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Sample_questions_for_undergraduate_Molec

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Uploaded on August 5, 2024
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samplequestionsforundergraduatemolec
1 from the usual optical objects made from glass
3 the square planar ab4 molecule is a symmetric t

Institution Undergraduate_Molec
Course Undergraduate_Molec

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1- From the usual optical objects made from glass (like mirrors, lens, …) which one can be
used to perform an experiment for a conclusive proof of superiority of the classical wave theory
of light against the classical particle theory of light? Why? (Note that all these are considered
within context of the nineteen century physics)

2- The diatomic AB molecule is made of A and B atoms each with two constituent isotopes;
(A1 and A2) with the relative abundances (0.1% and 99.9%) and (B1 and B2) with the relative
abundances (20% and 80%). If the rotational constant of the isotopically most abundant AB
species be 2 cm-1 and the masses of isotopes be: A1=12, A2=14, B1=10, B2=16 in arbitrary
units, then in practice what number of absorption lines will be observed for this molecule in
the Microwave region between 1-20 cm-1?

3- The square planar AB4 molecule is a symmetric top. However, just a single rotational
constant, instead of two, suffice to determine the rotational energy levels of this molecule. Can
you prove this mathematically? Hint: Check the matrix of the moment of inertia for this
molecule.

4- From the elemental analysis of a pure sample it emerged that the sample is described with
the formula AB2. On the other hand, the elements A and B are composed each of a single
isotope. In a study of the absorption lines in the Microwave region five spectral lines at 20, 40,
60, 80 and 100 cm-1 were observed when the evaporated AB2 sample was considered in a
spectroscopic study. What kind of information about the relative configuration of atoms and
the geometry of the molecule can be deduced?

5- In diatomic molecules the non-rigid rotor model, instead of the simpler rigid rotor model,
may be used to describe the rotational energy levels. Taking the experimental fact that by
increasing the rotational quantum number the energy of the rotational levels also increases, do
you think that using just the two term energy formula emerging from the non-rigid rotor model,
first term emerges from the rigid rotor model and the second term from the first order correction
to the rigid rotor model, suffice to reproduce the experimental rotational spectrum? Explain
possible limitations of the formula.

6- At least how many spectral lines one needs in the Microwave region for a diatomic molecule
to deduce its bond length (assume the masses of atoms are known)? If once the rigid rotor
model and then the non-rigid rotor model are used to interpret the spectrum, then what will be
the answer? Is there a difference?

7- In your opinion what is the least Jmax, i.e. the rotational quantum number of the rotational
energy level maximally populated, for a molecule with known bond length and masses of
atoms? Hint: Microwave spectrum of a molecule is recorded only in the gas phase.

8- If the selection rule of the rigid rotor model would suddenly change to: J  1, 2 ,
instead of the usual J  1 , then how many new lines would emerge in the Microwave
region for a diatomic molecule?

1

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