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The Quantum Mechanical Model of the Atom What’s wrong with the Bohr model? Heisenberg, de Broglie, Schrodinger • Developed a model of the atom based on wave mechanics (quantum mechanics) – The electron bound to the nucleus seemed similar to a standing wave • De Broglie – originated the idea that the electron also shows wave properties (in addition to particulate properties) • Schrodinger – put emphasis on the wave properties of the electron Standing Waves & Musical Instruments • A string attached to a violin or guitar vibrates to produce a musical tone • The waves are “standing” because they are stationary, they don’t travel the length of the string Figure 7.9 •The dots indicate the nodes, or points of zero lateral (sideway) displacement, for a given wave. •There are limitations on the allowed wavelengths of the standing wave. •Each end of the string is fixed, so there is always anode at each end • There must be a whole number of half wavelengths in any of the allowed motions of the string From Music Strings to Electrons • The electron in the hydrogen atom is imagined to be a standing wave. • Only certain circular orbits have a circumference into which a whole number of wavelengths of the standing electron wave will “fit” • All other orbits would produce destructive interference of the standing electron wave and are not allowed. • Explained by Schrodinger’s equation: H=E Schrodinger’s equation: H=E • is called the wave function (a function of the coordinate (x, y, and z) of the electron’s position in three-dimensional space • H is set of mathematical instructions called an operator that produce the total energy of the atom when they are applied to the wave function. • E is the total energy of the atom (the sum of the potential energy due to the attraction between the proton and electron and the kinetic energy of the moving electron) • When the equation is analyzed, many solutions are found. – Each solution consists of a wave function that is characterized by a particular value of E. – A specific wave function is often called an orbital. Quantum (wave) Mechanical Model of the Atom • The wave function corresponding to the lowest energy for the hydrogen atom is called the 1S orbital – An orbital is not a Bohr orbital (the electron is not moving around the nucleus in a circular orbit) – We don’t know exactly how it is moving. Heisenberg’s Uncertainty Principle • There is a limitation to just how precisely we can know both the position and momentum of a particle at a given time. x•(mv) > h/4 • The more accurately we know a particle’s position, the less accurately we can know its momentum, and vice versa. – Limitation is too small for large particles – Limitation is significant for small particles Heisenberg’s Uncertainty Principle • Applied to the electron: – We cannot know the exact motion of the electron as it moves around the nucleus – Therefore, it is not appropriate to assume that the electron is moving around the nucleus in a well-defined orbit, as in the Bohr model. The Physical Meaning of a Wave Function • Meaning…What is an atomic orbital? • The square of the function indicates the probability of finding an electron near a particular point in space. [ (X1, Y1, Z1]2 = N1 • Probability Distribution: [ (X , Y , Z ]2 = N 2 2 2 2 Probability Distribution for the 1s Wave Function Radial Probability Distribution Quantum Numbers •Principle Quantum Number (n): •Angular Momentum Quantum number (l) •Magnetic Quantum Number (ml) •Spin Quantum Number (ms) •(Pauli Exclusion Principle) •See Sample Exercise 7.6 Quantum Numbers for the First Four Levels of Orbitals in the Hydrogen Atom Orbital Shapes and Energies 1s Orbital Two Representation s of the Hydrogen 1s, 2s, and 3s Orbitals 2px Orbital 2py Orbital 2pz Orbital The Boundary Surface Representations of All Three 2p Orbitals 3d x2 y 2 Orbital 3dxy Orbital 3dxz Orbital 3dyz Orbital 3d z 2 Orbital The Boundary Surfaces of All of the 3d Orbitals Representation of the 4f Orbitals in Terms of Their Boundary Surfaces Polyelectronic Atoms A Comparison of the Radial Probability Distributions of the 2s and 2p Orbitals The Radial Probability Distribution of the 3s Orbital A Comparison of the Radial Probability Distributions of the 3s, 3p, and 3d Orbitals • Sketch a general orbital level diagram for atoms other than hydrogen. • Explain why it differs from hydrogen. Orbital Energies Explain how you can use the periodic table to determine the order in which orbitals fill in polyatomic atoms. Electron Configurations: arrangement of electron in an atom. • Order of increasing energies for atomic orbitals: • • • • Rules: Aufbau Principle Pauli’s Exclusion Principle Hund’s Rule Orbital Notation: • Unoccupied orbital is represented by a line, with the orbital’s name written underneath the line. • EX: Hydrogen and Helium Electron configuration Notation: • Number of electron in a sublevel is shown by adding a superscript to the sublevel designation. • We can use the structure of the periodic table to predict the filling order of the subshells when we write the electron configuration of an element. • As you move across the block of two columns, electrons are added to an s subshell that has a principal quantum number equal to the period number. • Every time we move across the block of six columns we add electrons to a p subshell that has a principal quantum number equal to the period number. • Use the periodic table to predict the electron configurations of Mg, Ge, Cd, The Orbitals Being Filled for Elements in Various Parts of the Periodic Table Noble-Gas Notation: • The first ten electrons in an atom of each of the 3rd period elements have the same configuration as neon. We can use a shorthand notation for the electron configurations of the third-period elements. • Outer main energy level is fully occupied, by eight electrons (octet rule) • Forth Period: Exceptions to the Rule Lowest energy state-Most Stable – (College Chemistry Book) • Chromium: [Ar] 3d54s1 • Copper: • Silver • Gold • Fifth Period • Helium – not • Sixth and Seventh Periods Determine the expected electron configurations for each of the following: 1. S 2. Ba 3. Ni2+ 4. Eu 5. Ti+