What type of bond would you expect fobk;6nq d a,n;lr
(a) the $N_2$ molecule,
(b) the HCl molecule,
(c) Fe atoms in a solid?

Describe how the moleculge) ;c( e( zzblrte;h9e $ \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 moleculex1nhyg( u.vv.a9)jj r $ \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 i z wlzr9+5yfcn 0kva-6nto four categories. What are they?

  Would you expect the moled7ahc,3kh a bc(wgifle5 j j1qy90uve:1.)pt cule $ \text{H}_2^+ $ to be stable? If so, where would the single electron spend most of its time?{yes|no}

Explain why the carbon akw k6qg2lb ez+p . eyyb)x7p*9tom ($ Z=6 $) usually forms four bonds with hydrogen-like atoms.

If conduction electro,d h gm9mws xi.09fl 3eb+vc:xns are free to roam about in a metal, why don't they leave the metal entirelyvl93xf:g 9mdm e.hcb +wsx, 0i?

Explain why the resistivity of metals increases with tem.z.qbq qm sur*7u.6ajperature whereas the resistivity of semicobq. sjqa.zmru6*7.uqnductors may decrease with increasing temperature.

(Fig. Below) shows a "bridge-t 9k 0 ;c:vkdjg)hpryv6ype" full-wave rectifier. Explain how the current is rectified and how curr)crv9pvk 0y 6k;dh:gj ent flows during each half cycle.

Compare the resistance of a pn junctt go*iwi q f,rq2r-5,r9:ide kion diode connected in forward bias to its resistancii qert-wr f52i*rq 9:od,,kge when connected in reverse bias.

Explain how a transistor /)i 2nm-uymf vcould be used as a switch.

What is the main difference between n-type and p-tst)vp 2yj kvrtsk .a,43,sijm:s)8 hq ype semiconductors?

Describe how a pnp transistor can operate as a nxfl5ii*-vgm .r +6scn amplifier.

In a transistor, the base-emitter junction anzze4o3 nn ,li0d the base-collector junction are essentially diodes. Are these junctions reverse-biased or forward-biased in the application shown in (Fige34on ,i0znlz . Below)?

A transistor can amplify an eler tjsvlfq;s dy(f(:):ctronic signal, meaning it can increase the power of av:l(qdjyf) f r(t;ss:n input signal. Where does it get the energy to increase the power?

A silicon semiconductor is doped witmbs. 5af* x, k0ymn8 (n5elhikfu24izh phosphorus. Will these atoms be donors or acceptors? What type of (k nmbe xi4y fu2m*ni. 0k,h8az5sl f5semiconductor will this be?

  Do diodes and transistors obey Ohm’s law? Explain. {yes k6ce7 hjvlhxdpn) 7z* 5xb3d4|no}

  Can a diode be used to amplify a signal? Exqvs 3*b2q n ok9,:q v9n-qnu -x:kqvhvplain. {yes|no}

  Estimate the binding u zf;f4.ovlwno693 baenergy of a KCl molecule by calculating the electrostatic potential energy z3f uo96l;anbf4ow. v when the $ \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 of Prb4 hdc, ;bgm7s o.z(keoblem 1, estimate the contribution to the binding energy of the,7d;.cs(gzkm hob4e b repelling electron clouds at the equilibrium distance $ r_0 = 0.28\ \text{nm} $. $PE_{\text{clouds}} =$    $\ \text{eV}$

  Estimate the binding energy of t.cz)xo ( 1+lsnb3mw c+es.yhghe $ \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 expql0b .nm00)ljpm,q3 tnb pcs) erimentally 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? Whqmmp0 0b0q.bn3) lc),nlt pjsat is the 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 similar to that in the text for the states .uutev3ooy0h(g5* d /j( jweh in the formation of tdhe3h(.(j v gw0e5y uuooj/*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 quantitemh bi 24fh8oi3*d f-ay $ \frac{\hbar^2}{2I} $ has units of energy.

  The so-called “characteristic rotational energkd6naxl , wou,w92a 9ny,” $ \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 encgd7 7hx nys p2nzj+2/wa2reo+nzv 0 +ergy, $ \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 separation of H atoms in theu+ pxy .sn o3h;gfr;ugbg(8.h7+ou lj $ \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 the NaCl molecule given7om89q3aud h l that three successive wavelengths for rotatda87u9 lhm3q oional transitions are 23.1 mm, 11.6 mm, and 7.71 mm. $r = $    $\times 10^{-10}\ \text{m}$

  (a) Use the curve of (Fig. Below) to ssibu;e0 d8qt6 3wf7 es9 .igzestimate 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 cryu:6;8hzsf sc 2m4*qef. olr dtsu p82astal is 0.24 nm. What is the spacing between two nearest neighbor Na2.h;o* ausu6rp m 2f8 q8e4sstc:lzfd ions? D =    nm

  Common salt, NaCl, has a denrota.5q 1 qc;bbyi:sao :)y0rrru1. gsity of $ 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 density tk zz,02npq.mis $ 1.99\ \text{g/cm}^3 $. $s$ =    nm

Explain on the basis of energy bands why the sodium chloride crystal is a i ;8blc,xhdw)rs (go) good insulator. [Hint: Consider hr 8;wi odcgs)(b), lxthe shells of $ \text{Na}^+ $ and $ \text{Cl}^- $ ions.]

