What type of bond would you e smu td)7a)w:axpect for
(a) the $N_2$ molecule,
(b) the HCl molecule,
(c) Fe atoms in a solid?

Describe how the molecul h7u,3amsh w uo)23kr6 :uyrbve $ \text{CaCl}_2 $ could be formed.

  Does the $ \text{H}_2 $ molecule have a permanent dipole moment? Does $ \text{O}_2 $? Does $ \text{H}_2\text{O} $? Explain.

Although the molecule euf 17yde .nt8$ \text{H}_3 $ is not stable, the ion $ \text{H}_3^+ $ is. Explain, using the Pauli exclusion principle.

The energy of a molecule can be divided gtx/ odn ;8c4hinto four categories. What are they?

  Would you expect the molecrg(d1y 33mk5pjbfd p8ule $ \text{H}_2^+ $ to be stable? If so, where would the single electron spend most of its time?{yes|no}

Explain why the carbos(1jpc (o sok8lge0gf9 5 :p2p rjqv9un atom ($ Z=6 $) usually forms four bonds with hydrogen-like atoms.

If conduction electrons are free to roam about in a metxug9s *udtda40,w9la e0 a wj6k(x- zral, why don't they leave ua awgj4 6d ,-kt*l0xw99z (a0usrdxethe metal entirely?

Explain why the resisu tj*50wf.val tivity of metals increases with temperature whereas the resistivity of semiconductors may decrease with increasinaul*t vw0j5 .fg temperature.

(Fig. Below) shows a "bridge-type" full-wave rectifier. Exp wf* aup5z7ufzovb/r(u.3 l/w lain how the current is rectified and how current flows durivu fz/aluwo*7./r3pw zub(f5 ng each half cycle.

Compare the resistance of a pn junction diode connected in forward bias to itfkgzx.t7p5,8tfmo+h n 0t b-ts resistance when connected it8kp, notf.xg0f- htzm57b + tn reverse bias.

Explain how a transistor could brq* +4n6oj5nui; mtaqzx*pd / e used as a switch.

What is the main difference between n-type and p-tym j1b gj02bah8s mr,,kpe semiconductors?

Describe how a pnp transisto e246k q;l3tv5zdtz wdr can operate as an amplifier.

In a transistor, the base-emitter junction and the base-collet tufe )vc(n,x1ani,3ctor junction are essentially diodes.itave)c(nt , ,3x fn1u Are these junctions reverse-biased or forward-biased in the application shown in (Fig. Below)?

A transistor can amplify an electronic si bga62x qc((kq38))anx a4cx5bj w ejdgnal, meaning it can increase the power of an 3a2c xexg)4kj b8qjd(6c 5xa)nb(qa winput signal. Where does it get the energy to increase the power?

A silicon semiconductor is doped with phosphorus. Will these atoms be 8u37y;tyivj 9h1ut ti donors or acceptorsihtt 9vjyt i7u1 uy;38? What type of semiconductor will this be?

  Do diodes and transistors obey Ohm’s law? Expl 2: zmev +fi8v;ei8x73muukmrain. {yes|no}

  Can a diode be used to amplifs09 h sthok ha5 5- xm.esi+/cuynv,;dy a signal? Explain. {yes|no}

  Estimate the binding energy of a KCl molecule by calcud, 7+zkbbv-h/z8almy dzlxy. 4,7zji lating the electrostatic potential energy when v.jmb,zy ya/-d77d4h+xliz ,bzzk8lthe $ \text{K}^+ $ and $ \text{Cl}^- $ ions are at their stable separation of 0.28 nm. Assume each has a charge of magnitude $ 1.0e $. Binding energy =    eV

  The measured binding energy of KCl is 4.43 eV. From the result ol nq/cx7ba r19-idu(q f Problem 1, estimate the contribution to the binding energy of the repelling electron clouds r qd79 b1nu(axi-lcq/ at the equilibrium distance $ r_0 = 0.28\ \text{nm} $. $PE_{\text{clouds}} =$    $\ \text{eV}$

  Estimate the binding energy oy9 bm0szrg49qf the $ \text{H}_2 $ molecule, assuming the two H nuclei are 0.074 nm apart and the two electrons spend 33% of their time midway between them. Binding energy =    eV

  Binding energies are often measured experimentally in kcal per mnj4src 0shuuqg ) nci(:h-f +0ole, 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 ths +g(c sj:0qn4 0crhuu)i hn-fe binding energy of $ \text{KCl} (= 4.43\ \text{eV}) $ in kcal per mole?
We convert the units =    $\text{eV/molecule}$
For KCl we have =    $kcal/mol$

(a) Apply reasoning simii 83;5iqun va*4qxhg mlar to that in the text for the states in the formation oiuq5 xh3;8viqangm *4f the $ \text{H}_2 $ molecule to show why the molecule $ \text{He}_2 $ is not formed.
(b) Explain why the $ \text{He}_2^+ $ molecular ion could form. (Experiment shows it has a binding energy of 3.1 eV at )

Show that the quantizv8 vqg (7m ha4 thuz*l/9k,rpty $ \frac{\hbar^2}{2I} $ has units of energy.

