University Physics

Samuel J. Ling, Jeff Sanny, William Moebs

Chapter 9 Condensed Matter Physics - all with Video Answers

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Chapter Questions

00:26

Problem 1

What is the main difference between an ionic bond, a covalent bond, and a van der Waals bond?

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00:46

Problem 2

For the following cases, what type of bonding is expected? (a) KCl molecule; (b) $\mathrm{N}_{2}$ molecule.

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00:33

Problem 3

Describe three steps to ionic bonding.

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00:22

Problem 4

What prevents a positive and negative ion from having a zero separation?

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00:41

Problem 5

For the $\mathrm{H}_{2}$ molecule, why must the spins the electron spins be antiparallel?

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00:13

Problem 6

Does the absorption spectrum of the diatomic molecule HCl depend on the isotope of chlorine contained in the molecule? Explain your reasoning.

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00:31

Rank the energy spacing $(\Delta E)$ of the following transitions from least to greatest: an electron energy transition in an atom (atomic energy), the rotational energy of a molecule, or the vibrational energy of a molecule?

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01:56

Problem 8

Explain key features of a vibrational-rotation energy spectrum of the diatomic molecule.

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00:31

Problem 9

Why is the equilibrium separation distance between $\mathrm{K}^{+}$ and $\mathrm{Cl}^{-}$ different for a diatomic molecule than for
solid KCl?

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00:23

Problem 10

Describe the difference between a face-centered cubic structure (FCC) and a body-centered cubic structure $(\mathrm{BCC})$

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00:43

Problem 11

In sodium chloride, how many $\mathrm{Cl}^{-}$ atoms are "nearest neighbors" of $\mathrm{Na}^{+}$ ? How many $\mathrm{Na}^{+}$ atoms are "nearest neighbors" of $\mathrm{Cl}^{-}$ ?

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00:32

Problem 12

In cesium iodide, how many $\mathrm{Cl}^{-}$ atoms are "nearest neighbors" of $\mathrm{Cs}^{+}$ ? How many $\mathrm{Cs}^{+}$ atoms are "nearest neighbors" of $\mathrm{Cl}^{-}$ ?

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00:42

Problem 13

The NaCl crystal structure is FCC. The equilibrium spacing is $r_{0}=0.282 \mathrm{nm} .$ If each ion occupies a cubic
volume of $r_{0}^{3},$ estimate the distance between "nearest
neighbor" $\mathrm{Na}^{+}$ ions (center-to-center)?

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00:33

Problem 14

Why does the Fermi energy $\left(E_{\mathrm{F}}\right)$ increase with the number of electrons in a metal?

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02:55

Problem 15

If the electron number density $(\mathrm{N} / \mathrm{V})$ of a metal increases by a factor $8,$ what happens to the Fermi energy $\left(E_{\mathrm{F}}\right) ?$

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00:25

Problem 16

Why does the horizontal line in the graph in Figure 9.12 suddenly stop at the Fermi energy?

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00:39

Problem 17

Why does the graph in Figure 9.12 increase gradually from the origin?

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00:36

Problem 18

Why are the sharp transitions at the Fermi energy "smoothed out" by increasing the temperature?

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00:17

Problem 19

What are the two main approaches used to determine the energy levels of electrons in a crystal?

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00:33

Problem 20

Describe two features of energy levels for an electron in a crystal.

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00:32

Problem 21

How does the number of energy levels in a band correspond to the number, $N$, of atoms.

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00:26

Problem 22

Why are some materials very good conductors and others very poor conductors?

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00:40

Problem 23

Why are some materials semiconductors?

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00:24

Problem 24

Why does the resistance of a semiconductor decrease as the temperature increases?

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00:39

Problem 25

What kind of semiconductor is produced if germanium is doped with (a) arsenic, and (b) gallium?

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00:38

Problem 26

What kind of semiconductor is produced if silicon is doped with (a) phosphorus, and (b) indium?

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00:21

Problem 27

What is the Hall effect and what is it used for?

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00:37

Problem 28

For an $n$ -type semiconductor, how do impurity atoms alter the energy structure of the solid?

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00:19

Problem 29

For a p-type semiconductor, how do impurity atoms alter the energy structure of the solid?

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00:17

Problem 30

When $p$ - and $n$ -type materials are joined, why is a uniform electric field generated near the junction?

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00:38

Problem 31

When $p$ - and $n$ -type materials are joined, why does the depletion layer not grow indefinitely?

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00:19

Problem 32

How do you know if a diode is in the forward biased configuration?

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00:25

Problem 33

Why does the reverse bias configuration lead to a very small current?

