362 Lecture 6 and 7Quantum NumbersEnergy Levels for Electron ConfigurationsSlide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8How to handle atoms larger than H? Effective Nuclear Charge or ZeffElectrons Characterized bySlater’s Rules for Calculating ZeffSlater’s Rules: ExamplesTrends in Atomic PropertiesSlide Number 14Slide Number 15Slide Number 16Slide Number 17Metallic Single-Bond Distances (useful for M-M bonding and intermetallic compounds)Slide Number 19Trends in Atomic PropertiesSlide Number 21Ionization EnergiesSlide Number 23Transition Metals - some complicationsSlide Number 25Slide Number 26Figure 1.7 The variation of the radial density distribution function with distance from the nucleus for electrons in the 1s, 2s, and 3s orbitals of a hydrogen atom.Slide Number 28Slide Number 29Slide Number 30Slide Number 31ElectronegativitySlide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38362 Lecture 6 and 7 Spring 2017 Monday, Jan 30Quantum Numbers n is the principal quantum number, indicates the size of the orbital, has all positive integer values of 1 to ∞(infinity) l is the angular momentum quantum number, represents the shape of the orbital, has integer values of (n – 1) to 0 ml is the magnetic quantum number, represents the spatial direction of the orbital, can have integer values of -l to 0 to l ms is the spin quantum number, has little physical meaning, can have values of either +1/2 or -1/2 l (angular momentum) orbital 0 s 1 p 2 d 3 f Pauli Exclusion principle: no two electrons can have all four of the same quantum numbers in the same atom (Every electron has a unique set.) Hund’s Rule: when electrons are placed in a set of degenerate orbitals, the ground state has as many electrons as possible in different orbitals, and with parallel spin. Aufbau (Building Up) Principle: the ground state electron configuration of an atom can be found by putting electrons in orbitals, starting with the lowest energy and moving progressively to higher energy. Other terms: electron configuration, noble gas configuration, valence shellEnergy Levels for Electron Configurations Guiding Principles for Electron Assignment: The Aufbau The Pauli Exclusion Principle Hund’s RulesAnd Why are s, p, d orbitals of different energy? Need both radial and angular functions Both radial and angular functions have nodes # Angular Nodes = lNodes, (not toads) Region of space of zero probability Summary: Total # Nodes = n – 1 # Angular Nodes = l # Radial Nodes = n - l - 1 Where n = principal quantum number; l = angular momentum quantum number Energies of the electronsCopyright © 2014 Pearson Education, Inc. Radial Wave Functions and Nodes # Radial Nodes = n - l - 1Copyright © 2014 Pearson Education, Inc. Radial Probability Functions and Nodes # Radial Nodes = n - l - 1The 4s electron “penetrates” Inner shell electrons more efficiently than does 3d in neutral atoms. Reverses in positive ions. Screening:How to handle atoms larger than H? Effective Nuclear Charge or ZeffElectrons Characterized by a) Principal energy level, n b) Orbital or angular momentum, l = # of angular nodes c) Zeff -----------------------------------------------------------In the presence of a magnetic field of l is oriented and composed of ml components. d) Spin-spin and spin-orbital couplingSlater’s Rules for Calculating Zeff 1) Write the electron configuration for the atom as follows: (1s)(2s,2p)(3s,3p) (3d) (4s,4p) (4d) (4f) (5s,5p) 2) Any electrons to the right of the electron of interest contributes no shielding. (Approximately correct statement.) 3) All other electrons in the same group as the electron of interest shield to an extent of 0.35 nuclear charge units 4) If the electron of interest is an s or p electron: All electrons with one less value of the principal quantum number shield to an extent of 0.85 units of nuclear charge. All electrons with two less values of the principal quantum number shield to an extent of 1.00 units. 5) If the electron of interest is an d or f electron: All electrons to the left shield to an extent of 1.00 units of nuclear charge. 6) Sum the shielding amounts from steps 2 - 5 and subtract from the nuclear charge value to obtain the effective nuclear charge.Slater’s Rules: Examples Calculate Zeff for a valence electron in fluorine. (1s2)(2s2,2p5) Rule 2 does not apply; therefore, for a valence electron the shielding or screening is (0.35 • 6) + (0.85 • 2) = 3.8 Zeff = 9 – 3.8 = 5.2 Calculate Zeff for a 6s electron in Platinum. (1s2)(2s2,2p6)(3s2,3p6) (3d10) (4s2,4p6) (4d10) (4f14) (5s2,5p6) (5d8) (6s2) Rule 2 does not apply, and the shielding is: (0.35 • 1) + (0.85 • 16) + (60 • 1.00) = 73.95 Zeff = 78 – 73.95 = 4.15 for a valence electron.Trends in Atomic Properties • Size (atomic, ionic, covalent, van der Waals radii) • Ionization Potential (A0(g) + I.E. A+ + e- ) • Electron Affinity Energies (A0(g) + e- A- + E.A.E.) • Electronegativity: Ability of an atom, within a molecule to attract electrons to itself.Inorganic Chemistry Chapter 1: Figure 1.23 © 2009 W.H. FreemanInorganic Chemistry Chapter 1: Table 1.3 © 2009 W.H. FreemanLanthanide Contraction: particulary large decrease in ionic radii size due to Particularly poor shielding by electrons in f orbitals.Inorganic Chemistry Chapter 1: Figure 1.24 © 2009 W.H. FreemanMetallic Single-Bond Distances (useful for M-M bonding and intermetallic compounds)Inorganic Chemistry Chapter 1: Table 1.4 © 2009 W.H. Freeman Anions are Larger than Neutral atom Cations are smaller than Neutral atomTrends in Atomic Properties • Size (atomic, ionic, covalent, van der Waals radii) • Ionization Potential energy (A0(g) + I.E. A+ + e- ) • Electron Affinity Energy (A0(g) + e- A- + E.A.E.) • Electronegativity: Ability of an atom, within a molecule to attract electrons to itself.https://www.nist.gov/pml/ground-levels-and-ionization-energies-neutral-atomsIonization EnergiesInorganic Chemistry Chapter 1: Figure 1.25 © 2009 W.H. FreemanTransition Metals - some complications kJ/mol Ionization EnergiesInorganic Chemistry Chapter 1: Table 1.6 © 2009 W.H. FreemanCopyright © 2014 Pearson Education, Inc.Figure 1.7 The variation of the radial density distribution function with distance from the nucleus for electrons in the 1s, 2s, and 3s orbitals of a hydrogen atom. The