  The so-called “charact.-3y+w- lisrl qfrmk6eristic rotational energy,” $ \frac{\hbar^2}{2I} $ for $ \text{N}_2 $ is $ 2.48 \times 10^{-4}\ \text{eV} $. Calculate the $ \text{N}_2 $ bond length. $r = $    $ \times 10^{-10}\ \text{m}$

  (a) Calculate the characteristic rotational en b,;zadnv9z5 bee47s gergy, $ \frac{\hbar^2}{2I} $ for the $ \text{O}_2 $ molecule whose bond length is 0.121 nm. $\frac{\hbar^2}{2I} =$    $ \times 10^{-4}\ \text{eV}$
(b) What are the energy and wavelength of photons emitted in a $ L=2 $ to $ L=1 $ transition? $\lambda $ =    mm

  The equilibrium separatio k(*o nmiyr:b7n of H atoms in the $ \text{H}_2 $ molecule is 0.074 nm (Fig. Below). Calculate the energies and wavelengths of photons for the rotational transitions
(a) $ L=1 $ to $ L=0 $, $hf $ $=$    $ \times 10^{-2}\ \text{eV}$$\;\;\;\;$$\lambda $ =    mm
(b) $ L=2 $ to $ L=1 $, $hf $ $=$    $ \times 10^{-2}\ \text{eV}$$\;\;\;\;$$\lambda $ =    mm
(c) $ L=3 $ to $ L=2 $. $hf $ $=$    $ \times 10^{-2}\ \text{eV}$$\;\;\;\;$$\lambda $ =    mm

  Calculate the bond length for 1 5cq :q1jj5ogiwyav/the NaCl molecule given that three successive wavelengths for rotational transi/ y5:v o1qqgcjj1wa5itions are 23.1 mm, 11.6 mm, and 7.71 mm. $r = $    $\times 10^{-10}\ \text{m}$

  (a) Use the curve of (Fig. Below ;xnrk8j 1vlb8:1g9ngnlp k7 *ezi*td) to estimate the stiffness constant $ k $ for the $ \text{H}_2 $ molecule. (Recall that $ PE = \frac{1}{2}kx^2 $) k =    N/m
(b) Then estimate the fundamental wavelength for vibrational transitions using the classical formula (Chapter 11), but use only the mass of an H atom (because both H atoms move).$\lambda$ =    $\mu m$

  The spacing between “nearest neighbor” Na and Cl ions in a NaCl crysta-q k3(/ yaqam5pwif9k 6hkfi,l is 0.24 nm. Whata9f yiq fw(mq/3ak,k- 6k hip5 is the spacing between two nearest neighbor Na ions? D =    nm

  Common salt, NaCl, has a density ofld 9,. 4gyvgnr $ 2.165\ \text{g/cm}^3 $. The molecular weight of NaCl is 58.44. Estimate the distance between nearest neighbor Na and Cl ions. [Hint: Each ion can be considered to have one "cube" or "cell" of side $ s $ (our unknown) extending out from it.] $s$ =    nm

  Repeat Problem 13 for KCl whose ig(0:b.kqp)iim mpo+i9kgi + vom(o8 density is $ 1.99\ \text{g/cm}^3 $. $s$ =    nm

Explain on the basis of energy bands why the sodium chloride creyvie.m r2g0+gw6c3x 68bsfx ystal is a good insulator. [Hint: Consider the shells6mv 2 3rgewg08fxy+. 6bixecs of $ \text{Na}^+ $ and $ \text{Cl}^- $ ions.]

