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.

Accepted Answer

Rapid cooling of the liquid prevents the molecules from forming strong bonds and arranges them in a disordered manner, resulting in the formation of an amorphous solid. Slow cooling (Option A) allows the molecules to form more organized bonds, leading to the formation of crystalline solids. Maintaining temperature while increasing pressure (Option C) or while decreasing pressure (Option D) can lead to changes in the state of matter, but not necessarily the formation of an amorphous solid. Warming the liquid while decreasing its pressure (Option E) would result in the conversion of the liquid into a gas.

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

Accepted Answer

D

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

Accepted Answer

The equilibrium spacing can be calculated using the formula:

r = (ρM/NA)^(1/3)

where
ρ = density = 2.48 g/cm³
M = molar mass of KF = 58.098 g/mol
NA = Avogadro's number = 6.022 × 10²³ mol⁻¹

Substituting the values, we get:

r = (2.48 g/cm³ × 58.098 g/mol / (6.022 × 10²³ mol⁻¹))^(1/3)
  = 4.413 × 10⁻² cm = 0.269 nm

Therefore, the equilibrium spacing between the K⁺ and F⁻ ions in KF crystal is 0.269 nm. The correct choice is (C).

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.

Accepted Answer

The classical free-electron theory of metals includes all these concepts: a metal's structure as a three-dimensional array of atoms or ions, the presence of free electrons moving throughout the metal, the maintenance of thermal equilibrium through electron collisions with lattice ions, and the behavior of electrons moving similarly to gas molecules in a container in the absence of an electric field.

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

Accepted Answer

The answer of KF has a face-centered-cubic lattice structure and...

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.

Accepted Answer

The answer of The crystalline structure known as face-centered-cubic
A) is...

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

Accepted Answer

In a body-centered-cubic unit cell, there are two types of atoms: one atom at each of the eight corners of the unit cell and one atom at the center of the unit cell. The eight corner atoms only contribute 1/8 of their volume to the unit cell, since they are shared with eight neighboring unit cells. The center atom, however, contributes its full volume to the unit cell. Therefore, the fraction of volume occupied by the atoms in a body-centered-cubic unit cell can be calculated as:

(1 center atom volume + 8 corner atom volumes) / unit cell volume
= (1 + 8(1/8)) / 1
= 2 / 1
= 2

So the atoms occupy 2/3 or 0.666... of the unit cell volume. Rounded to two decimal places, this is 0.68.

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

Accepted Answer

In a face-centered cubic (FCC) unit cell, atoms are located at each of the corners and the centers of all the faces. Each corner atom is shared among eight unit cells and each face-centered atom is shared between two, so the effective number of atoms per unit cell is 4. The packing efficiency, or the fraction of volume occupied by the atoms, in an FCC structure is 0.74, assuming the atoms are hard spheres.

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.

Accepted Answer

The Madelung constant is indeed related to the geometry of the crystal (D), involves a series where the terms can be related to the number of nearest neighbors (A) and their distances (B), and it acts as a constant of proportionality for the net attractive potential energy of an ion in a crystal lattice (C). Therefore, all provided statements 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.

Accepted Answer

Cooling the liquid slowly allows the molecules to lose their kinetic energy gradually, meaning they have more time to form stable bonds and arrange themselves in a crystal lattice structure. Rapid cooling (option B) would not provide this opportunity, and increasing or decreasing pressure (options C and D) would not necessarily lead to crystal formation. Warming the liquid (option E) would actually reduce the chances of crystal formation as the molecules would gain more energy and move around more, making it harder for them to form stable bonds with each other.

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)

Accepted Answer

The answer of Which of the following expressions correctly describes...

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.

Accepted Answer

Body-centered-cubic structure occurs when each ion has eight nearest-neighbor ions of opposite charge.

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.

Accepted Answer

The classical microscopic model of electric conduction does indeed predict Ohm's law, relates resistivity to mean speed and mean free path of electrons, but it also fails in accurately predicting resistivity values and distinguishing between insulators, semiconductors, and conductors, making all the statements correct.

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.

Accepted Answer

Molecules in a gas have little influence on one another except during their frequent but brief collisions. This is because the particles in a gas are constantly in motion and far apart from one another, so they don't exert significant forces on each other at a distance. However, when they collide, they do interact and exchange energy, which is how gases transfer heat and momentum.

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.

Accepted Answer

The hexagonal close-packed structure is characterized by the stacking of identical spheres in a close-packed pattern.

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.

Accepted Answer

Molecules in a liquid form temporary short-range bonds that continually break and reform due to the thermal kinetic energy of the molecules. These intermolecular forces are strong enough to keep the molecules in close proximity and moving collectively, but weak enough to allow the molecules to move past one another and flow. Therefore, option D is the best choice.

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.

Accepted Answer

The classical theory of conduction fails for several reasons: it does not account for the quantum nature of electrons, neglects the wave-like behavior of electrons and their scattering by the lattice, inaccurately describes electron-lattice ion collisions, and incorrectly applies a Maxwell-Boltzmann distribution to electron velocities.

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.

Accepted Answer

The answer of The classical free-electron theory of metals
A) correctly...

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

Accepted Answer

The kinetic energy of a neutron with a wavelength of 0.1 nm can be calculated using the de Broglie equation: λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the neutron. Rearranging this equation gives: p = h/λ. The kinetic energy of the neutron can then be calculated using the equation: K = p^2/2m, where m is the mass of the neutron.

Substituting in the values gives:

p = h/λ = (6.626 x 10^-34 J.s)/(0.1 x 10^-9 m) = 6.626 x 10^-25 kg.m/s
K = p^2/2m = (6.626 x 10^-25 kg.m/s)^2/(2 x 1.675 x 10^-27 kg) = 1.160 x 10^-19 J

Converting Joules to electron volts gives:

1.160 x 10^-19 J ÷ 1.602 x 10^-19 J/eV = 0.723 eV

Therefore, the answer is B) 0.082 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.

Accepted Answer

The close proximity of the molecules in a solid allows for intermolecular forces to be present, which are comparable in strength to the forces that hold atoms together in molecules. This is what gives solids their rigidity and resistance to deformation.

Quiz 18: Solids and the Theory of Conduction

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

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

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

In the classical free-electron theory of metals,

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

The crystalline structure known as face-centered-cubic

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

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

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?

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

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?

The crystalline structure known as body-centered-cubic

The classical microscopic model of electric conduction

Molecules in a gas

The crystalline structure known as hexagonal close-packed

Molecules in a liquid

The classical theory of conduction

The classical free-electron theory of metals

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?

The molecules in a solid