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# mt2 - Chem 110A Name_Answers Student ID Second Midquarter...

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Chem 110A MQII_2009 1 Name________ Answers _____________ Student ID___________________ Second Midquarter Exam – November 25, 2009 Chemistry 110A Professor McCurdy Instructions: You may use only a pencil or pen. You may have one sheet of equations that you have prepared yourself. No other materials are allowed. Write all answers on the exam in the spaces provided, or clearly continued on the backs of the pages and labeled unambiguously. There are three pages of equations distributed with the exam. Be sure to look at them before you begin the exams.

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Chem 110A MQII_2009 2 1. (30 points) ( Problem 8-22) The total spin angular momentum operator for a two- electron system is ˆ S z , total = ˆ S z 1 + ˆ S z 2 Show that ! (1,2) = 1 2 1 s " (1) 1 s # (1) 1 s " (2) 1 s # (2) is an eigenfunction of ˆ S z , total , and give the eigenvalue associated with it. ( The notation 1 s " (1) means " 1 s ( r 1 ) # (1) where " 1 s ( r 1 ) is a 1s orbital ) We start by writing the LHS of the eigenvalue equation ˆ S z , total " (1,2) = ˆ S z 1 + ˆ S z 2 ( ) 1 2 1 s # (1) 1 s \$ (1) 1 s # (2) 1 s \$ (2) = 1 2 ˆ S z 1 + ˆ S z 2 ( ) 1 s # (1)1 s \$ (2) % 1 s # (2)1 s \$ (1) ( )
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mt2 - Chem 110A Name_Answers Student ID Second Midquarter...

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