Notes2A

# Notes2A - Atomic Emission and Absorption Spectroscopy I...

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Atomic Emission and Absorption Spectroscopy I. Atomic Emission and Absorption Spectrum A. Experimental Facts 1. ___ Atoms _______ emit and absorb ONLY ____ Discrete _____ FREQUENCIES ( or WAVELENGTHS) of _ Electromagnetic Radiation _ . 2. The _ Emission __ and ____ Absorption ___________ spectrum of each ___ Atom __ is __ Unique _! "Atomic Fingerprints" 3. The ___ Wavelength __ ___ Absorbed ____ by an atom are the __ Same __ wavelengths __ Emitted ___. B. Explanations 1. The first condition is a consequence of the fact that electrons in the atom are _ Bound _. When ___ boundary ___ ____ conditions ___ are imposed

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upon a differential equation, ONLY __ certain __ possible _ solutions are __ allowed _. These solutions are called ___ eigen __ (German for "proper") __ functions __. The parameter value that distinguishes a particular solution in our case the wavelength (or equivalently energy) is called the ___ eigen ___ ____ value . Example: Wave on a string Unbounded String Bounded String Any wavelength is possible for the unbounded string. L x = 0 x = L
For the bounded string, the node conditions at the wall limit the wavelength to 2L/1, 2L/2, 2L/3, 2L/4, etc. . Thus, a particular solution to our bounded wave problem in the language of differential equations can be stated as follows "Nth" Eigenvalue: ..... 3, 2, 1, n where n 2L λ n = = "Nth" Eigenfunction: ( 29 L to 0 x for λ x π 2 Sin A x n n n = = Ψ

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## This note was uploaded on 01/16/2012 for the course PHYS 4353 taught by Professor Dr.danielk.marble during the Fall '07 term at Tarleton.

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Notes2A - Atomic Emission and Absorption Spectroscopy I...

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