Chapter7-1

# Key features of quantum mechanics 1 electrons act

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Unformatted text preview: ct like waves (2) They exist in speciﬁc modes, called wave functions (3) The wave functions are described using parameters called quantum numbers 40 Chem 6A Michael J. Sailor, UC San Diego Heisenberg’s Uncertainty Principle "You can't know both the exact position and the exact momentum of any particle at exactly the same time" h Δx ⋅ Δmv ≥ 4π so electrons randomly exist in some fuzzy haze around the nucleus € h = 6.6261 x 10-34 J.s 41 Chem 6A Michael J. Sailor, UC San Diego What is a wave function? Quantum mechanics treats the electron as a 3-dimensional standing wave Standing Waves: 1-d: Violin string y = sin(x) 2-d: the surface of a drum z = sin(x)cos(y) 3-d: real complicated to visualize z = sin(x)sin(y)sin(z) 42 Chem 6A Michael J. Sailor, UC San Diego Quantum numbers Quantum Number Called Describes n l Principle quantum number SIZE and ENERGY Angular momentum (Azimuthal) quantum number SHAPE ml ms Magnetic quantum number ORIENTATION Electron spin quantum number INTRINSIC ANGULAR MOMENTUM OF THE ELECTRON 43 Chem 6A Michael J. Sailor, UC San Diego The Particle in a Box An example of a 2-dimensional standing wave for an electron 20 e- edelocalized wave conﬁned wave Relative Energy localized particle n=4 15 10 n=3 5 n=2 n=1 0 -0.2 0 0.2 0.4 x 0.6 L Chem 6A Michael J. Sailor, UC San Diego 0.8 1 1.2 44 The Particle in a Box An example of a 2-dimensional standing wave for an electron 20 e- edelocalized wave Relative Energy localized particle n=4 15 10 n=3 5 conﬁned wave n=2 n=1 What are the energies of these wavefunctions? 0 -0.2 0 0.2 0.4 x 0.6 L Chem 6A Michael J. Sailor, UC San Diego 0.8 1 1.2 44 Derivation of Particle in a Box Equation Classical physics: E = ½ mv2 Allowed wavelengths for electrons in the box: λ= 2L/n, where n = 1, 2, 3, … de Broglie relationship: λ = h/mv Relative Energy 20 n=4 15 10 n=3 5 n=2 n=1 0 -0.2 0 0.2 0.4 x 0.6 L Chem 6A Michael J. Sailor, UC San Diego 0.8 1 1.2 45 Derivation of Particle in a Box Equation Allowed wavelen...
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## This note was uploaded on 08/31/2011 for the course CHEM 6A taught by Professor Pomeroy during the Winter '08 term at UCSD.

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