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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

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    w ill

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    u nt

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    e ap

    pr ov

    al o

    f t riv

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    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

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    A to

    m ic

    N