Deck 18: Solids and the Theory of Conduction

Question 1

If you want to produce an amorphous solid from a liquid, you

A) cool the liquid slowly so that the molecules gradually lose their kinetic energy and thus form a maximum number of bonds.
B) cool the liquid rapidly to remove its internal energy before the molecules have a chance to form many bonds.
C) maintain the temperature of the liquid while increasing the pressure applied to the liquid.
D) maintain the temperature of the liquid while decreasing the pressure applied to the liquid.
E) warm the liquid while decreasing its pressure.

Answer 1

cool the liquid rapidly to remove its internal energy before the molecules have a chance to form many bonds.

Question 2

The equilibrium spacing r₀ for NaCl is 0.282 nm and the mass of 1 mol of NaCl is
58)4 g. The density of NaCl must be

A) 10.2 g/cm³
B) 6.35 g/cm³
C) 3.68 g/cm³
D) 2.16 g/cm³
E) 1.08 g/cm³

Answer 2

2.16 g/cm³

Question 3

Using the measured mass density of 2.48 g/cm³, and the molar mass of 58.098 g for KF, the equilibrium spacing between the K⁺ and F^- ions is

A) 0.168 nm
B) 0.196 nm
C) 0.269 nm
D) 0.293 nm
E) 0.312 nm

Answer 3

0.269 nm

Question 4

In the classical free-electron theory of metals,

A) a metal is pictured as a regular three-dimensional array of atoms or ions.
B) a metal contains a large number of electrons that are free to move throughout the whole metal.
C) thermal equilibrium is maintained by collisions of electrons with the lattice ions.
D) electrons in the absence of an electric field move about the metal much as gas molecules move in a container.
E) All of these are true.

Question 5

KF has a face-centered-cubic lattice structure and the equilibrium spacing between the K⁺ and F^- ions is 0.269 nm. It has a dissociation energy of 498 kJ/mol. The constant n in the empirical potential energy, U_rep = A/rⁿ, is

A) 2.2
B) 4.3
C) 5.8
D) 6.9
E) 8.7

Question 6

The crystalline structure known as face-centered-cubic

A) is characterized by the stacking of identical spheres.
B) occurs when every ion has eight nearest-neighbor ions of opposite charge.
C) corresponds to an alternating pattern of ions.
D) occurs when an ion of either kind has six nearest neighbors of the other kind.
E) None of these is correct.

Question 7

If the atoms are treated as solid spheres, the fraction of volume occupied by the atoms in a body-centered-cubic unit cell is

A) 0.45
B) 0.52
C) 0.65
D) 0.68
E) 0.74

Question 8

If the atoms are treated as solid spheres, the fraction of volume occupied by the atoms in a face-centered-cubic unit cell is

A) 0.45
B) 0.52
C) 0.65
D) 0.68
E) 0.74

Question 9

The Madelung constant is given by the infinite sum $\alpha$ = 6 - 12/2^1/2 + 8/3^1/2 - ... . Which of the following statements is true?

A) The numerators in these terms are the number of nearest neighbors in the crystal.
B) The denominators in these terms are related to the distances to the nearest neighbors.
C) The Madelung constant is the constant of proportionality in the expression for the net attractive potential energy of an ion in a crystal.
D) The value of $\alpha$ depends on the geometry of the crystal.
E) All of these are correct.

Question 10

If you want to produce a crystal from a liquid, you

A) cool the liquid slowly so that the molecules gradually lose their kinetic energy and thus form a large number of stable bonds.
B) cool the liquid rapidly to remove its internal energy before the molecules have a chance to form many bonds.
C) maintain the temperature of the liquid while increasing the pressure applied to the liquid.
D) maintain the temperature of the liquid while decreasing the pressure applied to the liquid.
E) warm the liquid while decreasing its pressure.

