Tentative material to be covered for Exam 2 (Wednesday, October 27) Chapter 16Quantum Mechanics and the Hydrogen Atom 16.1Waves and Light 16.2Paradoxes in Classical Physics 16.3Planck, Einstein, and Bohr 16.4Waves, Particles, and the Schroedinger Equation 16.5The Hydrogen Atom Chapter 17Many-Electron Atoms and Chemical Bonding 17.1Many-Electron Atoms and the Periodic Table 17.2Experimental Measures of Orbital Energies 17.3Sizes of Atoms and Ions 17.4Properties of the Chemical Bond 17.5Ionic and Covalent Bonds 17.6Oxidation States and Chemical Bonding Chapter 18Molecular Orbitals, Spectroscopy, and Chemical Bonding 18.1Diatomic Molecules 18.2Polyatomic Molecules 18.3The Conjugation of Bonds and Resonance Structures 18.4The Interaction of Light with Molecules 18.5Atmospheric Chemistry and Air Pollution

Chapter 16Quantum Mechanics and the Hydrogen Atom 16.1Waves and Light Atomic Spectra I 16.2Paradoxes in Classical Physics Ultraviolet Catastrophe Photoelectric effect 16.3Planck, Einstein, and Bohr Planck’s Constant, Quanta and Photons Bohr Atom Atomic Spectra II 16.4Waves, Particles, and the Schroedinger Equation Schroedinger Equation (Wave Equation) 16.5The Hydrogen Atom Sizes and Shapes of Orbitals Electron Spin

Review of the development of the Bohr atom A Movie from the Mechanical Universe

Schroedinger: If electrons are waves, their postion and motion in space must obey a wave equation. Solutions of wave equations yield wavefunctions, , which contain the information required to describe ALL of the properties of the wave. Provides a picture of the electronic distributions of the electrons about an the nucleus of an atom and about the connected nuclei of a molecule. Schroedinger thinking about his equation.

Particles are out, waves are in. But the mathematics of waves is very complex!

Wavefunctions and orbitals Obital: defined by the quantum numbers n, l and m l Orbital is a wavefunction Orbital is a region of space occupied by an electron Orbitals has energies, shapes and orientation in space

Quantum Numbers (QN) Principal QN: n = 1, 2, 3, 4…… Angular momentum QN: l = 0, 1, 2, 3…. (n -1) Rule: l = (n - 1) Magnetic QN: m l = …-2, -1, 0, 1, 2,.. Rule: -l….0….+l Shorthand notation for orbitals Rule: l = 0, s orbital; l = 1, p orbital; l = 2, d orbital l = 3, f orbital 1s, 2s, 2p, 3s, 3p, 4s, 4p, 4d, etc.

Recall the gaps between the energy levels of the H atom. Big initial gap and then smaller and smaller gaps.

The energy of an orbital of a hydrogen atom or any one electron atom only depends on the value of n shell = all orbitals with the same value of n subshell = all orbitals with the same value of n and l an orbital is fully defined by three quantum numbers, n, l, and m l Each shell of QN = n contains n subshells n = 1, one subshell n= 2, two subshells, etc Each subshell of QN = l, contains 2l + 1 orbitals l = 0, 2(0) + 1 = 1 l = 1, 2(1) + 1 = 3

Sizes, Shapes, and orientations of orbitals n determines size; l determines shape m l determines orientation

Nodes in orbitals: s orbitals: 1s no nodes, 2s one node, 3s two nodes

Nodes in orbitals: 2p orbitals: angular node that passes through the nucleus Orbital is “dumb bell” shaped Important: the + and - that is shown for a p orbital refers to the mathematical sign of the wavefunction, not electric charge!

