Chem 101 Study Guide

Chem 101 Study Guide - Chem 101 Study Guide Schrodinger...

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Chem 101 Study Guide Schrodinger Equation (1-D Box) Potential Energy is Zero. No Potential Energy term in the operator. We use Sin because Cos would not give a node at x=0 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 Hamiltonian operator turns eigenvalue into kinetic energy Eigenvalue is the kinetic energy term Quantum mechanical oscillator Has potential energy V=.5kx^2 Energy levels of harmonic oscillators are uniformly spaced whereas PIB converges Wave functions of PIB terminate at the boundary, whereas harmonic oscillator waves overlap the edges You would add .5kx^2 to the operator in the schrodinger equation Degeneracy In 2-D and 3-D wave function models different permutations of quantum numbers give the same energy state (draw diagram) Average electron distance from the nucleus increases rapidly with increasing n for the same l Electron distance decreases slightly with increasing l for the same n Pauli Exclusion Principle- two electrons in the same orbital cannot have the same spin Debroglie- wavelength=h/momentum Planck- Explained the spectrum of Blackbody Radiation with the quantization of Energy Schrodinger- HW=EW. H is an operator. Photoelectron Spectroscopy Draw wavelength versus intensity with the orbitals as peaks 1-D Energy= n^2*h^2/(8mL^2), in 3-D n term is magnitude in three dimensions For harmonic oscillator zero point energy of 1/2hv ensures that energy cannot go to zero when v=0
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3-D wave function for a spherical system has polar coordinates and is broken down into (Y) angular and R (radial) components. Explain theta, phi, and r Find Rydberg constant and be able to convert from cm^-1 to Joules Draw a 1-D particle in a box model Assumptions: o Particle doesn’t leave the box o Potential energy is zero inside o Potential energy is infinite outside o Probability of finding the electron inside the box is 1 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 o 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 p-orbitals, 5 d-orbitals, etc. 3 quantum numbers needed to define an orbital in an H atom
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This note was uploaded on 01/10/2011 for the course HSOC 1 taught by Professor Tresh during the Spring '10 term at UPenn.

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Chem 101 Study Guide - Chem 101 Study Guide Schrodinger...

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