Question 11

Which of the following expressions correctly describes the dependence of the resistivity $\rho$ on the electric field E, the number of conduction electrons n_e, the electronic charge e, and the electron drift velocity v_d?

A)
B)
C)
D)
E)

Question 12

The crystalline structure known as body-centered-cubic

A) is characterized by the stacking of identical spheres.
B) occurs when each ion has eight nearest-neighbor ions of opposite charge.
C) corresponds to an alternating pattern of ions.
D) occurs when an ion of either kind has six nearest neighbors of the other kind.
E) None of these is correct.

Question 13

The classical microscopic model of electric conduction

A) successfully predicts Ohm's law.
B) relates the resistivity of conductors to the mean speed and the mean free path of the free electrons within the conductor.
C) fails to correctly predict the measured values of resistivity.
D) fails to account for the distinction between insulators, semiconductors, and conductors.
E) is described by all of these statements.

Question 14

Molecules in a gas

A) have little influence on one another.
B) have little influence on one another except during their frequent but brief collisions.
C) are close together and exert forces on one another that are comparable to the forces that bind atoms into molecules.
D) form temporary short-range bonds that continually break and re-form due to the thermal kinetic energy of the molecules.
E) are always arranged in a crystalline structure.

Question 15

The crystalline structure known as hexagonal close-packed

A) is characterized by the stacking of identical spheres.
B) occurs when every ion has eight nearest-neighbor ions of opposite charge.
C) corresponds to an alternating pattern of ions.
D) occurs when an ion of either kind has six nearest neighbors of the other kind.
E) None of these is correct.

Question 16

Molecules in a liquid

A) have little influence on one another.
B) have little influence on one another except during their frequent but brief collisions.
C) are close together and exert forces on one another that are comparable to the forces that bind atoms into molecules.
D) form temporary short-range bonds that continually break and re-form due to the thermal kinetic energy of the molecules.
E) are always arranged in a crystalline structure.

Question 17

The classical theory of conduction

A) fails because electrons are not classical particles.
B) does not take into account the scattering of electron waves by a lattice.
C) fails to correctly describe the collision of an electron with a lattice ion.
D) predicts a Maxwell-Boltzmann-like distribution of electron velocities.
E) is described by all of these.

Question 18

The classical free-electron theory of metals

A) correctly predicts the resistivity of a conductor but fails to predict the correct temperature dependence of the resistivity.
B) correctly predicts both the resistivity of a conductor and its temperature dependence.
C) incorrectly predicts the resistivity of a conductor but correctly predicts its temperature dependence.
D) incorrectly predicts both the resistivity of a conductor and its temperature dependence.
E) correctly predicts which materials are conductors, insulators, or semiconductors.

Question 19

The crystal structure of a substance can be determined using X-ray diffraction. It can also be determined using neutron scattering. What is the kinetic energy of a neutron that has a wavelength of 0.1 nm?

A) 0.14 eV
B) 0.082 eV
C) 0.034 eV
D) 0.23 eV
E) 0.38 eV

Question 20

The molecules in a solid

A) have little influence on one another.
B) have little influence on one another except during their frequent but brief collisions.
C) are close together and exert forces on one another that are comparable to the forces that bind atoms into molecules.
D) form temporary short-range bonds that continually break and re-form due to the thermal kinetic energy of the molecules.
E) are always arranged in a crystalline structure.

Question 21

Use the following to answer the next question.
The graph that represents the Fermi energy distribution function n(E) is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 22

Which of the following expressions correctly describes the dependence of the resistivity $\rho$ on the electronic mass, m_e, the number of conduction electrons n_e, the electronic charge e, the mean electron speed v_av, and the mean free path $\lambda$ ?

