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.

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.

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.

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.

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.

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.

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.

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

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

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:

Shells and Subshells atoms

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

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

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

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

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

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The periodic table is organized in a way to make determining atomic configuations easy -Hydrogen: 1s1 (one electron) -Carbon: [He] 2s2 2p2 (6 e- ; 4 e- valence ) -Phosphorus: [Ne] 3s2 3p3 (15 e- ; 5 e- valence) 18

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.