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00:13

Problem 34

What happens in the extreme case that where the $n$ and $p$ -type materials are heavily doped?

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00:33

Problem 35

Explain how an audio amplifier works, using the transistor concept.

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00:25

Problem 36

Describe two main features of a superconductor.

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00:23

Problem 37

How does BCS theory explain superconductivity?

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00:15

Problem 38

What is the Meissner effect?

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00:53

Problem 39

What impact does an increasing magnetic field have on the critical temperature of a semiconductor?

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01:18

Problem 40

The electron configuration of carbon is $1 s^{2} 2 s^{2} 2 p^{2}$ Given this electron configuration, what other element might exhibit the same type of hybridization as carbon?

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00:50

Problem 41

Potassium chloride (KCl) is a molecule formed by an ionic bond. At equilibrium separation the atoms are $r_{0}=0.279 \mathrm{nm}$ apart. Determine the electrostatic potential
energy of the atoms.

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01:14

Problem 42

The electron affinity of $\mathrm{Cl}$ is 3.89 eV and the ionization energy of $\mathrm{K}$ is $4.34 \mathrm{eV}$. Use the preceding problem to find the dissociation energy. (Neglect the energy of repulsion.)

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01:36

Problem 43

The measured energy dissociated energy of KCl is 4.43 eV. Use the results of the preceding problem to the determine the energy of repulsion of the ions due to the exclusion principle.

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05:04

Problem 44

In a physics lab, you measure the vibrationalrotational spectrum of HCl. The estimated separation between absorption peaks is $\Delta f \approx 5.5 \times 10^{11} \mathrm{Hz}$. The central frequency of the band is $f_{0}=9.0 \times 10^{13} \mathrm{Hz}$. (a) What is the moment of inertia ( $I$ )? (b) What is the energy of vibration for the molecule?

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02:43

Problem 45

For the preceding problem, find the equilibrium separation of the $\mathrm{H}$ and $\mathrm{Cl}$ atoms. Compare this with the actual value.

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03:44

Problem 46

The separation between oxygen atoms in an $\mathrm{O}_{2}$ molecule is about $0.121 \mathrm{nm}$. Determine the characteristic energy of rotation in eV.

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03:26

Problem 47

The characteristic energy of the $\mathrm{N}_{2}$ molecule is $2.48 \times 10^{-4} \mathrm{eV}$. Determine the separation distance between the nitrogen atoms

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03:38

Problem 48

The characteristic energy for $\mathrm{KCl}$ is $1.4 \times 10^{-5} \mathrm{eV}$ (a) Determine $\mu$ for the KCl molecule. (b) Find the separation distance between the $K$ and $C l$ atoms.

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07:10

Problem 49

A diatomic $\mathrm{F}_{2}$ molecule is in the $l=1$ state. (a) What is the energy of the molecule? (b) How much energy is radiated in a transition from a $l=2$ to a $l=1$ state?

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04:34

Problem 50

In a physics lab, you measure the vibrationalrotational spectrum of potassium bromide (KBr). The estimated separation between absorption peaks is $\Delta f \approx 5.35 \times 10^{10} \mathrm{Hz} .$ The central frequency of the band is $f_{0}=8.75 \times 10^{12} \mathrm{Hz} .$ (a) What is the moment of inertia
(I)? (b) What is the energy of vibration for the molecule?

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00:27

Problem 51

The Csl crystal structure is BCC. The equilibrium spacing is approximately $r_{0}=0.46 \mathrm{nm} .$ If $\mathrm{Cs}^{+}$ ion occupies a cubic volume of $r_{0}^{3},$ what is the distance of this
ion to its "nearest neighbor" I $^{+}$ ion?

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00:45

Problem 52

The potential energy of a crystal is -8.10 eV /ion pair. Find the dissociation energy for four moles of the crystal.

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02:19

Problem 53

The measure density of a NaF crystal is $2.558 \mathrm{g} / \mathrm{cm}^{3} .$ What is the equilibrium separate distance of $\mathrm{Na}^{+}$ and $\mathrm{Fl}^{-}$ ions?

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01:46

Problem 54

What value of the repulsion constant, $n$, gives the measured dissociation energy of 221 kcal/mole for NaF?

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03:27

Problem 55

Determine the dissociation energy of 12 moles of sodium chloride (NaCl). (Hint: the repulsion constant $n$ is approximately 8.)

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01:51

Problem 56

The measured density of a KCl crystal is $1.984 \mathrm{g} / \mathrm{cm}^{3} .$ What is the equilibrium separation distance of $\mathrm{K}^{+}$ and $\mathrm{Cl}^{-}$ ions?

