# Lecture 8 - Lecture8 Chapter3 CHMY141 Spring2016 The...

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1/31/2016 1 Lecture 8: Chapter 3 CHMY 141 Spring 2016 The Schrödinger Equation Relates the total energy of an electron, the actual energy of an electron, and the wave function of an electron H ψ = E ψ H : Hamiltonian operator ψ : Wave function E : Actual energy The wave function ( ψ ) describes the wave behavior of the electron A plot of ψ 2 represents the probability density map of the electrons (an orbital )

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1/31/2016 2 Solutions to the Equation The Schrödinger equation can be solved for a hydrogen atom An orbital is a graphical representation of the wave function that solves the equation Each orbital has three related quantum numbers that define the wave function Principal Quantum number (n) Angular Momentum Quantum number (l) Magnetic Quantum number (m l ) Electrons contribute a fourth, Spin Quantum number (m s ) Principal Quantum Number (n) Determines size and energy of an orbital Possible values are integers greater than 0 (n = 1, 2, 3…) Energy of an atom in an orbital can be calculated: ܧ ൌ െ2.18 ൈ 10 ିଵ଼ ܬ n is the only quantum number that determines the energy of an electron Rydberg constant (R H )
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