13.14.C2v
13.17. (a)C 2 (b)D2d(c)C 1 (e)C2v
13.18. (a)C2v(b)Cs(c)D3d(e)D3h
13.19. (a)C2v(b)D3h(c)C2v
13.20. (a)Cv(b)C2v(c) D3h
13.21. (a)C 4 H 4 , C 8 H 8 , C 12 H 12 , and C 20 H 20. The final Platonic
solid cannot exist as a hydrocarbon. All but C 4 H 4 have been
synthesized by organic chemists.
13.22. (a)yes (b)yes (c)yes (d)no (e)no (f)no (g)no
(h)no (i)yes
13.23.c, e, f, g, k, l, and m will not have permanent dipole
moments.
13.24. (a)C 1 (i.e., only the Esymmetry element is present)
(b)Still Cs, so no longer chiral (for rules in determining chi-
rality, consult an organic chemistry textbook)
13.30.At least one threefold (or higher) rotational axis is
necessary to have an Eirreducible representation.
13.31.The irreducible representations are from different point
groups, and have different symmetry classes and orders.
Therefore, the great orthogonality theorem does not apply.
13.32.In Cvand Dh, any value of is possible for a proper
or improper rotation.
13.33. (forbitals in Oh) A2uT1uT2u
13.34. (a)Sin has E, (xy), S 2 (the y-axis), and i. (b)Cos
has E, C 2 (the y-axis), and 2 ’s (the xyand the yzplanes).
13.35.The symmetry elements in this case would be the
same as for cos in answer 13.34b.
13.36.Either Cvor Dh
13.39. (a) 3 A 2 B(b)A 1 A 2 2 E
13.40. (a)A 2 (b)B 1 B 2 E 1 (c)E (d)A1u
13.41.Of the first four answered above, all of the integrals of
functions with those symmetry labels would be identically zero
because they do not contain the all-symmetric irreducible rep-
resentation (A 1 or A ).
13.42.Yes, a transition can occur, because in the C4vpoint
group the combination EEB 2 does contain A 1.
13.43.The transition is forbidden because Dg(0)Dg(0)Du(1)
does not contain Dg(1).
13.44.The dorbitals have ET 2 irreducible representations;
Eis doubly degenerate and T 2 is triply degenerate.
13.51.The three closely spaced lines are the three wave-
functions that make up the triplet state (see equation 13.22).
13.55.sp^2
13.57. 2 A 1 A 2 E
Chapter 14
14.1.There is no rotating dipole when a linear molecule ro-
tates about its molecular axis.
14.2. (a)exactly zero (b)exactly zero (c)may be nonzero
(d)exactly zero
14.3. (a)3.00 108 s^1 (b)6.28 1012 s^1 (c)3.798
1014 s^1 (d)1.575 105 s^1
14.4.No, it is not allowed.
14.5.3.728 10 ^5 m, c3.00 108 m/s, E5.328
10 ^21 J
14.7.(m) ~10,000
14.8.E0, 2.58 10 ^22 J, 7.74 10 ^22 J, 1.55 10 ^21 J
14.9. (a)prolate symmetric top (b)spherical top (c)spher-
ical top (d)asymmetric top (e)asymmetric top (f)asym-
metric top (g)oblate symmetric top (h)linear
14.10.B5.91 10 ^24 J 0.2979 cm^1
14.11.B(SF 6 ) 1.80 10 ^24 J, B(UF 6 ) 1.10 10 ^24 J.
The difference is due to the larger bond distances in UF 6 ; the
S and U atoms themselves do not contribute to the moment
of inertia because they are at the intersection of all symmetry
elements.
14.12.AB1.015 10 ^22 J (0.196 cm^1 ), C
8.368 10 ^23 J (0.237 cm^1 )
14.14.E0, 1.674 10 ^22 J, 2.030 10 ^22 J, 5.021
10 ^22 J, 6.090 10 ^22 J
14.16.b, c, e, h, i, and j will have pure rotational spectra.
14.17. (a)allowed (b)forbidden (c)forbidden (d)forbid-
den (e)forbidden (f)allowed (g)forbidden (h)allowed
14.19.r3.28 Å
14.20.r1.60 Å
14.21.450.5, 900.9, 1351.2, and 1801.6 GHz
14.22. (a)Jmax 4 (b)Jmax 7
14.23.T1600 K
14.29.D4.82 10 ^2 cm^1
14.30.Total degrees of freedom, vibrational degrees of free-
dom: (a)6, 1 (b)9, 3 (c)180, 174 (d)69, 63 (e)54, 48
14.32.CH 3 D should have more IR-active vibrations due to
loss of symmetry.
14.35.~(est) 1215 cm^1 (not a good approximation!)
14.36.1661.6 cm^1
14.43.De(HF) 47,550 cm^1 , a(HF) 2.26 1010 m^1
2.26 Å^1
14.45.xe(HBr) 0.02097, xee55.57 cm^1812 ANSWERS TO SELECTED EXERCISES