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http://ocw.mit.edu 5.80 SmallMolecule Spectroscopy and Dynamics
Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE OF TECHNOLOGY Chemistry 5.76 Spring 1994 Problem Set #3
1. An atom is in a (3d)2 3 P0 state.
(a) List all L–S–J terms to which an electric dipole allowed transition might occur.
(b) List all twoelectron conﬁgurations into which electric dipole allowed transitions can occur from (3d)2
3P .
0 2. A new superheavy element, Dk or Dreckium1 , has recently been discovered at Berkeley. Its atomic number is
120 and it is in Group IIA of the periodic table. The following Dk I spectral lines have been observed (relative
intensities in parentheses):
in absorption at
cm−1 39511
37474
34796
31176
27506
27228
26116
20179
19901
19484
19427
19149
19051
(� observed but no intensity available) T = 1000K
—
(0)
(2)
(10)
(0)
(1)
(55)
(80)
(1100)
(1900)
(900)
(1400)
(1200) T = 2000K
(0)
(1)
(4)
(20)
(0)
(1)
(110)
(60)
(1000)
(2400)
(700)
(1300)
(900) Emission
�
�
�
�
�
�
�
(100)
(2200)
(7000)
(1300)
(2800)
(1600) Additional lines observed in emission include (many others are omitted from this table)
20722 cm−1
18685
16007
12387
7327
1 Dk was independently discovered in the Soviet Union, but they call it Merdium, and, because of the peculiarities of the Cyrillic alphabet,
symbolize it by Sh. 5.76 Problem Set #3 Spring, 1994 page 2 and a group of 6 lines (listed in the main table above) with relative intensities quite diﬀerent from those
observed in absorption. The emission intensities for these 6 lines are included in the table of absorption lines.
(a) Assign the observed spectra and construct an energy level diagram. You should make use of all the tricks
used by spectroscopists:
(i) search for repeated frequency intervals;
(ii) search for progressions described by A − B/ n2 where A and B are constants and n is the principal
quantum number;
(iii) take advantage of relative intensity information, especially temperature dependent intensities;
(iv) analogies with other group IIA atomic spectra (HINT: note that the energy of (n − 2) f and (n − 1)d
orbitals decreases relative to n s and n p as n increases);
(v) Hund’s rules;
(vi) The Land´ interval rule.
e
You should also assume that I have not included any misleading information such as lines belonging to
another atom or to Dk II, transitions in which the lower level does not belong to one of the four predicted
low–lying conﬁgurations involving 8s, 8p, 7d and 6f orbitals, or transitions involving signiﬁcantly per
turbed levels. Atomic spectroscopists should be so fortunate! Because Dk is a heavy atom, there is at
least one (weak) intercombination transition.
(b) Can you explain why the lines 20179, 19901, and 19484 cm−1 exhibit intensity enhancements in emission
at high pressure and in regions of a discharge in which large electric potential gradients exist?
(c) Is the energy level diagram for Dk suﬃciently complete that the electronic partition function,
Qe = � gi exp[−Ei /kT ], all states i may be calculated at 3000K? If one or more electronic terms are missing, what would be the fractional
error in Qe , assuming plausible term energies? How would you devise an experiment which samples
Qe (T ) with accuracy suﬃcient to locate a missing low–lying electronic term? Is it likely that all of the
necessary quantities could be measured with suﬃcient accuracy to prove that a low–lying electronic term
had escaped detection?
3. Bernath, Chapter 6, Problem #3, page 197.
A triatomic molecule has the formula A2 B. Its microwave spectrum shows strong lines at 15, 30, 45,. . . MHz,
and no other lines. Which of the following structures is (are) compatible with this spectrum?
(a) linear AAB 5.76 Problem Set #3 Spring, 1994 page 3 (b) linear A BA
(c) bent AAB
(d) bent A BA
4. Bernath, Chapter 6, Problem #5, page 197.
The F2 O molecule of C2v symmetry has an O—F bond length of 1.405 Å and an FOF bond angle of 103.0◦ .
(a) Calculate A, B, and C for F2 O.
(b) Will the microwave spectrum of F2 O show a–, b–, or c–type transitions?
(c) Predict the frequency of the J = 1 − 0 microwave transition?
5. Bernath, Chapter 6, Problem #8, pages 197–198.
The following is a complete list of observed transitions involving levels J = 0, 1, and 2 for two isotopes of
formaldehyde in their vibrational ground states:
.
H12 C16 O
2
(MHz) 13
H2 C16 O
(MHz) 71.14
4,829.66
14,488.65
72,837.97
140,839.54
145,602.98
150,498.36 —
4,593.09
13,778.86
71,024.80
137,449.97
141,983.75
146,635.69 (a) Assign these microwave transitions for both isotopomers. Assume that H2 CO belongs to the C2v point
group and estimate a molecular geometry using bondlength tables. Assign the spectrum by prediction
of the expected rotational spectrum.
(b) What are A, B, and C for the two isotopic species? Since we have neglected centrifugal distortion, it will
not be possible to ﬁt all transitions exactly with only three rotational constants. Devise a procedure that
gives a “best ﬁt” to all lines.
(c) Explain why the inertial defect
Δ = IC − IA − IB
is a good test for planarity. Why does H2 CO appear not to be planar from the microwave spectrum?
(d) Obtain a best possible geometry for H2 CO using your A, B, C values for the two isotopes. 5.76 Problem Set #3 Spring, 1994 page 4 6. Bernath, Chapter 6, Problem #20, page 199.
The application of an electric ﬁeld to a molecular system partially lifts the M J degeneracy. This Stark eﬀect
may be treated as a perturbation of the rotational energies. The perturbation Hamiltonian H� = −µz Ez , where
z is a lab frame coordinate and Ez is the electric ﬁeld along the laboratory z–axis.
(a) Show that there will be no ﬁrstorder Stark eﬀect for a linear molecule.
(b) Develop a formula for the secondorder Stark eﬀect of a linear molecule. ...
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.
 Spring '04
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