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Unformatted text preview: Chem 110A 1 Name__________________________________ Student ID___________________ Midquarter Exam November 6, 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. There are four problems, and most of the answers do not require much algebra to find. Note that parts 4(b) and 4(c) do not require you to have completed 4(a). Chem 110A 2 1. (30 points) Quantum states. A hydrogen atom is in a superposition of 1s and 2p z states described by the wave function " ( r , # , $ ) = N 3 % 1,0,0 ( r , # , $ ) + 2 % 2,1,0 ( r , # , $ ) ( ) where the individual energy states are the ones in our usual notation where " n , l , m r , # , $ ( ) = R n , l ( r ) Y l , m ( # , $ ) , and they are orthonormal with the volume element r 2 sin " drd " d # (a) What is the value of the normalization constant? Use the orthornormality of the states to write " # 2 r 2 sin $ drd $ d % = N 2 3 & 100 ( r , $ , % ) + 2 & 210 ( r , $ , % ) ( ) 2 # r 2 sin $ drd $ d % = N 2 9 & 100 # 2 r 2 sin $ drd $ d % + 4 & 210 # 2 r 2 sin $ drd $ d % + 6 & 210 * & 100 # r 2 sin $ drd $ d % + 6 & 100 * & 210 # r 2 sin $ drd $ d % ( ) ) * + , , = N 2 (9 + 4 + + 0) = 13 N 2 which gives N 2 = 1 13 (b) What is the probably that the a measurement of the energy of the system yields the n = 2 energy level, i.e., E 2 = " 1 8 e 2 a 4 #$ % & ( ) * = " 1 8 27.211eV ( ) ?...
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