(II) The “characteristic rotational energy,” h2/2l, for N2

Problem 4Q Although the molecule is not stable, the ion is. Explain, using the Pauli exclusion principle.

The energy of a molecule can be divided into four categories. What are they?

Problem 6Q Would you expect the molecule H2+ to be stable? If so, where would the single electron spend most of its time?

Problem 6P I) Show that the quantity h2/l has units of energy.

Problem 5P (III) (a) Apply reasoning similar to that in the text for the S =0 and S =1 states in the formation of the H2 molecule to show why the molecule is not formed. (b) Explain why the He2+ molecular ion could form. (Experiment shows it has a binding energy of 3.1 eV at r0 = 0.11 nm.)

(II) The so-called "characteristic rotational energy," \(\hbar^2 / 2 I\), for \(\mathrm{N}_2\) is \(2.48 \times 10^{-4} \mathrm{eV}\). Calculate the \(\mathrm{N}_2\) bond length.

Explain why the carbon atom (Z = 6) usually forms four bonds with hydrogen-like atoms.

If conduction electrons are free to roam about in a metal, why don't they leave the metal entirely?

Problem 9Q Explain why the resistivity of metals increases with increasing temperature whereas the resistivity of semiconductors may decrease with increasing temperature.

Problem 1P (I) Estimate the binding energy of a KCI molecule by calculating the electrostatic potential energy when the K+ and Cl- ions are at their stable separation of 0.28 nm. Assume each has a charge of magnitude l.Oe.

Problem 2P (II) The measured binding energy of KCI is 4.43 eV. From the result of Problem 1, estimate the contribution to the binding energy of the repelling electron clouds at the equilibrium distance rO =0.28 nm

What type of bond would you expect for (a) \(\mathrm N_2\) the molecule, (b) the HCI molecule, (c) Fe atoms in a solid?

Describe how the molecule \(\mathrm{CaCI_2}\) could be formed.

Problem 3P (Ill) Estimate the binding energy of the H2 molecule, assuming the two H nuclei are 0.074 nm apart and the two electrons spend 33% of their time midway between them.

Problem 3Q Does H2 the molecule have a permanent dipole moment? Does 02 Does H20? Explain.

Problem 4P (II) Binding energies are often measured experimentally in kcal per mole, and then the binding energy in eV per molecule is calculated from that result. What is the conversion factor in going from kcal per mole to eV per molecule? What is the binding energy of KCI (=4.43 eV) in kcal per mole?

Figure 29–33 shows a “bridge-type” full-wave rectifier. Explain how the current is rectified and how current flows during each half cycle.

(III) (a) Use the curve of Fig. to estimate the stiffness constant for the \(\mathrm H_2\) molecule. (Recall that \(\mathrm{PE}=\frac{1}{2}kx^2\).) Then estimate the fundamental wavelength for vibrational transitions using the classical formula (Chapter 11 ), but use only \(\frac{1}{2}\) the mass of an atom (because both atoms move). ________________ Equation Transcription: Text Transcription: H_2 PE=frac{1}{2}kx^2 frac{1}{2}

Problem 11Q Compare the resistance of a pn junction diode connected in forward bias to its resistance when connected in reverse bias.

Problem 12P (II) The spacing between "nearest neighbor" Na and Cl ions in a NaCI crystal is 0.24 nm. What is the spacing between two nearest neighbor Na ions?

Problem 12Q Explain how a transistor can be used as a switch.

(II) Common salt, \(\mathrm{NaCl}\), has a density of \(2.165 \mathrm{~g} / \mathrm{cm}^3\). The molecular weight of \(\mathrm{NaCl}\) is 58.44. Estimate the distance between nearest neighbor \(\mathrm{Na}\) and \(\mathrm{Cl}\) ions. [Hint: each ion can be considered to have one "cube" or "cell" of side s (our unknown) extending out from it.]

Problem 14P (II) Repeat Problem 14 for KCI whose density is 1.99 g/cm3.

Problem 16Q A transistor can amplify an electronic signal, meaning it can increase the power of an input signal. Where does it get the energy to increase the power?

(II) Repeat Problem 13 for KCl whose density is \(\mathrm {1.99\ g/cm^3}\). ________________ Equation Transcription: Text Transcription: 1.99 g/cm^3

Problem 17Q A silicon semiconductor is doped with phosphorus. Will these atoms be donors or acceptors? What type of semiconductor will this be?

Problem 18P (II) The energy gap between valence and conduction bands in germanium is 0.72 eV. What range of wavelengths can a photon have to excite an electron from the top of the valence band into the conduction band?

