c120a_lecture33_extra

c120a_lecture33_extra - Chem 120A Spring 2007 Supplement -...

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Chem 120A Supplement - Term Symbols for Atoms 04/16/07 Spring 2007 Lecture 33 Reading: Ratner and Schatz Ch. 9 1 What are Term Symbols? A given electron configuration can result in several different atomic (molecular) states with different energies as a result of the inter-electronic interactions. States with the same energy are constitute a ’term’. Term symbols are thus labels for groups of states with the same energy for multiple electron systems (both atoms and molecules). The attached schematic shows the order in which the labels are evaluated, namely going from the largest interactions at the top to the smallest interactions at the bottom. Term symbols are written in the following way: 2 S + 1 L J (1) where L is the total orbital angular momentum. L tells us the magnitude of the angular momentum through ¯ h [ L ( L + 1 )] 1 / 2 . It has 2 L + 1 distinguished by the quantum number M L . Similar remarks apply to S , the total spin angular momentum (where 2 S + 1 is known as the multiplicity) as well as J , the total angular momentum J = L + S . The value of L is obtained by using what is known as the Clebsch-Gordon series, for a two electron system, this would be: L = l 1 + l 2 , l 1 + l 2 - 1 ,... | l 1 - l 2 | (2) where the modulus sign is attached to l 1 - l 2 as the value of L must be non-negative. The maximum value of L is obtained when the two orbital angular momenta are in the same direction. The lowest value, | l 1 - l 2 | is obtained when they are in opposite directions. The value of L is normally designated as a capital letter
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c120a_lecture33_extra - Chem 120A Spring 2007 Supplement -...

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