Chem 101 Study Guide
Schrodinger Equation (1D Box)
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Potential Energy is Zero. No Potential Energy term in the operator.
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We use Sin because Cos would not give a node at x=0
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Normalization constant “A” “root(2/L)” this is needed so that the integral
of the wave function squared is 1. Electron needs to be found somewhere
in the box
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Hamiltonian operator turns eigenvalue into kinetic energy
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Eigenvalue is the kinetic energy term
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Quantum mechanical oscillator
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Has potential energy V=.5kx^2
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Energy levels of harmonic oscillators are uniformly spaced whereas PIB
converges
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Wave functions of PIB terminate at the boundary, whereas harmonic
oscillator waves overlap the edges
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You would add .5kx^2 to the operator in the schrodinger equation
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Degeneracy
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In 2D and 3D wave function models different permutations of quantum
numbers give the same energy state (draw diagram)
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Average electron distance from the nucleus increases rapidly with
increasing n for the same l
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Electron distance decreases slightly with increasing l for the same n
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Pauli Exclusion Principle two electrons in the same orbital cannot have
the same spin
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Debroglie wavelength=h/momentum
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Planck Explained the spectrum of Blackbody Radiation with the
quantization of Energy
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Schrodinger HW=EW. H is an operator.
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Photoelectron Spectroscopy
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Draw wavelength versus intensity with the orbitals as peaks
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1D Energy= n^2*h^2/(8mL^2), in 3D n term is magnitude in three
dimensions
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For harmonic oscillator zero point energy of 1/2hv ensures that energy
cannot go to zero when v=0
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3D wave function for a spherical system has polar coordinates and is
broken down into (Y) angular and R (radial) components.
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Explain theta, phi, and r
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Find Rydberg constant and be able to convert from cm^1 to Joules
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Draw a 1D particle in a box model
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Assumptions:
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Particle doesn’t leave the box
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Potential energy is zero inside
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Potential energy is infinite outside
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Probability of finding the electron inside the box is 1
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There are two methods for finding momentum of electron in a box
o
Calculate wavelength from the length of the box and the number of
nodes
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Use p^2/2m
Degeneracy for a particle in a box: different quantum numbers giving rise to the same
energy value
Degeneracy for an atom: 3 porbitals, 5 dorbitals, etc.
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 Spring '10
 tresh
 Potential Energy

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