Problem 18P (II) The energy gap between valence and conduction bands in germanium is 0.72 eV. What range of wavelengths can a photon have to excite an electron from the top of the valence band into the conduction band?

Problem 18Q Do diodes and transistors obey Ohm’s law? Explain.

Problem 19Q Can a diode be used to amplify a signal? Explain.

When EM radiation is incident on diamond, it is found that light with wavelengths shorter than \(226 \mathrm{~nm}\) will cause the diamond to conduct. What is the energy gap between the valence band and the conduction band for diamond?

A TV remote control emits IR light. If the detector on theTV set is not to react to visible light, could it make use of silicon as a “window" with its energy gap \(E_g = 1.12 \mathrm {eV}\)?What is the shortest-wavelength light that can strike silicon without causing electrons to jump from the valence band to the conduction band?

For an arsenic donor atom in a doped silicon semiconductor, assume that the "extra" electron moves in a Bohr orbit about the arsenic ion. For this electron in the ground state, take into account the dielectric constant K=12 of the Si lattice (which represents the weakening of the Coulomb force due to all the other atoms or ions in the lattice), and estimate (a) the binding energy, and (b) the orbit radius for this extra electron. [Hint: substitute \(\epsilon=K \epsilon_0\) in Coulomb's law; see Section 17-8.]

Problem 40GP Most of the Sun’s radiation has wavelengths shorter thanl 100 nm. For a solar cell to absorb all this, what energy gap ought the material have?

Problem 42GP Green and blue LEDs became available many years afterred LEDs were first developed. Approximately whatenergy gaps would you expect to find in green (525 nm)and in blue (465 nm)LEDs?

Problem 8P (a) Calculate the characteristic rotational energy, ?2/2I, for the O2 molecule whose bond length is 0.121 nm. (b) What are the energy and wavelength of photons emitted in a L = 2 to L = 1 transition?

(II) The equilibrium separation of atoms in the \(\mathrm H_2\) molecule is (Fig. Calculate the energies and wavelengths of photons for the rotational transitions \((a)\ L=1\) to \(L=0\), \((b)\ L=2\) to \(L=1\), and \((c)\ L=3\) to \(L=2\). ________________ Equation Transcription: Text Transcription: H_2 (a) L=1 L=0 (b) L=2 L=1 (c) L=3 L=2

Problem 10P Calculate the bond length for the NaCl molecule given that three successive wavelengths for rotational transitions are 23.1 mm, 11.6 mm, and 7.71 mm.

Describe how a pnp transistor can operate as an amplifier.

Explain on the basis of energy bands why the sodium chloride crystal is a good insulator. [Hint: consider the shells of \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\) ions.]

Problem 16P A semiconductor, bombarded with light of slowly increased frequency, begins to conduct when the wavelength of light is 640 nm. Estimate the size of the energy gap Eg.

(II) Calculate the longest-wavelength photon that can cause an electron in silicon \(\left(E_{\mathrm{g}}=1.1 \mathrm{eV}\right)\) to jump from the valence band to the conduction band.

Problem 19P The energy gap Eg in germanium is 0.72 eV. When used as a photon detector, roughly how many electrons can be made to jump from the valence to the conduction band by the passage of a 760-keV photon that loses all its energy in this fashion?

Problem 20P We saw that there are 2N possible electron states in the 3s band of Na, where N is the total number of atoms. How many possible electron states are there in the (a) 2s band, (b) 2p band, and (c) 3p band? (d) State a general formula for the total number of possible states in any given electron band.

Problem 21P Suppose that a silicon semiconductor is doped with phosphorus so that one silicon atom in 106 is replaced by a phosphorus atom. Assuming that the “extra” electron in every phosphorus atom is donated to the conduction band, by what factor is the density of conduction electrons increased? The density of silicon is 2330 kg/m3, and the density of conduction electrons in pure silicon is about 1016 m?3 at room temperature.

Problem 22P At what wavelength will an LED radiate if made from a material with an energy gap Eg = 1.4 eV?

Problem 23P If an LED emits light of wavelength ? = 650 nm, what is the energy gap (in eV) between valence and conduction bands?

(II) A silicon diode, whose current-voltage characteristics are given in Fig. , is connected in series with a battery and a \(\text {960-}\Omega\) resistor. What battery voltage is needed to produce a 12-mA current? ________________ Equation Transcription: Text Transcription: 960-Ohms

(II) Suppose that the diode of Fig. is connected in series to a \(\text {100-}\Omega\) resistor and a 2.0-V battery. What current flows in the circuit? [Hint: draw a line on Fig. 29-28 representing the current in the resistor as a function of the voltage across the diode. The intersection of this line with the characteristic curve will give the answer.] ________________ Equation Transcription: Text Transcription: 100-Ohms

(II) Sketch the resistance as a function of current, for \(V>0\), for the diode shown in Fig. 29-28.