Nodes in orbitals: 3d orbitals: two angular nodes that passes through the nucleus Orbital is “four leaf clover” shaped d orbitals are important for metals

The fourth quantum number: Electron Spin m s = +1/2 (spin up) or -1/2 (spin down) Spin is a fundamental property of electrons, like its charge and mass. (spin up) (spin down)

Electrons in an orbital must have different values of m s This statement demands that if there are two electrons in an orbital one must have m s = +1/2 (spin up) and the other must have m s = -1/2 (spin down) This is the Pauli Exclusion Principle An empty orbital is fully described by the three quantum numbers: n, l and m l An electron in an orbital is fully described by the four quantum numbers: n, l, m l and m s

Chapter 17Many-Electron Atoms and Chemical Bonding 17.1Many-Electron Atoms and the Periodic Table 17.2Experimental Measures of Orbital Energies 17.3Sizes of Atoms and Ions 17.4Properties of the Chemical Bond 17.5Ionic and Covalent Bonds 17.6Oxidation States and Chemical Bonding

Chapter 17 The Many Electron Atom Goal: Construct the periodic table based on quantum numbers (1) Solve the wave equation exactly for the H atom (2) Use the exact orbitals for the H atom as a starting approximation for the many electron atom (3) Quantum numbers obtained for H atom used to describe the many electron atom

The orbital approximation for a many electron atom: The electrons are described by the same four quantum numbers as the H atom, but the energies of the orbits depend on both n and l (but not on m l )

Ground state electron configuration of a many electron atom : Governs reactivity under normal condition Imagine a bare nucleus of charge +Z Imagine empty orbitals surrounding the nucleus Fill the orbital with Z electrons for the neutral atom Two Principles: Aufbau principle: fill lowest energy orbital first Pauli exclusion principle: each electron must have four different quantum numbers (maximum of 2 electrons in an orbital).

The energy of an orbital of a hydrogen atom or any one electron atom only depends on the value of n shell = all orbitals with the same value of n subshell = all orbitals with the same value of n and l an orbital is fully defined by three quantum numbers, n, l, and m l

Relative orbital energies for the multielectron atom. The energy of an orbital of a multielectron atom depends on n and l (but not m l ) 2s < 2p 3s < 3p <3d Note energy levels are getting closer together for n = 3 This means that factors ignored may have to be considered

Constructing the periodic table by filling orbitals with electrons. Construction of the first row of the periodic table. Electron configurations. Aufbau: Fill 1s orbital first Pauli: no more than two electrons in the 1s orbital The basis of the octet rule: filling a shell 1s subshell filled with 2 He = stable electron core given symbol [He].

Filling the orbitals of 3 Li, 4 Be and 5 B Aufbau: Fill 1s orbital first, then 2s, then 2p Pauli: no more than two electrons in the 1s orbital. 2s subshell filled with 4 Be.

Filling the orbitals of 6 C and 7 N. The need for a third rule (Hund’s rule): When electrons occupy orbitals of the same energy, the lowest energy state corresponds to the configuration with the greatest number of orbitally and spin unpaired electrons. This avoids electron- electron repulsion and lowers the atom’s energy

Filling the orbitals of 8 O, 9 F and 10 Ne Filling the 2p subshell produces another stable configuration of electrons which serves as the core shell of the third row: symbol [Ne]

Orbital shells and the building up of the periodic table A shell is a set of orbitals with the same value of n and l for a H atom. The Ar atom has shells as shown in the profile of electron density as a function of distance from the nucleus These are the valence electrons of the Lewis structures

Summary From 1 H to 10 Ne. No new features from 11 Na to 18 Ar.

The ionization energy (IE) of an atom is the minimun energy required to remove an electron from an atom. X(g) X + (g) + e - Periodic trends ionization energies of the representative elements: What are the correlations across and down?

The electron affinity (EA) of an atom is the energy change which occurs when an atom gains an electron. X(g) + e - Xe - (g) Electron affinities of the representative elements: What are the correlations across and down?

Periodic properties of atomic radius: What are the correlations? General Rule: The size of an atom decreases in a row as the nuclear charge increases and the size of an atom increases in a column as the nuclear charge increases

Electronegativity (EN): a measure of the ability of an atom to attract electrons to itself in competition with other atoms

Practice Exam for Chapter 16 will go up tonight or tomorrow Slide show for Exam 2 is up in Persuasion Working on getting back your answer sheets for Exam 1

Bond lengths