?Bonding in Crystalline SolidsAn electron is confined to a metal cube of l = 0.8 cm on

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

Types of Molecular Bonds For the following cases, what type of bonding is expected? (a) KCl molecule; (b) \(\mathrm{N}_{2}\) molecule. Text Transcription: N_2

Types of Molecular Bonds Describe three steps to ionic bonding.

Types of Molecular Bonds What prevents a positive and negative ion from having a zero separation?

Types of Molecular Bonds For the \(\mathrm{H}_{2}\) molecule, why must the spins the electron spins be antiparallel? Text Transcription: H_2

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

Molecular Spectra 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? Text Transcription: Delta E

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

Bonding in Crystalline Solids Why is the equilibrium separation distance between \(\mathrm{K}^{+} \text {and } \mathrm{Cl}^{-}\) different for a diatomic molecule than for solid KC1? Text Transcription: K^+ and Cl^-

Bonding in Crystalline Solids Describe the difference between a face-centered cubic structure (FCC) and a body-centered cubic structure (BCC)

Bonding in Crystalline Solids In sodium chloride, how many \(\mathrm{Cl}^{-}\) atoms are "nearest neighbors" of \(\mathrm{Na}^{+}\)? How many \(\mathrm{Na}^{+}\) atoms are "nearest neighbors" of \(\mathrm{Cl}^{-}\)? Text Transcription: Cl^- Na^+

Bonding in Crystalline Solids In cesium iodide, how many \(\mathrm{Cl}^{-}\) atoms are "nearest neighbors" of \(\mathrm{Cs}^{+}\)? How many \(\mathrm{Cs}^{+}\) atoms are “nearest neighbors” of \(\mathrm{Cl}^{-}\)? Text Transcription: Cl^- Cs^+

Types of Molecular Bonds The electron affinity of Cl is 3.89 eV and the ionization energy of K is 4.34 eV. Use the preceding problem to find the dissociation energy. (Neglect the energy of repulsion.)

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

Bonding in Crystalline Solids 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)? Text Transcription: r_0=0.282 nm r_0^3 Na^+

Free Electron Model of Metals Why does the Fermi energy \(\left(E_{\mathrm{F}}\right)\) ions increase with the number of electrons in a metal? Text Transcription: E_F

Free Electron Model of Metals If the electron number density (N/V) of a metal increases by a factor 8, what happens to the Fermi energy \(\left(E_{\mathrm{F}}\right)\)? Text Transcription: E_F

Free Electron Model of Metals Why does the horizontal line in the graph in Figure 9.12 suddenly stop at the Fermi energy?

Free Electron Model of Metals Why does the graph in Figure 9.12 increase gradually from the origin?

Free Electron Model of Metals Why are the sharp transitions at the Fermi energy “smoothed out” by increasing the temperature?

Types of Molecular Bonds 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? Text Transcription: 1 s^2 2 s^2 2 p^2

Types of Molecular Bonds 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. Text Transcription: r_0=0.279 nm

Molecular Spectra In a physics lab, you measure the vibrational rotational spectrum of HCl. The estimated separation between absorption peaks is \(\Delta f \approx 5.5 \times 10^{11} \mathrm{~Hz}\). (a) What is the moment of inertia (I)? (b) What is the energy of vibration for the molecule? Text Transcription: Delta f approx 5.5 times 10^11 Hz

Molecular Spectra For the preceding problem, find the equilibrium separation of the H and Cl atoms. Compare this with the actual value.

Molecular Spectra The separation between oxygen atoms in an \(\mathrm{O}_{2}\) molecule is about 0.121 nm. Determine the characteristic energy of rotation in eV. Text Transcription: O_2

Molecular Spectra 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. Text Transcription: N_2 2.48 times 10^-4 eV

Molecular Spectra The characteristic energy for 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 Cl atoms. Text Transcription: 1.4 times 10^-5 eV mu

Molecular Spectra 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 and l = 2 state? Text Transcription: F_2

Molecular Spectra In a physics lab, you measure the vibrational rotational 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? Text Transcription: Delta d approx 5.35 times 10^10 HZ f_0=8.75 times 10^12 Hz

Bonding in Crystalline Solids The CsI 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” \(\mathrm{I}^{+}\) ion? Text Transcription: r_0=0.46 nm Cs^+ r_0^3 I^+

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

Bonding in Crystalline Solids The measured density of a NaF crystal is \(2.558 \mathrm{~g} / \mathrm{cm}^{3}\). What is the equilibrium separate distance of \(\mathrm{Na}^{+} \text {and } \mathrm{Fl}^{-}\) ion? Text Transcription: 2.558 g/cm^3 Na^+ and FI^-

Bonding in Crystalline Solids What value of the repulsion constant, n, gives the measured dissociation energy of 221 kcal/ mole for NaF?

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

Bonding in Crystalline Solids The measured density of a KCl crystal is \(1.984 \mathrm{~g} / \mathrm{cm}^{2}\). What is the equilibrium separation distance of \(\mathrm{K}^{+} \text {and } \mathrm{Cl}^{-}\) ion? Text Transcription: 1.984 g/cm^2 K^+ CI^-

Bonding in Crystalline Solids What value of the repulsion constant, n, gives the measured dissociation energy of 171 kcal/ mol for KCl?

