Hand in Assignment 3 Solutions

Hand in Assignment 3 Solutions - CHEM 212 (DE) HAND-IN...

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CHEM 212 (DE) HAND-IN ASSIGNMENT #3 (Fall 2008) page 1 of 5 1. (10 marks) Consider the following expressions for the sp 3 hybrid orbitals for some atom “X” which is located at the point (x,y,z) = (0,0,0). ⎡⎤ φ= ⎣⎦ 1 xyz 2 2s 2p 2p 2p +++ a 1 xy z 2 2s 2p 2p 2p --+ b 1 2 2s 2p 2p 2p +-- c 1 z 2 2s 2p 2p 2p -+- d a) Calculate the percentage composition of each hybrid to show that the hybrids are equivalent. b) Show that each of the hybrids is normalized. c) Show that φ a is orthogonal to φ b , φ c and φ d . For φ a : 2 1 2 2222 1111 () % 2s = ×100% = 25% ()+ 2 1 2 x % 2p = ×100% = 25% 2 1 2 y % 2p = ×100% = 25% 2 1 2 z % 2p = ×100% = 25% For the other hybrids, the coefficients are all equal to ± ½, so we will get exactly the same percentage compositions. Each hybrid is 25% 2s, 25%, 2p x , 25% 2p y and 25% 2p z . φ a normalized i i a 2 = 1 Since = 2 =1 i i a , then φ a is normalized. Similarly, φ b , φ c and φ d are all normalized. = 1 1 11 1 1 2 2 22 2 2 = 0 ( -)+ ( ii i ab φ a and φ b are orthogonal = 1 1 1 1 2 2 ( ( -) i ac φ a and φ c are orthogonal = 1 1 ( )( )+( )(- )+( )( )+( )(- ) i ad φ a and φ d are orthogonal
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CHEM 212 (DE) HAND-IN ASSIGNMENT #3 (Fall 2008) page 2 of 5 2. a)
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Hand in Assignment 3 Solutions - CHEM 212 (DE) HAND-IN...

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