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Introduction To Group Theory Question Paper

Introduction To Group Theory

Course:Bachelor Of Education Science

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE AND BACHELOR OF EDUCATION
SCH 307: INTRODUCTION TO GROUP THEORY

DATE: Tuesday 22nd December, 2009 TIME: 8.00 a.m. – 10.00 a.m.

INSTRUCTIONS
• Character tables are provided.
• Answer ALL FOUR questions.
Q1.
(a)
Explain the necessary conditions that a ser of molecular symmetry operations must satisfy in order to constitute a molecular point group. [6 marks]
(b)
Determine the schoenflies symbol for the point group to which each of the following species belongs:
(i)
trans-dichloroethene [2 marks]
(ii)
fluoro-trichloromethane [2 marks]
(iii)
para-dibromobenzene [2 marks]
(c)
Write concisely on the following:
(i)
Classes of symmetry operations [4 marks]
(ii)
Representations of a molecular point group. [6 marks]
Q2.
(a)
For the C4v point group, express the following direct product representations as direct sums of its IRREPS:
(i) B2 ? E [3 marks]
(ii) E2 = E ? E [3 marks]
(b)
Using the set of the N – H bonds, {h1, h2, h3}, in ammonia as a basis, determine the SALC that has the symmetry of the one-dimensional IRREP generated by the defined basis. [10 marks]
Q3.
(a)
State the selection rules for IR and Ramar activities of the fundamental transitions of molecules. [4 marks]
(b)
Determine the symmetries of the vibrational modes of chloromethane, and show which modes are IR active and which are Raman active. (No vibrational drawings would be shown). [10 marks]
Q4.
Consider the planar BF3 molecule, (D3h symmetry):
(a)
Using s, p and d atomic orbitals as based, work out the hybridization schemes by boron that are possible for s bond formation with the pendent atoms. [8 marks]
(b)
Derive the SALCs that are bases for the IRREP of order 2 in (a) above. [10 marks]

Introduction To Group Theory Question Paper

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