A)
B)
C)
D)
E)

Question 23

Use the following to answer the next question.
The graph that represents the Fermi factor F is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 24

The resistivity of copper at 20ºC is 1.7 *10^-8 $\Omega$ · m and the number of electrons per cubic centimeter is 8.47 * 10²². If you take the average speed of the electrons to be equal to their root-mean-square speed (at T = 300 K) of 1.17 *10⁵ m/s, it follows that their mean free path, $\lambda$ , must be

A) 1.23 nm
B) 1.86 nm
C) 2.35 nm
D) 2.89 nm
E) None of these is correct.

Question 25

The resistivity of iron at 20ºC is 10 *10^-8 $\sigma$ · m and the number of electrons per cubic centimeter is 17.0 *10²². If you take the average speed of the electrons to be equal to their root-mean-square speed (at T = 300 K) of 1.17 *10⁵ m/s, it follows that their mean free path, $\lambda$ , must be

A) 0.245 nm
B) 0.317 nm
C) 0.428 nm
D) 0.556 nm
E) None of these is correct.

Question 26

The classical free-electron theory of metals is inadequate in that it

A) assumes the average energy of the electrons to be 3kT/2.
B) assumes the energy distribution to be a Maxwell-Boltzmann distribution.
C) fails to incorporate the exclusion principle.
D) assumes the applicability of the equipartition theorem.
E) incorporates all of these.

Question 27

Which of the following statements is false?

A) The probability of an energy state being occupied is called the Fermi factor.
B) At temperatures greater than T = 0, some electrons occupy higher energy states because of thermal energy gained during collisions with the lattice.
C) An electron cannot move to a higher or lower energy state unless it is unoccupied.
D) Since the kinetic energy of lattice ions is of the order of kT, electrons cannot gain much more energy than kT in collisions with these ions.
E) None of these is false.

Question 28

If the energy levels are given as E_n = nE₁, by what factor is the total energy of seven fermions greater than seven bosons, both of which are in the ground state?

A) zero
B) 1
C) 1.5
D) 2.3
E) 2.9

Question 29

An 8-gauge copper wire (diameter = 3.665 mm) carries a current of 40 A. The current density of the wire is

A) 1.52 * 10⁷ A/m²
B) 3.79 * 10⁶ A/m²
C) 1.90 * 10⁶ A/m²
D) 1.21 * 10⁶ A/m²
E) None of these is correct.

Question 30

The resistivity of copper at 20ºC is 1.7* 10^-8 $\Omega$ · m. You have copper wire whose diameter is 2.00 mm and need a resistance of 1.00 $\Omega$ . How long would a piece of this wire need to be to provide this resistance?

A) 19.6 m
B) 49.1 m
C) 185 m
D) 317 m
E) 542 m

Question 31

Use the following to answer the next question.
The graph that represents the density of states g(E) in a Fermi gas is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 32

The average energy of a Fermi electron gas at T = 0 is

A) 3kT/2
B) E_F
C) kT
D) zero
E) 3E_F/5

Question 33

Use the following to answer the next question.

The Fermi energy in three dimensions at T = 0 is given by
E_F = 0.365 eV · nm² (N/V)^2/3
The Fermi energy for potassium is approximately

A) 11.7 eV
B) 3.24 eV
C) 5.53 eV
D) 2.11 eV
E) 9.46 eV

Question 34

Use the following to answer the next question.

The Fermi energy in three dimensions at T = 0 is given by
E_F = 0.365 eV · nm² (N/V)^2/3
The Fermi energy for aluminum is approximately

A) 11.7 eV
B) 3.24 eV
C) 5.53 eV
D) 2.11 eV
E) 9.46 eV

Question 35

Copper has a mass density of 8.93 g/cm³ and its molar mass is 63.55 g. If each copper atom contributes one free electron, the carrier density is

A) 8.46 * 10²⁸ m^-3
B) 3.12*10²⁸ m^-3
C) 4.15 *10²⁸ m^-3
D) 6.48 *10²⁸ m^-3
E) None of these is correct.

