinger equation that represent the probability of finding an electron in a given volume element.

4. Wave Functions and Quantum Numbers
Chapter 3: Periodicity and the Electronic Structure of Atoms
11/11/2018
Wave Functions and Quantum Numbers
Probability of finding
electron in a region
of space ( 2)
Wave
equation
Wave function
or orbital ( )
solve
A wave function is characterized by three parameters called quantum numbers, n, l, ml.
Since we can’t ever be certain of the electron’s position, we work with probabilities.
Copyright © 2010 Pearson Prentice Hall, Inc.

5. Wave Functions and Quantum Numbers
Chapter 3: Periodicity and the Electronic Structure of Atoms
11/11/2018
Wave Functions and Quantum Numbers
Principal Quantum Number (n)
Describes the size and energy level of the orbital
Commonly called shell
Positive integer (n = 1, 2, 3, 4, …)
As the value of n increases:
The energy of the electron increases
The average distance of the electron from the nucleus increases
Copyright © 2010 Pearson Prentice Hall, Inc.

6. Wave Functions and Quantum Numbers
Chapter 3: Periodicity and the Electronic Structure of Atoms
11/11/2018
Wave Functions and Quantum Numbers
Angular-Momentum Quantum Number (l)
Defines the three-dimensional shape of the orbital
Commonly called subshell
There are n different shapes for orbitals
If n = 1 then l = 0
If n = 2 then l = 0 or 1
If n = 3 then l = 0, 1, or 2
etc.
Commonly referred to by letter (subshell notation)
l = 0 s (sharp)
l = 1 p (principal)
l = 2 d (diffuse)
l = 3 f (fundamental)
After f, the series goes alphabetically (g, h, etc.).
Copyright © 2010 Pearson Prentice Hall, Inc.

7. Wave Functions and Quantum Numbers
Chapter 3: Periodicity and the Electronic Structure of Atoms
11/11/2018
Wave Functions and Quantum Numbers
Magnetic Quantum Number (ml )
Defines the spatial orientation of the orbital
There are 2l + 1 values of ml and they can have any integral value from -l to +l
If l = 0 then ml = 0
If l = 1 then ml = -1, 0, or 1
If l = 2 then ml = -2, -1, 0, 1, or 2
etc.
Copyright © 2010 Pearson Prentice Hall, Inc.

8. Chapter 3: Periodicity and the Electronic Structure of Atoms
11/11/2018
Copyright © 2010 Pearson Prentice Hall, Inc.

9. Chapter 3: Periodicity and the Electronic Structure of Atoms
11/11/2018
Copyright © 2010 Pearson Prentice Hall, Inc.

10. The specification of atomic orbitals
Principle Quantum number (n)- An electron with the quantum number n has an energy of:
Angular momentum quantum numbers (l,ml) – an electron in an orbit with an angular momentum (ώ):
Z-component angular momentum (ml)- The z-component of the angular momentum is:

11. Shells and Subshells atoms

12. 1s orbital of Hydrogen 1s orbital of Hydrogen
90% probability of finding an electron

13. P-orbitals distribution function
l =1 (p-series)
ml = -1, 0, 1
90% probability of finding an electron

14. Distribution function of d-orbitals
l =2 (d-series)
ml = -2, -1, 0, 1, 2
90% probability of finding an electron

15. Orbital approximation
The total wavefunction is a product of each individual wavefunctions 15

16. Three rules dictate how electrons tend will fill-up orbitals.
Aufbau principle- electrons fill the orbitals from lowest to highest.
Pauli Exclusion Principle- electrons spin on an axis, each electron pair in an orbital has opposite spins.
Hund’s Rule- when electrons occupy degenerate orbitals, each will first occupy each orbital with parallel spins. 16

17. 17

18. The periodic table is organized in a way to make determining atomic configuations easy
-Hydrogen: s (one electron)
-Carbon: [He] 2s2 2p (6 e- ; 4 e- valence )
-Phosphorus: [Ne] 3s2 3p (15 e- ; 5 e- valence) 18

19. Pauli Exclusion Principle
Wolfgang Pauli (1924)
“When any two identical fermions are
exchanged, the total wavefunction must
change its sign”
The total wavefunction can
change its sign when spins
are opposite.