Lecture 10

Lecture 10 - EEE 352: Lecture 11 The Atom and its Energy...

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EEE 352: Lecture 11 The Atom and its Energy Levels * Describe atomic structure [web] * The Schrödinger equation for the hydrogen atom Spherical coordinate representation * Quantum numbers * Real atomic structure and the periodic table * Molecules and bonding 25 nm gate length FET
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Describing Atomic Structure One of the triumphs of quantum mechanics is its ability to explain ATOMIC STRUCTURE * This CANNOT be accounted for using the principle of classical physics * HYDROGEN has the simplest atom and consists of a single ELECTRON That circulates around a central NUCLEUS + e - e r THE HYDROGEN ATOM an attractive force!
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Describing Atomic Structure An earlier treatment of the shell model of the atom was given by Bohr in 1912 (this has become known as the Bohr-Sommerfeld model). Bohr received the Nobel prize for his model. Electrons were located in shells, whose radius was determined by classical quantization (just like oscillations on a string) There was no radiation decay… Transitions between shells agreed with optical properties of atoms for some series of lines, but not for others ( a problem remained ). It remained for quantum mechanics, as described by both Heisenberg and Schrödinger, to fully explain the properties. Niels Hendrik David Bohr Nobel Prize in physics, 1922
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De Broglie then theorized that the reason the shell structure existed was that the electrons in the atom were waves . As waves, they had a specific wavelength, and this wavelength had to fit into the orbit shell of the atom. Hence, a more correct solution would follow from use of the Schrödinger equation (which didn't exist when Bohr put his model together).
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The Schrödinger Equation for the Hydrogen Atom We solve the Schrödinger equation for the ELECTRON in the presence of the electric field of the PROTON * To do this we solve the time INDEPENDENT Schrödinger equation using a spherical coordinate representation TIME INDEPENDENT SCHRÖDINGER EQUATION FOR THE HYDROGEN ATOM y z x r θ φ POLAR COORDINATE SYSTEM
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The Schrödinger Equation for the Hydrogen Atom In one dimension, we had one quantum number , n This quantum number related to the energy . Hence, in three dimensions, we expect three quantum numbers! In spherical coordinates, one of these quantum numbers will be associated with the energy n . This is the radial number. The other two will be associated with the angular variations: We connect θ with the quantum number l. We connect φ with the quantum number m z . We use m z to distinguish from the mass m
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The Schrödinger Equation for the Hydrogen Atom The radial quantum number n gives the energy E n : n = 1, 2, 3, … Bohr radius The polar angle ( θ ) solutions are Legendre polynomials P l (cos θ ) l = 0, 1, 2, …, n ± 1 The polar angle ( φ ) solutions are simple exponentials m z = 0, ± 1, ± 2, ± 3, ± l
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Map of the probability for each of the lower orbitals:
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Quantum States ( Now, we have shown the Schrödinger equation for the
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Lecture 10 - EEE 352: Lecture 11 The Atom and its Energy...

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