  A semiconductor, bombarded with light of slowly increased frequttwnc; 2r*6hd b do.e 7o/tyq;ency, begins to conduct when the wavelength of light is 640 nm. Estimate the size of the e rtq.y2wcod/en6 t7bo t*h;; dnergy gap $ E_g $. $ E_g $ =    eV

  Calculate the longest-wavelength photon that can cause an electron in silrir*wmdo 1ho +8lek8/ icon ($ E_g = 1.14\ \text{eV} $) to jump from the valence band to the conduction band. $\lambda $ =    $\mu m$

  The energy gap between valence and conduction bands in germanium is 0.72 eV. Wh/e4f4m.u o7m , uhpzbuat range of wavelengths can a photon have to excite an electron from the top of the valence ba uf/ehzu,m4. pm7bu 4ond into the conduction band? $\lambda \leq$    $ \ \mu\text{m}$

  The energy gap $ E_g $ 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? N =    $ \times 10^6$

We saw that there are jb7s-z*b (o xqzc6ei +$ 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,
(c) 3p band?
(d) State a general formula for the total number of possible states in any given electron band.

  Suppose that a silicon semiconductor is doped wi(rqby+x6xibkp wv.. 6xw1l 9 r72ciunth phosphorus so that one silicon atom xxrqy9ic62.p. lbwr ( k7vxn+iwu1b6 in $ 10^6 $ 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\ \text{kg/m}^3 $, and the density of conduction electrons in pure silicon is about $ 10^{16}\ \text{m}^{-3} $ at room temperature. $\frac{N_{\text{doping}}}{N_{\ce{Si}}} = $    $ \times 10^6$

  At what wavelength will an LED radiate if made from a ma :.ek3ln o/adzterial with an energy gapkl3 .:d en/azo $ E_g = 1.4\ \text{eV} $? $\lambda $ =    $\mu m$

  If an LED emits lighq4; qb6zky)my t of wavelength $ \lambda = 650\ \text{nm} $, what is the energy gap (in eV) between valence and conduction bands? $e_g$ =    eV

  A silicon diode, whose current-voltage characteristics are g) h+hdw7bt,xpy60 )rgi ddns .iven in (Fig. Below), is connected in series with a batddpn6ih ,)hx+7gb)wr d0. ysttery and a $ 960-\Omega $ resistor. What battery voltage is needed to produce a 12-mA current? $V_{\text{battery}}$=    V

  Suppose that the diode of (Fig. Below) ix/z)g7y. rm zfrb8a2ys connected in series to a $ 100-\Omega $ resistor and a 2.0-V battery. What current flows in the circuit? [Hint: Draw a line on (Fig. Below) 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.]    mA

Sketch the resistancek)jwvz1kxo* 2m3 hmd: as a function of current, for $ V > 0 $, for the diode shown in(Fig. Below).

  An ac voltage of 120 V rms is to be rectified. Estimate very roughly the averag07bp h fr;b vqfuc;1o8e current in the output resistofh ;pufc;1oqrb0v8b7r $ R $ ($ 25\ \text{k}\Omega $) for
(a) a half-wave rectifier(Fig. Below a), $I_{av}$ =    mA
(b) a full-wave rectifier (Fig. Below b) without capacitor.$I_{av}$ =    mA

a

b

  A silicon diode passes significant current only if the forward-bias voltagevddu t: z.q8fdz -)td8 z(.bow exceeds about 0.6 V. Make a ro)8ut wdft8zv (d- .dd:b qz.ozugh estimate of the average current in the output resistor $ R $ of
(a) a half-wave rectifier (Fig. Below a),$I _{av}$ =    mA
(b) a full-wave rectifier (Fig. Below b) without a capacitor. Assume that $ R = 150\ \Omega $ in each case and that the ac voltage is 12.0 V rms in each case. $I _{av}$ =    mA
a
b

  A 120-V rms 60-Hz voltage is to be rectified with a fuidl41 unx +nun)8n 0xggyh g24*pk:coll-wave rectifier (Fig. Below), whp02inoxnc)1yn nu lgkhd :8gxu +44* gere $ R = 21\ \text{k}\Omega $ and $ C = 25\ \mu\text{F} $.
(a) Make a rough estimate of the average current. $I_{av}$ =    mA(smooth)
(b) What happens if $ C = 0.10\ \mu\text{F} $?$I_{av}$ =    mA (rippled)

From !num!2%, write an equatmz;ysb2hnka3 :0w5 uzion for the relationship between the base current $ I_B $, the collector current $ I_C $, and the emitter current $ I_E $ (not labeled in the figure).

