What type of bond would you expeoj,uej6;.(o y 8klxygct for
(a) the $N_2$ molecule,
(b) the HCl molecule,
(c) Fe atoms in a solid?

Describe how the molxh kxka.:lv1;mwz:f+ q8 zse:ecule $ \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 moleculnooq*x+ cvi :;-zs-xue $ \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 into four categories. What agdfyuwfkaiba f)28 9tn+0 1 j,re they?

  Would you expect the molecb/ pj75a5:sx pe1upnjv7-thc ule $ \text{H}_2^+ $ to be stable? If so, where would the single electron spend most of its time?{yes|no}

Explain why the carbono15kyvww 2u dt2yuadf2.ru,- atom ($ Z=6 $) usually forms four bonds with hydrogen-like atoms.

If conduction electrons are free to roam about in a metazzc08ovs;v7* ifd bjk38x p z*l, why don't they leave the mcz z; kvsz7d8*v8 3fjx0pbi*oetal entirely?

Explain why the resistivity of metals increases with temperature whereas th r4 b/w-tj)rtm-c k.tb0u5xgbe resistivity of semiconductors may djbmg)w .burktc- tx/54t-0rbecrease with increasing temperature.

(Fig. Below) shows a "brp67ih fbdpq7 /idge-type" full-wave rectifier. Explain how the current is rectifiedpbd7f/p h7i6q and how current flows during each half cycle.

Compare the resistance of a pn junction diodg.:yo5;sh y uce connected in forward bias to its resistance when conne 5y ;gyhcou:s.cted in reverse bias.

Explain how a transistor could besxvq,: *pm4 vo used as a switch.

What is the main diffbr,dja0b++nrtc-f v* m 1f+kaerence between n-type and p-type semiconductors?

Describe how a pnp transistor can o30c,bedyuo be1z0c: h perate as an amplifier.

In a transistor, the base-emitter junction and the base-collector junction are eu+ o m1p2 :cx14f5eeb.qvixtbssentially diodes. Are these junctions reverse-biased or forward-biased in the appli+2b1fq xcopue1v.be 4i x tm:5cation shown in (Fig. Below)?

A transistor can amplify an electronic signal, meaning it can increase tk/47ugffc-pma 3whr c qnsg+5c:s *gp + )nf0qhe power of an input signal. Wh* g/r5:u qf knf0cc p73ms+cp-gqs)4+hng awfere does it get the energy to increase the power?

A silicon semiconductor is doped with phosphorus. Will these atoms be donors or l m2lcpu6t/v q/ jzs2 n 7hr*ow8iw7:zacceptors? What type of semicondwpullto/zsqz/v2ric87 m 7jh: 6*wn 2uctor will this be?

  Do diodes and transistors obey Ohm’s law? Explain. {yes|not.1 oan/ ):c 9kuslfidsdb/y9}

  Can a diode be used to amplify a signal? Explain.(y h8 a0hmfoe* {yes|no}

  Estimate the binding energy of a KCl molecule by calculaox,uvvupo ,;unnffj +26.e z+ ting the electrostatic potential en6+vfu 2,p,of;unv nux.ez +ojergy 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. g 57ivyf m(w3) 5hjuhxFrom the result of Problem 1, est)u hfgyxw3miv7(h5j 5imate the contribution to the binding energy of the repelling electron clouds at the equilibrium distance $ r_0 = 0.28\ \text{nm} $. $PE_{\text{clouds}} =$    $\ \text{eV}$

  Estimate the binding enerz67-mtk 5p e dwcqbl:-gy of 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 mf k wy+ xwi4pc7 rj(y:v63ttz)ole, and then th wfy:tycjt x)p+6 (iw74kzr3v e 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 $ \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 teglli4 ib 9)ep3xt for the states in the formation pil43gibl9e)of 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 quantitqh enk;gv/4zi:.5cxm7 he/ tby $ \frac{\hbar^2}{2I} $ has units of energy.

  The so-called “characteristic rhm 2.ut+b9 s68gksfop otational 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 rohyz,k d w(sh(0+ :yf ij3lid-otational energy, $ \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 th(xb ;,shu bg a8.1 hbktalo,u2e $ \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 g(u*:oso 9jpqpbkbv :evj 8s3vz9n94miven that three successive wavelens(:euq3knzvbjm vbjpo8: 99ov4 p 9* sgths for rotational transitions are 23.1 mm, 11.6 mm, and 7.71 mm. $r = $    $\times 10^{-10}\ \text{m}$

  (a) Use the curve of (Fig. Beyxbwq76.pp1q c;:s 1dh wi ,wklow) 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 crystalmzvb :1 /pwotvwq41j it:5 v,q is 0.24 nm. What is the spacing between two nearest 4m, pwb:ov5qv w1: ivjtzt/1q neighbor Na ions? D =    nm

  Common salt, NaCl, has a densitdvba;a 9vf+ :u 9 s;n(lo(wbxmy 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 densit,g swxmaic ,7erk /7f)5.yr eey is $ 1.99\ \text{g/cm}^3 $. $s$ =    nm

Explain on the basis otc 3jsm/hjg4)6s+ 7c;yas7ihy kbo 7p f energy bands why the sodium chloride crystal is a good insulator. [Hint: Consider the shells o7hct6k sp4a scj+/gmy ) 7ys 3hbo;7ijf $ \text{Na}^+ $ and $ \text{Cl}^- $ ions.]