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01:35

Problem 57

What value of the repulsion constant, $n,$ gives the

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01:35

Problem 58

The measured density of a CsCl crystal is $3.988 \mathrm{g} / \mathrm{cm}^{3} .$ What is the equilibrium separate distance of $\mathrm{Cs}^{+}$ and $\mathrm{Cl}^{-}$ ions?

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01:43

Problem 59

What is the difference in energy between the $n_{x}=n_{y}=n_{z}=4$ state and the state with the next higher energy? What is the percentage change in the energy between the $n_{x}=n_{y}=n_{z}=4$ state and the state with the next higher energy? (b) Compare these with the difference in energy and the percentage change in the energy between the $n_{x}=n_{y}=n_{z}=400$ state and the state with the next higher energy.

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05:10

Problem 60

An electron is confined to a metal cube of $l=0.8 \mathrm{cm}$
(a) on each side. Determine the density of states at $E=0.80 \mathrm{eV} ;$ (b) $E=2.2 \mathrm{eV} ;$ and $(\mathrm{c}) E=5.0 \mathrm{eV}$

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02:51

Problem 61

What value of energy corresponds to a density of states of $1.10 \times 10^{24} \mathrm{eV}^{-1} ?$

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01:47

Problem 62

Compare the density of states at $2.5 \mathrm{eV}$ and $0.25 \mathrm{eV}$.

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03:05

Problem 63

Consider a cube of copper with edges $1.50 \mathrm{mm}$ long. Estimate the number of electron quantum states in this cube whose energies are in the range 3.75 to 3.77 eV.

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01:24

Problem 64

If there is one free electron per atom of copper, what is the electron number density of this metal?

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03:15

Problem 65

Determine the Fermi energy and temperature for copper at $T=0 \mathrm{K}$

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00:40

Problem 66

For a one-dimensional crystal, write the lattice spacing
(a) in terms of the electron wavelength.

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00:22

Problem 67

What is the main difference between an insulator and
a semiconductor?

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01:29

Problem 68

What is the longest wavelength for a photon that can excite a valence electron into the conduction band across an energy gap of $0.80 \mathrm{eV} ?$

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01:52

Problem 69

A valence electron in a crystal absorbs a photon of wavelength, $\lambda=0.300 \mathrm{nm} .$ This is just enough energy to allow the electron to jump from the valence band to the conduction band. What is the size of the energy gap?

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00:57

Problem 70

An experiment is performed to demonstrate the Hall effect. A thin rectangular strip of semiconductor with width
$10 \mathrm{cm}$ and length $30 \mathrm{cm}$ is attached to a battery and immersed in a $1.50-T$ field perpendicular to its surface. This produced a Hall voltage of 12 V. What is the drift velocity of the charge carriers?

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01:47

Problem 71

Suppose that the cross-sectional area of the strip (the area of the face perpendicular to the electric current) presented to the in the preceding problem is $1 \mathrm{mm}^{2}$ and the current is independently measured to be $2 \mathrm{mA}$. What is the number density of the charge carriers?

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01:26

Problem 72

A current-carrying copper wire with cross-section $\sigma=2 \mathrm{mm}^{2}$ has a drift velocity of $0.02 \mathrm{cm} / \mathrm{s}$. Find the total current running through the wire.

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00:51

Problem 73

The Hall effect is demonstrated in the laboratory. A thin rectangular strip of semiconductor with width $5 \mathrm{cm}$ and cross-sectional area $2 \mathrm{mm}^{2}$ is attached to a battery and immersed in a field perpendicular to its surface. The Hall voltage reads $12.5 \mathrm{V}$ and the measured drift velocity is 50 m/s. What is the magnetic field?

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01:18

Problem 74

Show that for $V$ less than zero, $I_{\text {net }} \approx-I_{0}$

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02:16

Problem 75

A p-n diode has a reverse saturation current $1.44 \times 10^{-8} \mathrm{A} .$ It is forward biased so that it has a current
of $6.78 \times 10^{-1}$ A moving through it. What bias voltage is being applied if the temperature is $300 \mathrm{K}$ ?

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00:44

Problem 76

The collector current of a transistor is $3.4 \mathrm{A}$ for a base current of $4.2 \mathrm{mA}$. What is the current gain?

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01:36

Problem 77

Applying the positive end of a battery to the $p$ -side and the negative end to the $n$ -side of a $p-n$ junction, the measured current is $8.76 \times 10^{-1} \mathrm{A}$. Reversing this polarity give a reverse saturation current of $4.41 \times 10^{-8} \mathrm{A} .$ What is the temperature if the bias voltage is $1.2 \mathrm{V} ?$

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00:38

Problem 78

The base current of a transistor is $4.4 \mathrm{A}$, and its current gain $1126 .$ What is the collector current?

