Prentice-Hall © 2002General Chemistry: Chapter 9Slide 1 of 50 General Chemistry Principles and Modern Applications Petrucci Harwood Herring 10 th Edition Chapter 8: Electrons in Atoms

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 2 of 50 Contents 8-1Electromagnetic Radiation 8-2Atomic Spectra 8-3Quantum Theory 8-4The Bohr Atom 8-5Two Ideas Leading to a New Quantum Mechanics 8-6Wave Mechanics 8-7Quantum Numbers and Electron Orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 3 of 50 Contents 8-8Interpreting and Representing Orbitals of the Hydrogen Atom 8-9Electron Spin: A Fourth Quantum Number 8-10Multi-electron Atoms 8-11Electron Configurations 8-12Electron 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 Å 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. Energy quantum: є = h E = n h ν

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 Vs stop voltage

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. mv 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 = mv 2 + eV o 2 1 mv 2 = h - eV o eV s = 2 1 E photon = E k + E binding E k = E photon - E binding

The Photoelectric Effect General Chemistry: Chapter 9Slide 19 of 50

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 20 of The Bohr Atom (1913) E = -R H n2n2 R H = J

General Chemistry: Chapter 9Slide 21 of 50 Energy-Level Diagram ΔE = E f – E i = -R H nf2nf2 ni2ni2 – = R H ( ni2ni2 1 nf2nf2 – 1 ) = h = hc/λ

H atom spectral series General Chemistry: Chapter 9Slide 22 of 50

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 23 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 24 of 50 Emission and Absorption Spectroscopy

General Chemistry: Chapter 9Slide 25 of 50 Visible atomic emission spectra

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 26 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 27 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 28 of 50 X-Ray Diffraction

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 29 of 50 The Uncertainty Principle Δx Δp ≥ h 4π4π Werner Heisenberg 1927

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 30 of Wave Mechanics 2L n Standing waves. –Nodes do not undergo displacement. λ =, n = 1, 2, 3…

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 31 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. E n = (n π /L) 2 /2

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 32 of 50 Probability of Finding an Electron

Quantum physics and chemistry 33 E. Schrödinger The fundamental idea of wave mechanics Theory of electrons and positrons P. A. M. Dirac

Operators In quantum mechanics operator acts on a function and it transfers the function into another function. Typical example: derivation –x 2 is transformed to 2x –sin(x) is transformed to cos(x) –e x is transformed to e x –e xk is transformed to k e xk Prentice-Hall © 2002General Chemistry: Chapter 9Slide 34 of 50

Hamilton operator Total energy = kinetic + potential Slide 35 of 60

Hamilton operator 2. The operator of potential energy, atomic unit Nuclear charge: Electron charge: r Z is the position of the nucleus: r Z = 0,0,0 Slide 36 of 60

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 37 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 38 of Quantum Numbers and Electron Orbitals 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 39 of 50 Orbital Energies

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 40 of Interpreting and Representing the Orbitals of the Hydrogen Atom.

Simplified wave functions (Z=1, a 0 =1) Slide 41 of 60 nlm R nl (r) Y(  ) real Complex 1001s2e -r s- 2102p z - 21(±1)2p x,y Yes e ±i 

R n,0 (r) for s orbitals for Z=1 Slide 42 of 60 Radial part of the 3s orbital Radial part of the 4s orbital Radial part of the 1s orbitalRadial part of the 2s orbital

R n,1 (r) for p orbitals for Z=1 Slide 43 of 60 Radial part of the 2p orbital Radial part of the 3p orbital

Slide 44 of Interpreting and Representing Orbitals of the Hydrogen Atom 0 in the yz plane 0 in the xz plane 0 in the xy plane

Slide 45 of 60 d orbitals

The shape of the atomic orbitals Slide 46 of 60

Slide 47/61 The electron density of s orbitals s orbitals r (distance)

Slide 48 of 60 The electron density of p orbitals

Slide 49 of 60 Radial electron density  (r) = 4  r 2  2 (r) The probability of finding electrons on the surface of a sphere with radius r. The surface area = 4  r 2

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 50 of Electron Spin: A Fourth Quantum Number

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 51 of Multi-electron Atoms Schrödinger equation was for only one e -. Electron-electron repulsion in multi- electron atoms. Hydrogen-like orbitals (by approximation).

Általános Kémia, Periódikus tulajdonságok Slide 52 of 60 Shielding Z eff = Z – S E n = - RHRH n2n2 Z eff 2

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 53 of 50 Shielding Slater rules: For a 1s electron, S = 0.3. For electrons in an s or p orbital with n > 1, the screening constant is given by S = 1.00·N ·N ·N0 N0 represents the number of other electrons in the same shell, N1 represents the number of electrons in the next smaller shell (n-1), and N2 is the number of electrons in other smaller shells (n-2 and smaller). The effective nuclear charge is Z eff = Z - S

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 54 of Electron Configurations Aufbau principle. –Build up and minimize energy. Pauli exclusion principle. –No two electrons can have all four quantum numbers alike (n, l, m l, s). Hund’s rule. –Degenerate orbitals are occupied singly first, and the spins of the electrons are parallel.

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 55 of 50 Orbital Energies

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 56 of 50 Orbital Filling

Dia 57/61 Aufbau Process and Hunds Rule C E(1s) < E(2s) < E(2p) B

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 58 of 50 Filling p Orbitals

Electron configuration Short notation. For example: B: 1s 2 2s 2 2p 1 C: 1s 2 2s 2 2p 2 N: 1s 2 2s 2 2p 3 O: 1s 2 2s 2 2p 4 F: 1s 2 2s 2 2p 5 Ne: 1s 2 2s 2 2p 6 is: [Ne] (10 electrons) Dia 59/61

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 60 of 50 Filling the d Orbitals

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 61 of 50 Electon Configurations of Some Groups of Elements

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 62 of Electron Configurations and the Periodic Table

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 63 of 50 Focus on He-Ne Lasers

Prentice-Hall © 2002General Chemistry: Chapter 9Slide 64 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