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Unformatted text preview: X X is the distance from the nucleus Electron “moves” along the black line only – Ψ = mx + c At any point along the line Ψ 2 is proportional to the “probability” of finding the electron at that point. CHEM2110 Basic Molecular Orbital Theory: 1. The Atom – Schrodinger Wave Equation: The most important part of an atom is the electrons and the motion and energies they obtain around the central nucleus, this is represented by the following Hamiltonian equation: H.Ψ = E. Ψ Where: H = the Hamiltonian operator E = the Energy The Hamiltonian operator can also be defined as: H = - (h 2 /2mπ 2 ) x V 2 x V; where V = Laplacian operator An operator such as the Hamiltonian is something that tells us to perform a mathematical function (subtract, multiply etc). A wavefunction is a mathematical name for an atomic orbital (e.g. s, p, d), also it will show you how the electron moves around the nucleus – for example an s orbital is a sphere and p orbitals are a dumbbell shape. As we know a straight line on a graph can be described as the equation: y = mx + c, in the form of a wavefunction this can be represented as Ψ = mx + c. This then means that the wavefunction is a straight line and the electron will move along the line. Graphical Representation: Ψ IE 1 IE 2 Continuum IE 1 = -VOE 1 IE 2 = -VOE 2 VOE 2 < VOE 1 VOE 2 state is therefore more electronegative due to lower VOE energy value Finally lower the VOE value the more stable the system. Therefore Ψ 2 vs X charts the probability of finding electron at any point X from the nucleus. Ψ can be defined as a mathematical equation describing how that electron moves. The important points to know about the Schrödinger wave equation are:- Every atomic orbital has its own mathematical form with a certain shape. - Each atomic orbital represents how an electron moves around a single nucleus.- Finally that each atomic orbital has its own energy value....
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This note was uploaded on 02/25/2012 for the course FIN 4319 taught by Professor Toles during the Fall '08 term at Texas State.
- Fall '08