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### Transcript of Physics 308: Statistical, Molecular, and Solid State kbeach/phys308/docs/Final.pdf Physics 308:...

• Physics 308: Statistical, Molecular, and Solid State Physics

Final Exam

Wednesday, April 23, 2008, 09:00–12:00

Student’s Name:

Constants

kB = 8.617× 10−5 eV/K

kBTroom = 0.025 eV

h̄ = 1.055× 10−34 J s

hc = 1.24× 10−6 eV m = 1240 eV nm

mec 2 = 5.11× 105 eV = 0.511 MeV

h̄2

2me =

(hc)2

8π2(mec2) = 0.0381 eV nm−2

1 u = 1.661× 10−27 kg = 931.4 MeV/c2

c = 299792458 m/s

a0 = 4π�0h̄

2

mee2 = 5.292× 10−2 nm

e = 1.602× 10−19 C

µB = eh̄

2me = 5.7883× 10−5 eV T−1

1

• Formulas

volume and surface area of a sphere:

V = 4

3 πR3 A = 4πR2

particle in a box:

ψ ∼ sin nπx L

En = h2n2

8mL2

quantum of light:

E = h̄ω = hf c = λf

dipole moment:

p = (∆q)r0

binding energy in an ionic solid:

U = − α 4π�0a

Leonard-Jones potential:

U(r) = U0

[( a

r

)12 − 2 ( a

r

)6] reduced mass:

1

µ =

1

m1 +

1

m2

current density and resistivity:

j = nqv ρ = mv

nq2l

2

• R ef

er en

ce T

ab le

s fo

r Ph

ys ic

al S

et tin

g/ C

H E

M IS

T R

Y 9

8 R

ef er

en ce

T ab

le s

fo r

Ph ys

ic al

S et

tin g/

C H

E M

IS T

R Y

(2 23

) Fr 87 -18

-3 2-

18 -8

-1

+1 22

6. 02

5 Ra 88 -18

-3 2-

18 -8

-2

+2 22

7. 02

8 Ac 89 -18

-3 2-

18 -9

-2

+3 (2

61 ) Rf

10 4

13 8.

90 6 La

57 2-8 -1

8- 18

-9 -2

+3 17

8. 49 H

f 72 **

18 -3

2- 10

-2

+4

91 .2

24 Zr 40 2-8

-1 8-

10 -2

+4

47 .8

8 Ti 22 2-8

-1 0-

2

+2 +3 +4

50 .9

41 5 V

23 2-8 -1

1- 2

+2 +3 +4 +5

51 .9

96 Cr 24 2-8

-1 3-

1

+2 +3 +6

95 .9

4 M o

42 2-8 -1

8- 13

-1

+3 +6

18 3.

85 W 74 -18

-3 2-

12 -2

+6

54 .9

38 0 M n

25 2-8 -1

3- 2

+2 +3 +4 +7

55 .8

47 Fe 26 2-8

-1 4-

2

+2 +3 58

.9 33

2 Co 27 2-8

-1 5-

2

+2 +3 58

.6 9 N

i 28 2-8

-1 6-

2

+2 +3 63

.5 46 Cu

29 2-8 -1

8- 1

+1 +2

10 7.

86 8 Ag

47 2-8 -1

8- 18

-1

+1

65 .3

9 Zn 30 2-8

-1 8-

2

+2 69

.7 2 Ga

31 2-8 -1

8- 3

+3

26 .9

81 54 Al

13 2-8 -3

+3

10 .8

1

B 5 2-3

+3 12

.0 11

1 C 6 2-4

–4 +2 +4

15 .9

99 4 O

8 2-6

–2 18

.9 98

40 3 F

9 2-7

–1 20

.1 79 Ne

10 2-8

0

4. 00

26 0 He

2 2

0

28 .0

85 5 Si

14 2-8 -4

–4 +2 +4

72 .5

9 Ge 32 2-8

-1 8-

4

–4 +2 +4

74 .9

21 6 As

33 2-8 -1

8- 5

–3 +3 +5

78 .9

6 Se 34 2-8

-1 8-

6

–2 +4 +6

12 7.

60 Te 52 2-8

-1 8-

18 -6

–2 +4 +6

12 6.

90 5 l

53 2-8 -1

8- 18

-7

–1 +1 +5 +7

13 1.

29 Xe 54 2-8

-1 8-

18 -8

0 +2 +4 +6

(2 09

) Po 84 -18

-3 2-

18 -6

+2 +4 (2

10 ) At

85 -18 -3

2- 18

-7

79 .9

04 Br 35 2-8

-1 8-

7

–1 +1 +5

83 .8

0 Kr 36 2-8

-1 8-

8

0 +2

(2 22

) Rn 86 -18

-3 2-

18 -8

0

17 4.