  A semiconductor, bombarded with light of slowly in1kqti +ut1 r8t8ztwc m2d( 0qjcreased frequency, begins to conduct when the wavelength of li cqqtkwm+ j (2t8uz1rt0it1d8ght is 640 nm. Estimate the size of the energy gap $ E_g $. $ E_g $ =    eV

  Calculate the longest-wavelength photon thad-*ap7t i:d8jt 0uq6*rq jifq.gwl* jt can cause an electron in silicon ($ 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. W cd5 x:hp62ptb0ijciay.m72y hat range of wavelengths can a photon have to excite an electron from the top of the valence band into the conduction band? 6h y:a22y 5p cbim jtx.pdc0i7$\lambda \leq$    $ \ \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 ars5osr0jg 4 fcb qa.5t6e $ 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 with phosphorus so that one vbnc mp ps*i72h* o;)ly,zu 5vsilicon );lyzci *vs m2pb5ou*, 7vhnpatom 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_{doping}}{N_{Si}} = $    $ \times 10^6$

  At what wavelength will an LED radiate if maluh ,-)1ihzqr a(+1y ydqzc:ode from a material with an energy gap )c +a1qr1 oy-qhld: zui,y(hz $ E_g = 1.4\ \text{eV} $? $\lambda $ =    $\mu m$

  If an LED emits light of wah ;6 rb98qi4pmtt1an kvelength $ \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 given in (Fig. Betv0v r, qrh2:q+2 cfv2c rpvz:low), r v:q0ft ,2vrq+vvhc2zp 2c:ris connected in series with a battery 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) is connected in seriesiy84txray 1w5 n-ysg0b d47)w imz/zy 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 resistance as a functj:sset;ucb q5 xc 07t(zrc(1sion of current, for $ V > 0 $, for the diode shown in(Fig. Below).

  An ac voltage of 120 V rms is to be rc/pxzk523i- v9 ulterectified. Estimate very roughly the average curr- 3xc/zv 25e u9tklirpent in the output resistor $ 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 fo9:ujtyiz,3 us rward-bias voltage exceeds about 0.6 V. Make a rou:z , sitj39yuugh 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 i9zf;3n ;je wvrectified with a full-wave rectifier (Fig. Below), whfzi j;9nev3; were $ 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 equation forwaqkph;x46-):pxsiu m fi5pntt r100lgz,7 y 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 wl, 1(d wnr5e zdc3*hgenergy of the $ \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 kgxca3 we(2wgg, xo: 5vinetic energy of an atom or molecule 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 sepai.kbqt4tmfolqlk ) (7 6jid4.ration 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 $). 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 wi3 hh+dymbw (7-k j*nyzth a weakly bound cubic lattice, with each atom connected to six neighbors, each bond having a bind*+dy -wnmyk3 jz(7hhb ing 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 energy of 1.4 gp(8rkwz;ug na19ce8c ya 7.qeV. When the mol9r cayeqcz7gu(p aw81 .ng;8 kecule is disassociated, 1.6 eV of energy is released. Draw a potential energy curve for this molecule.

  When EM radiation is incident on diaqw0u5 j b6mcq1mond, it is found that light with wavelengths shorter than 226 nm will cause the diaquj56w0 1 cqbmmond 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 the detector on thvohet py5/ d54e TV set is not to react to5dtev54 o/ pyh visible light, could it make use of silicon as a "window" with its energy 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 semiconductor, ahgy8z8fpl;s pp-51sl ssume that the "extra" electron moves in a Bohr orbit about the arsenic ion. For this electron in the ground state, take into s-z1y 5ppl ls8f g8h;paccount 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, E =    eV
(b) the orbit radius for this extra electron. r =    nm

  Most of the Sun's radiation haka,tl2z pz qhs) 9)zyq/(q/ozc7w y* is wavelengths shorter than 1000 nm. For a solar cell to absorb allk) yq/y7lp2ta/, w)qs(o9qzchz z* zi this, what energy gap ought the material have? $E_g$ =    eV

  For a certain semiconductor, the longest wavelength radiation that can be absl6w0vh8h-xnrzl , j;e2xxj -nb9z-qlorbed is 1.92 mm. What is the energy gap in this semiconduc0r6lzn lxl qxxb -,j; -h8hwje2 vz-9ntor? $E_g$ =    $ \times 10^{-4}\ \text{eV}$

  Green and blue LEDs became avail1;bf:hj 0yq rtable many years after red LEDs were first developed. Approximately what energy gaps would you expect to find in green (525 nm) and i 0:hfjtrbq;y 1n blue (465 nm) LEDs?
the green $E_g$ =    eV
the blue $E_g$ =    eV

  A zener diode voltage regulator is shown in (Fig. Below). Suppose that +e -n7pe45fay 8u wppv$ 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?    $\ \text{k}\Omega \leq R_{\text{load}} < \infty$