Bonding in Crystalline Solids The measured density of a CsCl crystal is \(3.988 \mathrm{~g} / \mathrm{cm}^{3}\). What is the equilibrium separate distance of \(\mathrm{Cs}^{+} \text {and } \mathrm{Cl}^{-}\) ions? Text Transcription: 3.988 g/cm^3 Cs^+ and CI^-

Bonding in Crystalline Solids 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. Text Transcription: n_x=n_y=n_z=4 n_x=n_y=n_z=400

Bonding in Crystalline Solids An electron is confined to a metal cube of l = 0.8 cm on each side. Determine the density of states at (a) E = 0.80 eV; (b) E =2.2 eV; and (c) E= 5.0eV.

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 eV and the ionization energy of K is 4.34 eV. Determine dissociation energy. (Neglect the energy of repulsion.) Text Transcription: r_0=0.255 nm

For the preceding problem, sketch the potential energy versus separation graph for the bonding of \(\mathrm{K}^{+} \text {and } \mathrm{Fl}^{-}\) ion. (a) Label the graph with the energy required to transfer an electron from K to Fl. (b) Label the graph with the dissociation energy. Text Transcription: K^+ and FI^-

The separation between hydrogen atoms in a \(\mathrm{H}_{2}\) molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV. Text Transcription: H_2

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. Text Transcription: CI_2 2.95 times 10^-5 eV

Determine the lowest three rotational energy levels of \(\mathrm{H}_{2}\). Text Transcription: H_2

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

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

Why is bonding in \(\mathrm{H}_{2}{ }^{+}\) favorable? Express your answer in terms of the symmetry of the electron wave function. Text Transcription: H_2^+

Astronomers claim to find evidence of \(\mathrm{He}_{2}\) from light spectra of a distant star. Do you believe them? Text Transcription: He_2

For an electron in a three-dimensional metal, show that the average energy is given by \(\bar{E}=\frac{1}{N} \int_{0}^{E_{\mathrm{F}}} E g(E) d E=\frac{3}{5} E_{\mathrm{F}}\) WhereNis the total number electrons in the metal. Text Transcription: bar E=1/N Int_0^E_F Eg(E)d E=3/5 E_F.

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

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

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

Band Theory of Solids Why are some materials very good conductors and others very poor conductors?

Band Theory of Solids Why are some materials semiconductors?

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

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

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

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

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

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

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

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

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

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

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

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

Superconductivity Describe two main features of a superconductor.

Superconductivity How does BCS theory explain superconductivity?

Superconductivity What is the Meissner effect?

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

Free Electron Model of Metals What value of energy corresponds to a density of states of \(1.10 \times 10^{24} \mathrm{eV}^{-1}\)? Text Transcription: 1.10 times 10^24 eV^-1

Free Electron Model of Metals Compare the density of states at 2.5 eV and 0.25 eV.

Free Electron Model of Metals Consider a cube of copper with edges 1.50 mm long. Estimate the number of electron quantum states in this cube whose energies are in the range 3.75 to 3.77 eV.

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

Free Electron Model of Metals Determine the Fermi energy and temperature for copper at T = 0 K.

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

Band Theory of Solids What is the main difference between an insulator and a semiconductor?

Band Theory of Solids 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 eV?

Band Theory of Solids 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? Text Transcription: lambda=0.300 nm

Semiconductors and Doping An experiment is performed to demonstrate the Hall effect. A thin rectangular strip of semiconductor with width 10 cm and length 30 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?

Semiconductors and Doping 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 mA. What is the number density of the charge carriers? Text Transcription: 1 mm^2

Semiconductors and Doping A current-carrying copper wire with cross section \(\sigma=2 \mathrm{~mm}^{2}\) has a drift velocity of 0.02 cm/s. Find the total current running through the wire. Text Transcription: sigma=2 mm^2

Semiconductors and Doping The Hall effect is demonstrated in the laboratory. A thin rectangular strip of semiconductor with width 5 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 V and the measured drift velocity is 50 m/s. What is the magnetic field? Text Transcription: 2 mm^2

Semiconductor Devices Show that for V less than zero, \(I_{\text {net }} \approx-I_{0}\). Text Transcription: I_net approx -I_0

Semiconductor Devices 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 \(6.78 \times 10^{-1} \mathrm{~A}\) moving through it. What bias voltage is being applied if the temperature is 300 K? Text Transcription: 1.44 times 10^-8 A 6.78 times 10^-1 A

Semiconductor Devices The collector current of a transistor is 3.4 A for a base current of 4.2 mA. What is the current gain?

Semiconductor Devices 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 V? Text Transcription: 8.76 times 10^-1 A 4.41 times 10^-8 A

Semiconductor Devices The base current of a transistor is 4.4 A, and its current gain 1126. What is the collector current?

Superconductivity At what temperature, in terms of \(T_{C}\), is the critical field of a superconductor one-half its value at T = 0 K. Text Transcription: T_C

Superconductivity What is the critical magnetic field for lead at T = 2.8 K.

Superconductivity A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 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 have when the superconductivity of the wire is destroyed? Text Transcription: 50-Omega

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

Show that the moment of inertia of a diatomic molecule is \(I=\mu r_{0}^{2}\), where \(\mu\) is the reduced mass, and \(r_{0}\) is the distance between the masses. Text Transcription: I=mu r_0^2 mu r_0

Show that the average energy of an electron in a one-dimensional metal is related to the Fermi energy by \(\bar{E}=\frac{1}{2} E_{\mathrm{F}}\). Text Transcription: bar E=1/2 E_F

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

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

Transition in the rotation spectrum are observed at ordinary room temperature (T = 300 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.

Determine the Fermi energies for (a) Mg, (b) Na, and (c) Zn.

Find the average energy of an electron in a Zn wire.

What value of the repulsion constant, n, gives the measured dissociation energy of 158 kcal/ mol for CsCl?

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