Question 36

The resistivity of nichrome at 20ºC is 100 *10^-8 $\Omega$ · m. You have nichrome wire whose diameter is 2.50 mm and need a resistance of 100 $\Omega$ 0. How long would a piece of this wire need to be to provide this resistance?

A) 196 m
B) 491 m
C) 543 m
D) 867 m
E) 1.96 km

Question 37

Use the following to answer the next question.

The Fermi energy in three dimensions at T = 0 is given by
E_F = 0.365 eV · nm² (N/V)^2/3
The Fermi energy for sodium is approximately

A) 11.7 eV
B) 3.24 eV
C) 5.53 eV
D) 2.11 eV
E) 9.46 eV

Question 38

Which of the following statements is false?

A) The behavior of free electrons in a metal is very different from the behavior of the molecules in an ordinary gas.
B) Ordinary gas molecules are described by the classical Maxwell-Boltzmann energy distribution function.
C) The main features of a Fermi electron gas can be understood by assuming an electron in a metal to be a particle in a box.
D) No two electrons in an atom can be in the same quantum state.
E) None of these is false.

Question 39

If the energy levels of a Fermi gas is given by E_n = nE₁, the total energy of seven fermions in the ground state is

A) 7E₁
B) 9E₁
C) 11E₁
D) 14E₁
E) 16E₁

Question 40

An 8-gauge copper wire (diameter = 3.665 mm) carries a current of 40 A. The drift velocity of the charge carriers is

A) 1.12 mm/s
B) 0.140 mm/s
C) 0.038 mm/s
D) 0.280 mm/s
E) None of these is correct.

Question 41

Reverse biasing of a pn junction tends to

A) increase the potential difference across a junction, thereby encouraging diffusion.
B) decrease the potential difference across a junction, thereby encouraging diffusion.
C) decrease the potential difference across a junction, thereby inhibiting diffusion.
D) increase the potential difference across a junction, thereby inhibiting diffusion.
E) None of these is correct.

Question 42

A semiconductor for which it is true that the major charge carriers are holes

A) is called an n-type semiconductor.
B) is called a p-type semiconductor.
C) accepts positive charges from filled valence bands.
D) is devoid of acceptor levels.
E) None of these is correct.

Question 43

Use the following to answer the next question.


-The speed of a conduction electron whose energy is equal to the Fermi energy E_F for magnesium is

A) 1.42 * 10⁶ m/s
B) 1.84 *10⁶ m/s
C) 1.21 * 10⁶ m/s
D) 2.03 * 10⁶ m/s
E) 1.58*10⁶ m/s

Question 44

Insulators are poor conductors of electricity because

A) there is a small energy gap between the valence band and the next higher band in which electrons can collect.
B) there is a large energy gap between the valence band and the next higher band in which electrons can collect.
C) the valence band has a few vacancies for electrons.
D) the valence band is only partly full.
E) None of these is correct.

Question 45

Use the following to answer the next question.

The Fermi temperature for aluminum is

A) 106,000 K
B) 135,700 K
C) 81,700 K
D) 53,400 K
E) 245,000 K

Question 46

A pn junction of germanium is connected through a resistor to a variable dc power supply as shown. Which of the following graphs best describes the current I in the circuit as the voltage V of the power supply is varied in the range of approximately -10 V to +10 V?

A) 1
B) 2
C) 3
D) 4
E) None of these is correct.

Question 47

One of the principal advantages of the transistor over the thermionic triode as a circuit element is that the transistor

A) is a linear element.
B) does not require a B battery.
C) does not require power to heat a filament.
D) has only two connections.
E) can be made from ordinary resistor materials.

Question 48

Use the following to answer the next question.


-You place sodium and copper in contact. The contact potential you would expect to measure is

A) 4.1 V
B) 2.3 V
C) 1.8 V
D) 1.13 * 10¹⁹ V
E) 6.4 V

Question 49

The graph that shows the current as a function of applied voltage across a pn junction is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 50

When a pnp junction transistor is used as an amplifier, a small signal in the _____ current results in a large signal in the _____ current.

