Prentice-Hall © 2002General Chemistry: Chapter 9Slide 1 of 50 Philip Dutton University of Windsor, Canada Prentice-Hall © 2002 General Chemistry Principles and Modern Applications Petrucci Harwood Herring 8 th Edition Chapter 9: Electrons in Atoms

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 2 of 50 Contents 9-1Electromagnetic Radiation 9-2Atomic Spectra 9-3Quantum Theory 9-4The Bohr Atom 9-5Two Ideas Leading to a New Quantum Mechanics 9-6Wave Mechanics 9-7Quantum Numbers and Electron Orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 3 of 50 Contents 9-8Quantum Numbers 9-9Interpreting and Representing Orbitals of the Hydrogen Atom 9-9Electron Spin 9-10Multi-electron Atoms 9-11Electron Configurations 9-12Electron Configurations and the Periodic Table Focus on Helium-Neon Lasers

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 4 of Electromagnetic Radiation Electric and magnetic fields propagate as waves through empty space or through a medium. A wave transmits energy.

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 5 of 50 EM Radiation Low High

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 6 of 50 Frequency, Wavelength and Velocity Frequency ( ) in Hertz—Hz or s -1. Wavelength (λ) in meters—m. cm  m nm  pm (10 -2 m)(10 -6 m)(10 -9 m)( m)( m) Velocity (c)—  10 8 m s -1. c = λ λ = c/ = c/λ

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 7 of 50 Electromagnetic Spectrum

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 8 of 50 R ed O range Y ellow G reen B lue I ndigo V iolet Prentice-Hall ©2002 General Chemistry: Chapter 9 Slide 8 ROYGBIV 700 nm450 nm

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 9 of 50 Constructive and Destructive Interference

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 10 of 50

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 11 of 50 Refraction of Light

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 12 of Atomic Spectra

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 13 of 50 Atomic Spectra

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 14 of Quantum Theory Blackbody Radiation: Max Planck, 1900: Energy, like matter, is discontinuous. є = h

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 15 of 50 The Photoelectric Effect Light striking the surface of certain metals causes ejection of electrons. > o threshold frequency e -  I e k 

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 16 of 50 The Photoelectric Effect

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 17 of 50 The Photoelectric Effect At the stopping voltage the kinetic energy of the ejected electron has been converted to potential. mu 2 = eV s 1 2 At frequencies greater than o : V s = k ( - o )

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 18 of 50 The Photoelectric Effect E o = h o E k = eV s o = eV o h eV o, and therefore o, are characteristic of the metal. Conservation of energy requires that: h = mu 2 + eV o 2 1 mu 2 = h - eV o eV s = 2 1 E photon = E k + E binding E k = E photon - E binding

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 19 of The Bohr Atom E = -R H n2n2 R H =  J

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 20 of 50 Energy-Level Diagram ΔE = E f – E i = -R H nf2nf2 ni2ni2 – = R H ( ni2ni2 1 nf2nf2 – 1 ) = h = hc/λ

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 21 of 50 Ionization Energy of Hydrogen ΔE = R H ( ni2ni2 1 nf2nf2 – 1 ) = h As n f goes to infinity for hydrogen starting in the ground state: h = R H ( ni2ni2 1 ) = R H This also works for hydrogen-like species such as He + and Li 2+. h = -Z 2 R H

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 22 of 50 Emission and Absorption Spectroscopy

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 23 of Two Ideas Leading to a New Quantum Mechanics Wave-Particle Duality. –Einstein suggested particle-like properties of light could explain the photoelectric effect. –But diffraction patterns suggest photons are wave-like. deBroglie, 1924 –Small particles of matter may at times display wavelike properties.

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 24 of 50 deBroglie and Matter Waves E = mc 2 h = mc 2 h /c = mc = p p = h/λ λ = h/p = h/mu

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 25 of 50 X-Ray Diffraction

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 26 of 50 The Uncertainty Principle Δx Δp ≥ h 4π4π Werner Heisenberg

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 27 of Wave Mechanics 2L n Standing waves. –Nodes do not undergo displacement. λ =, n = 1, 2, 3…

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 28 of 50 Wave Functions ψ, psi, the wave function. –Should correspond to a standing wave within the boundary of the system being described. Particle in a box.

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 29 of 50 Probability of Finding an Electron

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 30 of 50 Wave Functions for Hydrogen Schrödinger, 1927 Eψ = H ψ –H (x,y,z) or H (r,θ,φ) ψ (r,θ,φ) = R(r) Y(θ,φ) R(r) is the radial wave function. Y(θ,φ) is the angular wave function.

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 31 of 50 Principle Shells and Subshells Principle electronic shell, n = 1, 2, 3… Angular momentum quantum number, l = 0, 1, 2…(n-1) l = 0, s l = 1, p l = 2, d l = 3, f Magnetic quantum number, m l = - l …-2, -1, 0, 1, 2…+ l

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 32 of 50 Orbital Energies

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 33 of Interpreting and Representing the Orbitals of the Hydrogen Atom.

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 34 of 50 s orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 35 of 50 p Orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 36 of 50 p Orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 37 of 50 d Orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 38 of Electron Spin: A Fourth Quantum Number

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 39 of Multi-electron Atoms Schrödinger equation was for only one e -. Electron-electron repulsion in multi- electron atoms. Hydrogen-like orbitals (by approximation).

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 40 of 50 Penetration and Shielding Z eff is the effective nuclear charge.

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 41 of Electron Configurations Aufbau process. –Build up and minimize energy. Pauli exclusion principle. –No two electrons can have all four quantum numbers alike. Hund’s rule. –Degenerate orbitals are occupied singly first.

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 42 of 50 Orbital Energies

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 43 of 50 Orbital Filling

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 44 of 50 Aufbau Process and Hunds Rule

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 45 of 50 Filling p Orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 46 of 50 Filling the d Orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 47 of 50 Electon Configurations of Some Groups of Elements

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 48 of Electron Configurations and the Periodic Table

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 49 of 50 Focus on He-Ne Lasers

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 50 of 50 Chapter 9 Questions 1, 2, 3, 4, 12, 15, 17, 19, 22, 25, 34, 35, 41, 67, 69, 71, 83, 85, 93, 98