CHAPTER 1 (part 3)_Atkins

CHAPTER 1 (part 3)_Atkins - Models of Atoms Just like a...

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Models of Atoms Just like a particle in a box, an electron is confined to the atom. Therefore, its wavefunction has to obey certain boundary conditions. Just like the particle in a box, this results in quantized energy or discrete energy levels. Schrödinger solved his own equation to find the actual energy levels in a hydrogen atom. He inserted the expression for the potential energy of the electron as: V(r) = -e 2 /(4πε 0 r) and was able to solve the equation to get: E n = -h R /n 2 R =  3.29 x 10 15 Hz (same as Rydberg’s empirical equation!!) For other species with one electron, this expression becomes: E n = (-Z 2 h )/n 2 The Integration of the Schrödinger equation, gives a set of four numbers, the quantum numbers (n, l, m l , and s). Each electron around the nucleus has its own set of quantum numbers that distinguishes it from each and every other electron in the same atom. THE FOUR QUANTUM NUMBERS Principle Quantum Number, n: It corresponds to the main energy level. The principle quantum number is the volume of space in which an electron moves around a nucleus. The allowed values for n are: n = 1,2,3,4,. .. Angular Momentum Quantum Number,
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This note was uploaded on 03/19/2008 for the course CH 301 taught by Professor Fakhreddine/lyon during the Fall '07 term at University of Texas at Austin.

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CHAPTER 1 (part 3)_Atkins - Models of Atoms Just like a...

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