A) collector; base
B) base; collector
C) emitter; base
D) emitter; collector

Question 51

Forward biasing of a pn junction

A) lowers the potential across a junction and increases the diffusion of holes and electrons.
B) raises the potential across a junction and increases the diffusion of holes and electrons.
C) raises the potential across a junction and decreases the diffusion of holes and electrons.
D) lowers the potential across a junction and decreases the diffusion of holes and electrons.
E) None of these is correct.

Question 52

Use the following to answer the next question.


-The speed of a conduction electron whose energy is equal to the Fermi energy E_F for aluminum is

A) 1.57* 10⁶ m/s
B) 1.84 * 10⁶ m/s
C) 1.21 * 10⁶ m/s
D) 2.03 * 10⁶ m/s
E) 3.14 * 10⁶ m/s

Question 53

A metal is a good conductor because the valence energy band for electrons is

A) empty.
B) completely full.
C) full, but there is only a small gap to a higher empty band.
D) partly full.
E) None of these is correct.

Question 54

Silicon is one of the Group IV semiconductors and has an energy gap of 1.12 eV. Generally only metals have highly shiny surface, yet as shown in the figure, silicon appears to reflect like a metal. This is because

A) silicon is a good semiconductor with a well defined energy gap.
B) visible light has energies in the range 2-3 eV which is much larger than the energy gap allowing electrons to be promoted from the valence band to the conduction band.
C) the surface of silicon is smooth making it reflect like a metal.
D) silicon can be grown in very high purity. It is the impurities that make a semiconductor dull looking.
E) None of these is correct.

Question 55

A semiconductor for which it is true that the major charge carriers are electrons

A) is called an n-type semiconductor.
B) is called a p-type semiconductor.
C) accepts positive charges from filled valence bands.
D) is devoid of acceptor levels.
E) None of these is correct.

Question 56

An alternating-current generator is producing a voltage with a frequency of 60 Hz. In the diagram, D is a solid-state diode made from a pn germanium junction. Which graph best describes the current I through the resistor R as a function of time?

A) 1
B) 2
C) 3
D) 4
E) None of these is correct.

Question 57

The free-electron model of metals gives a good account of electrical conduction if

A) the classical mean speed v_av is replaced by the Fermi speed u_F.
B) the collisions between electrons and the lattice ions are interpreted in terms of the scattering of electron waves.
C) the collisions between electrons and the lattice ions are interpreted in terms of the scattering of hard spheres.
D) the classical mean speed v_av is retained in the model and the collisions between electrons and the lattice ions are interpreted in terms of the scattering of electron waves.
E) the classical mean speed v_av is replaced by the Fermi speed u_F and the collisions between electrons and the lattice ions are interpreted in terms of the scattering of electron waves.

Question 58

When light strikes the p-type semiconductor in a pn junction solar cell,

A) only free electrons are created.
B) only positive holes are created.
C) both electrons and holes are created.
D) positive protons are created.
E) None of these is correct.

Question 59

If you increase the temperature of a semiconductor, you can expect to measure

A) no change in its resistance.
B) an increase in its resistance.
C) an increase in the potential difference across it.
D) a decrease in the potential difference across it.
E) no change in the potential difference across it.

Question 60

Insulated electrical wires often have a maximum voltage rating, i.e., the insulation on the wire is safe up to the rated voltage. The reason why the insulator is not safe at higher voltage is because

A) there is a possibility of electric breakdown, which will cause electrons in the valence band of the insulator to be promoted to the conduction band making the insulator a conductor.
B) the wire will then carry more current, making the wire unsafe.
C) most households only have 240 V maximum so there is no point having a higher voltage rating.
D) it is the manufacturer's way of preventing users from transmitting higher voltage.
E) None of these is correct.

Question 61

The graph that shows the current as a function of applied voltage across a tunnel diode is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 62

Use the following to answer the next question.

