Physical Chemistry , 1st ed.

9.36.baseball1.49  10 ^34 m; e1.64  10 ^5 m (or
16.4 microns)

9.37.ve7.27  106 m/s; vp3.96  103 m/s

Chapter 10

10.2.Finite, continuous, single-valued, integrable

10.3. (a)yes (b)no; not bounded (Note that the fact that
the function is imaginary for negative values of xis not an
issue, as functions are not required to be real!) (c)no; not
continuous (d)yes, if it can be normalized (e)no; not bounded
(f)yes (g)no; not single-valued

10.4. (a)multiplication (b)addition (c)natural logarithm
(d)sine (e)exponential function (f)first derivative with re-
spect to x

10.5. (a) 6 (b) 9 (f) 12 x^2  7 7/x^2

10.6. (a) 12 x^2  4 x^3 (b) 2 (c)sin ^23 x(d)^110 

(e) 45 x^1  (^2) y 2
10.7.(4, 5, 6) (b)(0, 4, 1)
10.8. (a)no (b)yes; eigenvalue  4
2
(c)no (d)yes;
eigenvalue m(e)no (f)yes; eigenvalue ^41  8
2
m

^2 0.5



10.13.pm

10.14. xbaseball3.80  10 ^34 m, xe8.04  10 ^2 m

10.15. x4.71  10 ^9 m

10.17. t2.65  10 ^12 s

10.18. (a)P0.0000526 (b)P0.0200 (c)P0.0400
(d)P0.0200 (e)P0.0000526

10.19. (a)^12 eim(b)P^13 

10.28.E 2

2

m

^2 , 

2

2

m

^2 0.5

10.30. (a)E 2

2

m

K^2 (b)E

2

2

m

K^2 k(c)E

8



m

(^2) 
a
2
 2
10.33.length 5.74 Å
10.34.4, 9, and 99 nodes, respectively
10.37.P0.0200, 0.000008, 0.01998, 0.000028
10.42. x 0.5a
10.43. p  0
10.45.p 3 , p  3 
10.50.The five lowest energies are, in order, (1, 1, 1),
(1, 1, 2), (1, 1, 3), (1, 2, 1), and (2, 1, 1) (where the
quantum numbers are listed in order of the dimensions given).
10.51.Degeneracy first appears when one of the quantum
numbers equals 2 [i.e., E(1, 1, 2) E(1, 2, 1) E(2, 1, 1)].
The first appearance of “accidental” degeneracy occurs for
E(3, 3, 3) E(5, 1, 1) E(1, 5, 1) E(1, 1, 5).
10.54. x a/2, y b/2, z c/2.
10.58. (a) 1 (b) 0 (c)16h^2 /8ma^2 (d) 0 (e) 1 (f) 0 (g)
h^2 /8m(1/a^2 1/b^2 1/c^2 ) (h) 0
Chapter 11
11.1.335.8 N/m
11.2.k1515 N/m
11.9. (a) E6.63  10 ^34 J (b)3.00  108 m
11.10. (a) E3.976  10 ^20 J (b)5.00  10 ^6 m
(c)infrared region
11.11.4.36  1014 s, 6.88  10 ^7 m
11.14. px 0 for both (0) and (1)
11.16. (a)zero (b)zero (c)probably not identically zero
(d)zero (e)indeterminate (f)indeterminate; it depends on
the form of the potential energy, V

11.17.x(2nk1)h

1/2

11.18.9.109  10 ^31 kg versus (a)9.104  10 ^31 kg, (b)

9.107  10 ^31 kg, (c)~9.109  10 ^31 kg

11.20. (a)6.504  1013 s^1 (b)6.359  1013 s^1

11.21.Approximately 2660 cm^1

11.24.E(0) 0, E(1) 2.68  10 ^19 J, E(2) 1.07  10 ^18 J,

E(3) 2.41  10 ^18 J, E(4) 4.28  10 ^18 J

11.26.(0) ^12 , (1) ^12 (cos isin ), (2) 

^12 (cos 2isin 2), (3) ^12 (cos 3isin 3)

11.27. (b)E(2) E(1) 62.1 cm^1

11.32. r cannot be evaluated for Y^2  2 because ris not a vari-

able of the spherical harmonic.

11.34. (a)E7.506  10 ^22 J (b)Ltot2.583  10 ^34 Js

(c)The zcomponent of the total angular momentum could

be  2 ,  1 , 0, 1, or 2.

11.35. (b)E(2) E(1) 41.3 cm^1. (Compare with 11.27.)

11.36. E( 5 →6) 5.95  10 ^19 J, equivalent to

334 nm (cf. 328 nm experimentally).

11.41.V4.36  10 ^18 J

11.42.V1.92  10 ^57 J

11.49.4 is not allowed for n4.

11.50.EH1312 kJ/mol, EHe5249 kJ/mol.

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