  Estimate the binding energy of tlo t:k/avg ) 8twk5.zrhe $ \text{H}_2 $ 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 $ \Delta 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 $ \Delta x $ to be the separation of the nuclei, 0.074 nm. [Hint: Let $ p \approx \Delta p \approx \hbar/\Delta x $]    eV

  The average translational kinetic energy of an atom or molecuj(slic*1jr:y f4b,g zle is about $ KE = \frac{3}{2}kT $ (Eq. 13-8), where $ k = 1.38 \times 10^{-23}\ \text{J/K} $ is Boltzmann's constant. At what temperature $ T $ will $ KE $ be on the order of the bond energy (and hence the bond likely to be broken by thermal motion) for
(a) a covalent bond of binding energy 4.5 eV (say $ \text{H}_2 $), $T =$    $ \times 10^4\ \text{K}$
(b) a "weak" hydrogen bond of binding energy 0.15 eV? $T = $    $ \times 10^3\ \text{K}$

  In the ionic salt KF, the separation distance between ax j*ef7o2+kyqn3kk;ions is about 0.27 nm.
(a) Estimate the electrostatic potential energy between the ions assuming them to be point charges (magnitude $ 1e $). PE =    eV
(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. Binding energy =   eV

  Consider a monoatomic solid with a weakly bica+lxmg 5:o4;q9z :jee 3c mfound cubic lattice, with each atom conneefmqc e;ix 4z :5a+j93 mcg:olcted to six neighbors, each bond having a binding energy of $ 3.9 \times 10^{-3}\ \text{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 $ \text{J/kg} $. [Hint: Show that in a simple cubic lattice (Fig. Below), there are three times as many bonds as there are atoms, when the number of atoms is large.]$L_{\text{fusion}} =$    $\times 10^4\ \text{J/kg}$

  For $ \text{O}_2 $ with a bond length of 0.121 nm, what is the moment of inertia about the center of mass? I =    $\times 10^{-46}\ \text{kg·m}^2$

A diatomic molecule is found to have an activation ener6sgt, .e;mot .uyh3oi f*q0j ldm zs6)gy of 1.4 eV. When the molecule is disassociated, 1.6 eV of energy is released. Draw a potential energy curve for,otoith6q)y zus6*;jsemdf. m3 l0.g this molecule.

  When EM radiation is incident ,m- thse:peq.p s 7izkc sky5i,-mz)1on diamond, it is found that light with wavelengths shorter than 226 nm will cause the s1e - 57hitekzkpcsm.py- miqsz,):,diamond to conduct. What is the energy gap between the valence band and the conduction band for diamond? $E_g$ =    eV

  A TV remote control emits IR light. If tbzb2 4k.x v2hthe detector on the TV set is not to react to visible light, could it make use of silicon as a "window" with its v2kh bb. 2zxt4energy gap $ E_g = 1.14\ \text{eV} $? $\lambda $ =    $\mu m$
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 semicb:;2uxzbz *gbu(x: xz(hy z;h onductor, 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 bbzuxhg:x* z( 2bu(zx;;y :zh 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, E =    eV
(b) the orbit radius for this extra electron. r =    nm

  Most of the Sun's radiation has wavelengths shorter than 1000 nm. For a sola 0csy5r /e4dc7 wxvg3e rn 3exw5:ntp5r cell to absorb all this, what energy gap ought thtnvenyxe cr347xsp e0g r /d:c55w3w5e material have? $E_g$ =    eV

  For a certain semiconductor, the longest wavelen3,s(;0p.,b kh sd4dcoeh ghdm gth radiation that can be absorbe,d ( db gm,s0hdk3eh4phoc.s;d is 1.92 mm. What is the energy gap in this semiconductor? $E_g$ =    $ \times 10^{-4}\ \text{eV}$

  Green and blue LEDs became available many years after red LEDs were first dqnli5 2 9(zliieveloped. Approximately what energy gaps would you expect to finliqi5 n9l (i2zd in green (525 nm) and in blue (465 nm) LEDs?
the green $E_g$ =    eV
the blue $E_g$ =    eV

  A zener diode voltage regulator is shown in (Fkaa.-re.kh 3m,gs:n v /fq/wuujq4:vig. Below). Suppose that $ R = 1.80\ \text{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\ \text{V} $ on that diagram.) The diode is rated at a maximum current of 120 mA.
(a) If $ R_{\text{load}} = 15.0\ \text{k}\Omega $, over what range of supply voltages will the circuit maintain the output voltage at 130 V?   $\ \text{V} \leq V \leq $    $\ \text{V}$
(b) If the supply voltage is 200 V, over what range of load resistance will the voltage be regulated?    $\ \text{k}\Omega \leq R_{\text{load}} < \infty$