Introduction to Quantum Theory for General Chemistry By Doba Jackson, Ph.D. Associate Professor of Chemistry & Biochemistry Huntingdon College

Introduction to Quantum Theory Elements have unique Atomic Spectra Mathematical Properties of Atomic Spectra Ionization energies of elements Electromagnetic radiation Photoelectric effect Debroglie equation Energy is quantisized

Elements have a unique spectra

Elements have a unique atomic spectra

Electromagnetic Energy and Atomic Line Spectra Chapter 3: Periodicity and the Electronic Structure of Atoms 8/28/2018 Electromagnetic Energy and Atomic Line Spectra Johann Balmer in 1885 discovered a mathematical relationship for the four visible lines in the atomic line spectra for hydrogen.  1 = R∞ n2 22 - Johannes Rydberg in 1888 later modified the equation to fit every line in the entire spectrum of hydrogen. The top equation is the Balmer equation while the bottom one is the Balmer-Rydberg equation.  1 = RH n2 m2 - RH (Rydberg Constant) = 1.097 x 10-2 nm-1 Copyright © 2010 Pearson Prentice Hall, Inc. 5

Evidence for Quantization in Atomic and Molecular Structure Spectrum of Radiation emitted by Iron atoms Spectrum of Radiation absorbed by sulfur dioxide

Quantum Mechanics and Atomic Line Spectra Chapter 3: Periodicity and the Electronic Structure of Atoms 8/28/2018 Quantum Mechanics and Atomic Line Spectra Copyright © 2010 Pearson Prentice Hall, Inc. 7

Chapter 3: Periodicity and the Electronic Structure of Atoms 8/28/2018 Copyright © 2010 Pearson Prentice Hall, Inc. 8

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.

Electromagnetic radiation Chapter 3: Periodicity and the Electronic Structure of Atoms 8/28/2018 Electromagnetic radiation This is the electromagnetic spectrum. Copyright © 2010 Pearson Prentice Hall, Inc. 12

Light and the Electromagnetic Spectrum Chapter 3: Periodicity and the Electronic Structure of Atoms 8/28/2018 Light and the Electromagnetic Spectrum Wavelength x Frequency = Speed  =  m s 1 c x The speed of light is defined to be 2.997 924 58 x 108 m/s. The units for frequency are also called “hertz.” Wavelength and frequency are inversely proportional to each other. c is defined to be the rate of travel of all electromagnetic energy in a vacuum and is a constant value—speed of light. s m c = 3.00 x 108 Copyright © 2010 Pearson Prentice Hall, Inc. 13

Compute the wavelength, and frequency of the n=6 to n=4 transition in Li+2.

Blackbody Radiation An Ideal Black-Body is substance that absorbs all (100%) radiation uniformly incident upon it (Black color). No substance has been found to do this but graphite comes very close (absorbs 97%) of radiation incident upon it. Experimental blackbody curves

The Photoelectric effect Electrons can be ejected from a metal surface when radiation is applied. Experimental No electrons are ejected unless the frequency exceeds the threshold of the metal The kinetic energy of the electron increases linearly with frequency of radiation

Photoelectric effect: Einstein Albert Einstein in 1905, explained the photoelectric effect by considering light as a particle (not a wave) of energy hv. The particle of light will collide with an electron and eject it from its orbit only when it has sufficient energy. V is velocity Me is mass of the electron H is planks constant

Photoelectric effect: Einstein Albert Einstein in 1905, explained the photoelectric effect by considering light as a particle (not a wave) of energy hv. The particle of light will collide with an electron and eject it from its orbit only when it has sufficient energy. 1- Photoejection cannot occur if hv < Φ because there is insufficient energy. 2- Excess energy when hv > Φ is used to Increase the kinetic energy of the electron. 3- A plot of kinetic energy verses frequency will yield a slope (h) and intecept (Φ).

Problem: A potassium surface with a work function of 2 Problem: A potassium surface with a work function of 2.40 eV absorbs radiation with a wavelength of 325 nm. What is the kinetic energy and velocity of the electrons ejected?

Historical Overview of Quantum Mechanical Discoveries James Cedric Maxwell (1865) proposed that light consist of a series 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). 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 Broglie (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-Particle Duality Louis De Broglie (1924) suggested that any particle should have wavelike properties. Evidence for wave/particle duality comes from the Davisson-Germer experiment The wavelength is inversely proportional the speed

Problem 1: To what speed must an electron have in order to have a wavelength of 3.0 cm.

Problem 2: The fine-structure constant α has a special role in the structure of matter. The approx value is 1/137. What is the wavelength of an electron traveling at the speed αc. C is the speed of light.

Problem 3: Calculate the linear momentum of photons of wavelength 350 nm. What speed does a hydrogen molecule need to travel to have the same linear momentum?