Posted: September 13th, 2017

Advanced molecular Spectroscopy

Advanced molecular Spectroscopy

CH3203 / CH3503 Continuous Assessment #1, Semester 2, 2015
Instructions:

The deadline for submitting your continuous assessment work is 1pm on Thursday 12th March.
Please post your work into the tutorial “post-box” under the staff pigeonholes – please clearly label
your script with “CH7041 Molecular Spectroscopy – Dr Andrew Hudson”.
This is an individually-assessed piece of work to generate an individual mark for each student.
Please ensure that the work you submit is yours and yours alone. The University’s policy on
collusion & plagiarism is at http://www2.le.ac.uk/offices/sas2/assessments/plagiarism/plagiarism
(1) The lifetime of the 2P excited-electronic state of Na is 16ns. What is the minimum width of the
2S (2s) ? 2P (3p) transition that could be observed in an emission spectrum of Na. [2]
(2) A resonant wavelength of 589 nm for the 2S (2s) ? 2P (3p) transition in Na has been measured
in a laboratory instrument. However, a measurement using a space telescope directed towards a
nearby galaxy has identified that the same transition at 595 nm. How fast is the galaxy moving
relative to us? Justify the answer by clearly explaining the calculation required. [3]
(3) The structure of diborane, B2H6 (A), with D2h symmetry, is shown below:
(i) Determine the symmetry representation for the 3N coordinates of all the atoms in (A)
and hence identify the irreducible representation for the normal modes of vibration involving both
the stretching and bending of bonds. [6]
(ii) State the number of bands that should appear in the IR and Raman spectra of (A) in the
gas phase. [2]
(4) Prismane (B) is a cage-shaped molecule with D3h symmetry.
(B)
(i) Determine the symmetry representation for the 3N coordinates of all the atoms in B and hence identify the irreducible representation for the normal modes of

vibration involving both the stretching and bending of bonds. [6]
(ii) Prismane and benzene are structural isomers with formula C6H6. The irreducible representation for the normal modes of vibration of benzene in the D6h point group

is
2A1g+A2g+2B2g+E1g+4E2g+A2u+2B1u+2B2u+3E1u+2E2u.
Describe how the molecules prismane and benzene could be distinguished experimentally. [3]
(5) The structure of the cage-shaped molecule dodecahedrane, C20H20, is shown below. This molecule possess icosahedral, Ih, symmetry, and the point group contains the

following symmetry transformations: C5,C52,C3,C2, i, S10, S103, S6, ?. Illustrate these symmetry transformations on the structure diagram provided on the separate

answer sheet. You need to show only one example of each symmetry transformation (i.e. ONLY ONE of the axes of the C5 rotation axes, ONLY ONE of the C52 rotation axes,

…., and ONLY ONE of the ? planes). [3]
SEPARATE ANSWER SHEET – PLEASE DETACH FROM THE QUESTION SHEET AND SUBMIT WITH YOUR WRITTEN ANSWERS

                            
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