96 7 Lu

71

+3 17

3. 04 Yb

70

+2 +3 16

8. 93

4 Tm 69

+3 16

7. 26 Er

68

+3 16

4. 93

0 Ho 67

+3 16

2. 50 Dy

66

+3 15

8. 92

5 Tb 65

+3 15

7. 25 Gd

64

+3 15

1. 96 Eu

63

+2 +3 15

0. 36 Sm 62

+2 +3 (1

45 ) Pm 61

+3 14

4. 24 Nd

60

+3 14

0. 90

8 Pr 59

+3 14

0. 12 Ce

58

+3 +4

23 2.

03 8 Th

90

+4 23

1. 03

6 Pa 91

+4 +5 23

8. 02

9 U 92

+3 +4 +5 +6

23 7.

04 8 Np

93

+3 +4 +5 +6

(2 44

) Pu 94

+3 +4 +5 +6

(2 43

) Am 95 +3 +4 +5 +6

(2 47

) Cm 96 +3

(2 47

) Bk 97

+3 +4 (2

51 ) Cf

98

+3 (2

52 ) Es

99

(2 57

) Fm 10

0

(2 58

) M d

10 1

(2 59

) No 10

2

(2 60

) Lr 10

3

30 .9

73 76 P

15 2-8 -5

–3 +3 +5

32 .0

6

S 16 2-8

-6

–2 +4 +6

39 .9

48 Ar 18 2-8

-8

0 35

.4 53 Cl

17 2-8 -7

–1 +1 +3 +5 +7

11 8.

71 Sn 50 2-8

-1 8-

18 -4

+2 +4

14 .0

06 7 N

7 2-5

–3 –2 –1 +1 +2 +3 +4 +5

11 2.

41 Cd 48 2-8

-1 8-

18 -2

+2 11

4. 82 In

49 2-8 -1

8- 18

-3

+3

20 0.

59 Hg 80 -18

-3 2-

18 -2

+1 +2 20

4. 38

3 Tl 81 -18

-3 2-

18 -3

+1 +3 20

7. 2 Pb

82 -18 -3

2- 18

-4

+2 +4 20

8. 98

0 Bi 83 -18

-3 2-

18 -5

+3 +5

12 1.

75 Sb 51 2-8

-1 8-

18 -5

–3 +3 +5

10 6.

42 Pd 46 2-8

-1 8-

18

+2 +4

19 5.

08 Pt 78 -18

-3 2-

17 -1

+2 +4 19

6. 96

7 Au 79 -18

-3 2-

18 -1

+1 +3

10 1.

07 Ru 44 2-8

-1 8-

15 -1

+3

19 0.

2 Os 76 -18

-3 2-

14 -2

+3 +4 19

2. 22

Ir 77 -18

-3 2-

15 -2

+3 +4

10 2.

90 6 Rh

45 2-8 -1

8- 16

-1

+3 (9

8)

Tc 43 2-8

-1 8-

14 -1

+4 +6 +7

18 6.

20 7 Re

75 -18 -3

2- 13

-2

+4 +6 +7

92 .9

06 4 Nb

41 2-8 -1

8- 12

-1

+3 +5

18 0.

94 8 Ta

73 -18 -3

2- 11

-2

+5

(2 62

) Db 10

5

(2 63

) Sg 10

6

(2 64

) Bh 10

7

(2 65

) Hs 10

8

(2 68

) M t

10 9

(2 69

) Uu n

(2 72

) Uu u

11 1

(2 77

) Uu b

11 2

(2 85

) Uu q

11 4

88 .9

05 9 Y

39 2-8 -1

8- 9-

2

+3

44 .9

55 9 Sc

21 2-8 -9

-2

+3

13 7.

33 Ba 56 2-8

-1 8-

18 -8

-2

+2

87 .6

2 Sr 38 2-8

-1 8-

8- 2

+2

40 .0

8 Ca 20 2-8

-8 -2

+2

24 .3

05 M g

12 2-8 -2

+2

9. 01

21 8 Be

4 2-2

+2

13 2.

90 5 Cs

55 2-8 -1

8- 18

-8 -1

+1

85 .4

67 8 Rb

37 2-8 -1

8- 8-

1

+1

39 .0

98 3 K

19 2-8 -8

-1

+1

22 .9

89 77 Na

11 2-8 -1

+1

6. 94

1 Li 3 2-1

+1

1. 00

79 4 H

1 1

+1 –1

*T he

s ys

te m

at ic

n am

es a

nd s

ym bo

ls fo

r el

em en

ts o

f a to

m ic

n um

be rs

a bo

ve 1

09

w ill

b e

us ed

u nt

il th

e ap

pr ov

al o

f t riv

ia l n

am es

b y

IU PA

C .

** D

en ot

es th

e pr

es en

ce o

f ( 2-

8- )

fo r

el em

en ts

7 2

an d

ab ov

e

Period 1 2

11

2 G

ro up

17 16

15 14

13 1818

G ro

up

10 9

8 7

6 5

4 3

11 12

G ro

up 3 4 5 6 7

P er

io di

c Ta

bl e

of t

he E

le m

en ts

C 12

.0 11

–4 +2 +4

6 2-4

A to

m ic

M as

s

S ym

bo l

A to

m ic

N