  A semiconductor, bombarded with lhqf+ i( a( 9uhx:uo/ cm3aful7ight of slowly increased frequency, begins to conduct when the wavel(u ifh f3cma: +h(7o qaxu9lu/ength of light is 640 nm. Estimate the size of the energy gap $ E_g $. $ E_g $ =    eV

  Calculate the longest-wavelength photon thatpxax) t ztb6zj a.jj9tt p+7c+w:4i j6 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 1 l8ah)pk(*zba o2pau,q:pyrconduction bands in germanium is 0.72 eV. What range of wavelengths can a photon have to excite an electron from the top of:,hu8( rpba*k azap)qoly p1 2 the valence band 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 arug r1are1m*wjxihxob y 8102+e $ 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 / ,qk0bvu v*mb8txfi81)wo qk with phosphorus so that one silicon aqwkbvx1m/bvfi)t8, 0q u*8ok tom 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 made from a material with an energy g2 :t.jrpyea.6n9hs w mapp haj6wems .. 9y:n2tr $ E_g = 1.4\ \text{eV} $? $\lambda $ =    $\mu m$

  If an LED emits light of wavuc.olgqqr9l46 vas -/ elength $ \lambda = 650\ \text{nm} $, what is the energy gap (in eV) between valence and conduction bands? $e_g$ =    eV

  A silicon diode, whose current-v2p9 t4jx ae7ploltage characteristics are given in (Fig. Below), is connected in series with a bj pap94l2x7et attery and a $ 960-\Omega $ resistor. What battery voltage is needed to produce a 12-mA current? $V_{\text{battery}}$=    V

  Suppose that the diode ofb-mv 32crncv s/tf57n (Fig. Below) is 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 resistance as a vjy6+kb fvn (j8:aw2f function of current, for $ V > 0 $, for the diode shown in(Fig. Below).

  An ac voltage of 120 V rhdq u1 8yfjko u87o .yp50zr,p y4;brtms is to be rectified. Estimate very roughly the average c;yfy0u 8 4pzyobr r okuj,.8ht1q57pd urrent 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 cuv81ojp qze ;a+z* m;rorrent only if the forward-bias voltage exceeds about 0.6 V. Make a rough estimate of the average current in the output resiszpre ;1ozmqa j;v8*o+tor $ 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 recti63 z;8uk ,yk-hszjqhpfied with a full-wave rectifier (Fig. Bep83kzkzsh;hq y,-6 j ulow), where $ 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 a 5obqo475tdqpi:* ik j.bhpa (n equation 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 the u0fo igapmx9+a+y5 ) z$ \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 dn8wmp z 9h ;s1kl z/1,phsj:qkinetic 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 separation distance between ions is aboum)m h7bj*i4p9 t8uh eot 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 bound cubic lattice, with each atom c)6lb w6sq ujp1zv8pg0onnecte86pu1j bqsw0lpzv g)6 d 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 ha+v(xb6 2mk( gyrjxw7sve an activation energy of 1.4 eV. When the molecule is disassociated, 1.6 eV of enerx+gy s2(bxk6vr 7(jw mgy is released. Draw a potential energy curve for this molecule.

  When EM radiation is incident on mi6 9ttz mjj 0e.2t6ipdiamond, it is found that light with wavelengths shorter than zj6 0t mtem6p.2i 9itj226 nm will cause the 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 the e:jk.(ksac unw(i .6bu,au5g detector on the TV set is not to react to visible light, could it make use of ,u kwkega .s6c:nuu( b 5j.(aisilicon 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 doe8xn,/yt2 */llglen1xvm:mh ped silicon semiconductor, assume that the "extra" electron moves in a Boh/y/8g, nxmxhlenl1*2mel: tv r 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, E =    eV
(b) the orbit radius for this extra electron. r =    nm

  Most of the Sun's radiation has wavelengths shorte mseo7* *zt 5tf3u:imkr than 1000 nm. For a solar cell to absorb all this, what energyimfkutz3t* e5:o* ms7 gap ought the material have? $E_g$ =    eV

  For a certain semiconductor, the longest wavelength radxht c 5da-8-we,h6fz jiation that can be absorbehw6ae 8-- cf,j5th dxzd 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 aftere:nh9*8 xhbz3 xp gc1k red LEDs were first developed. Approximately what energy gaps would you expect to find in green (52z:pk*b9e 8xh 1cnxgh35 nm) and in blue (465 nm) LEDs?
the green $E_g$ =    eV
the blue $E_g$ =    eV

  A zener diode voltage regulator is shown invei i,dj 4w3g; (Fig. 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?    $\ \text{k}\Omega \leq R_{\text{load}} < \infty$