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01:42

Problem 79

At what temperature, in terms of $T_{C}$, is the critical field of a superconductor one-half its value at $T=0 \mathrm{K}$ ?

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01:18

Problem 80

What is the critical magnetic field for lead at $T=2.8 \mathrm{K} ?$

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02:36

Problem 81

A Pb wire wound in a tight solenoid of diameter of
$4.0 \mathrm{mm}$ is cooled to a temperature of $5.0 \mathrm{K}$. The wire is connected in series with a $50-\Omega$ resistor and a variable source of emf. As the emf is increased, what value does it

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02:04

Problem 82

A tightly wound solenoid at 4.0 K is 50 cm long and is constructed from Nb wire of radius $1.5 \mathrm{mm}$. What maximum current can the solenoid carry if the wire is to remain superconducting?

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02:01

Problem 83

Potassium fluoride (KF) is a molecule formed by an ionic bond. At equilibrium separation the atoms are $r_{0}=0.255 \mathrm{nm}$ apart. Determine the electrostatic potential energy of the atoms. The electron affinity of $F$ is 3.40 $\mathrm{eV}$ and the ionization energy of $\mathrm{K}$ is $4.34 \mathrm{eV}$. Determine dissociation energy. (Neglect the energy of repulsion.)

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05:58

Problem 84

For the preceding problem, sketch the potential energy versus separation graph for the bonding of $\mathrm{K}^{+}$ and $\mathrm{F}^{-}$ ions. (a) Label the graph with the energy required to transfer an electron from $K$ to $F$. (b) Label the graph with the dissociation energy.

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02:47

Problem 85

The separation between hydrogen atoms in a $\mathrm{H}_{2}$ molecule is about $0.075 \mathrm{nm}$. Determine the characteristic energy of rotation in eV.

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02:46

Problem 86

The characteristic energy of the $\mathrm{Cl}_{2}$ molecule is
$2.95 \times 10^{-5} \mathrm{eV} .$ Determine the separation distance between the nitrogen atoms.

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03:40

Problem 87

Determine the lowest three rotational energy levels of $\mathrm{H}_{2}$

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00:31

Problem 88

A carbon atom can hybridize in the $s p^{2}$ configuration. (a) What is the angle between the hybrid orbitals?

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00:33

Problem 89

List five main characteristics of ionic crystals that result from their high dissociation energy.

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00:40

Problem 90

Why is bonding in $\mathrm{H}_{2}^{+}$ favorable? Express your answer in terms of the symmetry of the electron wave function.

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00:09

Problem 91

Astronomers claim to find evidence of $\mathrm{He}_{2}$ from light spectra of a distant star. Do you believe them?

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02:48

Problem 92

Show that the moment of inertia of a diatomic molecule is $I=\mu r_{0}^{2},$ where $\mu$ is the reduced mass, and

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06:13

Problem 93

Show that the average energy of an electron in a one-dimensional metal is related to the Fermi energy by $\bar{E}=\frac{1}{2} E_{\mathrm{F}}$

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01:16

Problem 94

Measurements of a superconductor's critical magnetic field (in $T$ ) at various temperatures (in $\mathrm{K}$ ) are given below. Use a line of best fit to determine $B_{\mathrm{c}}(0) .$ Assume
$T_{c}=9.3 \mathrm{K}$

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00:24

Problem 95

Estimate the fraction of Si atoms that must be replaced by As atoms in order to form an impurity band.

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00:44

Problem 96

Transition in the rotation spectrum are observed at ordinary room temperature $(T=300 \mathrm{K}) .$ According to your lab partner, a peak in the spectrum corresponds to a transition from the $l=4$ to the $l=1$ state. Is this possible? If so, determine the momentum of inertia of the molecule.

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05:08

Problem 97

Determine the Fermi energies for (a) $\mathrm{Mg},$ (b) $\mathrm{Na}$, and (c) Zn.

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00:41

Problem 98

Find the average energy of an electron in a 2 n wire.

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01:43

Problem 99

What value of the repulsion constant, $n$, gives the

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00:32

Problem 100

A physical model of a diamond suggests a BCC packing structure. Why is this not possible?

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03:35

Problem 101

For an electron in a three-dimensional metal, show that the average energy is given by $$\bar{E}=\frac{1}{N} \int_{0}^{E_{F}} E g(E) d E=\frac{3}{5} E_{F}$$

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