(II) An ac voltage of 120 Vrms is to be rectified. Estimate very roughly the average current in the output resistor \(R\ (25\ \mathrm {k}\Omega)\) for (a) a half-wave rectifier (Fig. 29-29), an (b) a full-wave rectifier (Fig. 29-30) without capacitor.

(III) A silicon diode passes significant current only if the forward-bias voltage exceeds about 0.6 V. Make a rough estimate of the average current in the output resistor of (a) a half-wave rectifier (Fig. 29-29), and a full-wave rectifier (Fig. 29-30) without a capacitor. Assume that \(R=150\ \Omega\) in each case and that the ac voltage is 12.0 V rms in each case. ________________ Equation Transcription: Text Transcription: R=150 Ohms .

(III) A 120-V rms 60-Hz voltage is to be rectified with a full-wave rectifier (Fig. 29-30), where \(R=21\ \mathrm k\Omega\), and \(C=25\ \mu \mathrm F\). (a) Make a rough estimate of the average current. (b) What happens if \(C=0.10\ \mu \mathrm F\)? [Hint: see Section ] ________________ Equation Transcription: Text Transcription: R=21 k{Ohms} C=25 muF C=0.10 muF

(II) From Fig. 29-32, write an equation for the relationship between the base current \((I_\mathrm B)\), the collector current \((I_\mathrm C)\), and the emitter current \((I_\mathrm E)\), not labelled in the figure.) ________________ Equation Transcription: Text Transcription: (I_B) (I_C) (I_E)

The average translational kinetic energy of an atom or molecule is about \(\mathrm {\overline{KE}}=\frac{3}{2}kT\) (Eq. 13-8), where \(k=1.38 \times 10^{-23}\ \mathrm {J/K}\) is Boltzmann's constant. At what temperature will \(\overline {\mathrm {KE}}\) be on the order of the bond energy (and hence the bond likely to be broken by thermal motion) for a covalent bond of binding energy 4.5 eV (say \(H_2\)), and a "weak" hydrogen bond of binding energy 0.15 eV? ________________ Equation Transcription: Text Transcription: overline{KE}=frac{3}{2}kT k=1.38x10^-23 J/K overline{KE} H_2

Problem 31GP Estimate the binding energy of the H2 molecule by calculating the difference in kinetic energy of the electrons between when they are in separate atoms and when they are in the molecule, using the uncertainty principle. Take ?x for the electrons in the separated atoms to be the radius of the first Bohr orbit, 0.053 nm, and for the molecule take ?x to be the separation of the nuclei, 0.074 nm. [Hint: let p ? ?px.]

Problem 33GP In the ionic salt KF, the separation distance between ions is about 0.27 nm. (a) Estimate the electrostatic potential energy between the ions assuming them to be point charges (magnitude 1e). (b) It is known that F releases 4.07 eV of energy when it “grabs” an electron, and 4.34 eV is required to ionize K. Find the binding energy of KF relative to free K and F atoms, neglecting the energy of repulsion.

Consider a monoatomic solid with a weakly bound cubic lattice, with each atom connected to six neighbors, each bond having a binding energy of \(3.9 \times 10^{-3}\) eV. When this solid melts, its latent heat of fusion goes directly into breaking the bonds between the atoms. Estimate the latent heat of fusion for this solid, in J/kg. [Hint: show that in a simple cubic lattice (Fig. 29–34), there are three times as many bonds as there are atoms, when the number of atoms is large.] Equation Transcription: Text Transcription: 3.91x0^-3 J/kg

Problem 35GP For O2 with a bond length of 0.121 nm, what is the moment of inertia about the center of mass?

Problem 36GP A diatomic molecule is found to have an activation energy of 1.4 eV. When the molecule is disassociated, 1.6 eV of energy is released. Draw a potential energy curve for this molecule.

Problem 41GP For a certain semiconductor, the longest wavelength radiation that can be absorbed is 1.92 mm. What is the energy gap in this semiconductor?

A zener diode voltage regulator is shown in Fig. 29–35. Suppose that \(R=1.80\ \mathrm k \Omega\) and that the diode breaks down at a reverse voltage of 130 V. (The current increases rapidly at this point, as shown on the far left of Fig. 29–28 at a voltage of ?12 V on that diagram.) The diode is rated at a maximum current of 120 mA. (a) If \(R_{\text {load}}=15.0\ \mathrm k \Omega\), over what range of supply voltages will the circuit maintain the output voltage at 130 V? (b) If the supply voltage is 200 V, over what range of load resistance will the voltage be regulated?