At what energy is the Fermi factor equal to 0.1 for magnesium at T = 300 K?

A) 7.08 eV
B) 7.17 eV
C) 7.05 eV
D) 7.02 eV
E) 7.18 eV

Question 63

The effect known as avalanche breakdown occurs at point

A) 1
B) 2
C) 3
D) 4
E) 5

Question 64

The frequency of the current observed at a Josephson junction is 345 MHz. The voltage applied to the junction to produce this current was

A) 1.43 µV
B) 1.43 V
C) 0.715 µV
D) 0.715 mV
E) 1.28 µV

Question 65

According to the BCS theory,

A) electrons in a superconductor are coupled in pairs at low temperatures.
B) electrons in a Cooper pair have equal and opposite spins.
C) electrons in a Cooper pair act as a single particle with zero spin.
D) any number of Cooper pairs may be in the same quantum state with the same energy.
E) All of these are true.

Question 66

The probability that an energy state in copper 0.05 eV above the Fermi energy is occupied at T = 300 K is

A) 1.26%
B) 2.52%
C) 3.78%
D) 12.6%
E) 14.5%

Question 67

The graph that correctly shows the dependence of resistance on temperature for mercury is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 68

The frequency of the current observed at a Josephson junction is 976 MHz. The voltage applied to the junction to produce this current was

A) 202 µV
B) 1.43 V
C) 1.43 µV
D) 2.02 µV
E) 1.28 µV

Question 69

Use the following to answer the next question.

At what energy is the Fermi factor equal to 0.2 for copper at T = 300 K?

A) 7.08 eV
B) 7.00 eV
C) 7.06 eV
D) 7.02 eV
E) 7.18 eV

Question 70

If you apply a voltage of 3 µV to a Josephson junction, you can expect to measure a frequency of

A) 145 MHz
B) 1450 MHz
C) 346 kHz
D) 346 Hz
E) 527 Mhz

Question 71

The probability that an energy state in magnesium 0.2 eV above the Fermi energy is occupied at T = 300 K is

A) 0.0365%
B) 0.0404%
C) 0.0438%
D) 0.0457%
E) 0.0496%

Question 72

The probability that an energy state in copper 0.2 eV below the Fermi energy is occupied at T = 300 K is

A) 5.52%
B) 20.6%
C) 47.1%
D) 83.9%
E) 99.9%

Question 73

A Josephson junction consists of

A) two superconductors separated by a thin insulating barrier.
B) a superconductor sandwiched between two insulating barriers.
C) two different superconductors in contact with each other.
D) a superconductor in contact with a conductor warmer than 4.2 K.
E) None of these is correct.

Question 74

The probability that an energy state in copper 0.2 eV above the Fermi energy is occupied at T = 300 K is

A) 0.0365%
B) 0.0404%
C) 0.0438%
D) 0.0457%
E) 0.0496%

Question 75

The probability that an energy state in magnesium 0.05 eV above the Fermi energy is occupied at T = 300 K is

A) 1.26%
B) 2.52%
C) 3.78%
D) 12.6%
E) 14.5%

Question 76

A Josephson junction is a junction of

A) two ordinary conductors.
B) an ordinary conductor and a superconductor.
C) an insulator and a superconductor.
D) two superconductors.
E) an insulator and an ordinary conductor.

Question 77

The symbol for an npn transistor is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 78

Metallic compounds have been found to exhibit superconductivity at temperatures as high as

A) 273 K
B) 164 K
C) 176 K
D) 188 K
E) 243 K

Question 79

If you apply a voltage of 0.3 µV to a Josephson junction, you can expect to measure a frequency of approximately

A) 327 MHz
B) 484 Hz
C) 145 kHz
D) 484 MHz
E) 145 MHz

Question 80

The symbol for a pnp transistor is

A) 1
B) 2
C) 3
D) 4
E) 5