What type of bond would you expect f.w(bed+ hpx1mnybg zb. x17h*or
(a) the $N_2$ molecule,
(b) the HCl molecule,
(c) Fe atoms in a solid?

Describe how the molk 5sde.ayq-9gecule $ \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 moleculebob:( -dst)/:i i bxlj nib:t2 $ \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 divwtw,jr5wz 7 a2ided into four categories. What are they?

  Would you expect the molecuopt+th ) styo:yb--c/7f w a4yqc xg8;le $ \text{H}_2^+ $ to be stable? If so, where would the single electron spend most of its time?{yes|no}

Explain why the carbon awilf j-re;hm20 )ul. usc *e l7x7ikf9tom ($ Z=6 $) usually forms four bonds with hydrogen-like atoms.

If conduction electroyemugfb )pn/ha)hwiid8g/u 4 t/,a: +ns are free to roam about in a metal, why don't they leave the metahyf+/ia umg4w)/t pu:8 h,a edign )b/l entirely?

Explain why the resistivity of metals increases w3fjbhq) 1rdq*8s 5npd ith temperature whereas the resistivity of semiconductors mar8jds*q5n3f)qphb1 d y decrease with increasing temperature.

(Fig. Below) shows a "bridge-type" full-wave rectifier. Explain how the curre,0ru,e 5znm bnnt is rectified and how cureb n urzn0m,5,rent flows during each half cycle.

Compare the resistanc61xe d o3pun0- eiq-fac .n1iie of a pn junction diode connected in forward bias to its resistance when connected in reverse ba 10fe.iie6co dinpxn- u1q- 3ias.

Explain how a transistor coul594nz,j sl-9tmot 18dathwwbd be used as a switch.

What is the main differ2)lc38z i7kgqww r+x jence between n-type and p-type semiconductors?

Describe how a pnp treg( 4wfuv5vg wj )kuq1 y1h(i4ansistor can operate as an amplifier.

In a transistor, the base-emitter junction and the base-coll ;nrfzt-bd n4*a,bj+ 4-muuboector junction are essentially diodes. Are these junctions reverse-biased or forward-brduu taz-n n4bbfb,o*j+; 4 m-iased in the application shown in (Fig. Below)?

A transistor can amplify an electronic signal,vkonpw l5du-i/*.h.t meaning it can increase the power of an input signalkh ln5 p.vud/*it-.o w. Where does it get the energy to increase the power?

A silicon semiconductor is doped with phosphorus. Will these atoms be dzs 5c a2huxkikgp 1.o.sz nuly;- +xz:4o3 fb4onors or cxinfz k y1.-4;5uh:3s .upazb+k42ogz x o slacceptors? What type of semiconductor will this be?

  Do diodes and transi+j-eews9n 2mzf+ cn v9stors obey Ohm’s law? Explain. {yes|no}

  Can a diode be used to amplify a signal? Explain. {ye,vwqa a51i,+,lijq ,: f9rbz a*oi wess|no}

  Estimate the binding energy of a KCl molecule by calculatip pnoexb()4e x)w( e;o ir/p-hng the electrostatic potential peh 4( (p-o);xpniwee) bro/xenergy 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. Fro r5w qj(dzru/(m the result of Problem 1, estimate the contribution to the binding eneuj/ 5zq w(r(rdrgy of the repelling electron clouds at the equilibrium distance $ r_0 = 0.28\ \text{nm} $. $PE_{\text{clouds}} =$    $\ \text{eV}$

  Estimate the binding energy of5h lpvo+p(n3w 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 often89-b nq na,ktar(6 noqd4ibx8ht4 dl6 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 k al,4rak9i -8(bhno6t4x bq 8dtn6ndqcal 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 iz . x2ofydz3o5n the text for the states in the formation o 3o.z x5fydzo2f 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 quantity mv8ge +aep)4z $ \frac{\hbar^2}{2I} $ has units of energy.

  The so-called “characteristic rotational enww*ftt8g w*n(rl dn- :xy k:/hergy,” $ \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 rotatioji/fj ;-x5+wz nwr,3qe*hb jq k/ rk6dnal 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 tk wz) 0 h;tlz1cfz):alhe $ \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 given that three successive wave 9.gognro5mnxa7y, d7.x8 uo elengths for rotational transitions are 23.1 mm, 11.ygx7m n7 x.oao.dr,n5eo 8ug96 mm, and 7.71 mm. $r = $    $\times 10^{-10}\ \text{m}$

  (a) Use the curve of (Fig. Below) to e6)4g j r4jc9(dt ui l symgun.*eoht0:stimate 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 crm l4 sf4x1azd0ystal is 0.24 nm. What is the s4al14 fm dzxs0pacing between two nearest neighbor Na ions? D =    nm

  Common salt, NaCl, has a density omcvh nm 3nx r5py a1yez((*yf9k939t kf $ 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 whq2e,4m palr+ aose density is $ 1.99\ \text{g/cm}^3 $. $s$ =    nm

Explain on the basis o l)tv yutx69e4f energy bands why the sodium chloride crystal is a good insulator. [Hinttulv y) 946xte: Consider the shells of $ \text{Na}^+ $ and $ \text{Cl}^- $ ions.]

  A semiconductor, bombarded with light of slowly increased frequency,vc/k* m*w m13j.tbf2 emh6xw y begins to conduct when the wavelength of light is 640 n*hjwwbkf 1vyx. tec6 *3m m/m2m. Estimate the size of the energy gap $ E_g $. $ E_g $ =    eV

  Calculate the longest-wavelen m -)z+.olguffkew 3h*gth photon that 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. Wha v) fa0p6k sf. :wj.2kus1wruut range of wavelengths can a photon have to excite an electron from the top of the valence band into the cwusu kf ..f:0 pjka)srwvu 612onduction 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 arvkx ( e.id8l (rqjqua v2jm-k.+t)uc: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 with phospho jd;j.p+syh5 urus so that one silicon +pj hys ;.5udjatom 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 matydx 6 ckf(u5joa 6(c p8ux4ar(erial with an energy ga fura(ky (84j(a5x6px udocc6p $ E_g = 1.4\ \text{eV} $? $\lambda $ =    $\mu m$

  If an LED emits light of wavelength c:73nror xjk*$ \lambda = 650\ \text{nm} $, what is the energy gap (in eV) between valence and conduction bands? $e_g$ =    eV

  A silicon diode, whose current-voltagoit/z qs2 i f22dm) 13hayxd9ie characteristics are given in (Fig. Below), is connected in series with a battery and ti2dm1 f 29ih y zxiqosa/)d23a $ 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 * p1f y+t b y39;wpu2yxu5to**vupgyhconnected 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 fu2 huqw33 91kc2iwniyi nction 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 t 8k nq fstg4hl6qz-l+aqpw1 +/he average current in the output ra/q-kll+ 4t+ 68sqnz qg1h fpwesistor $ 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-bh9 wwwv./06 o pqq0az 2bgi*ovias voltage exceeds about 0.6 V. Make a rough estimate of the average current in the output re/ .26qbz0ahwov*9wp0qi gvw osistor $ 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 wit d/w/z7pf7m pz:u+ koyszr05zh a full-wave rectifier (Fig. Belop+ ufk5/ws:0p7zozm 7dr zzy/ w), 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 an equation for the relatiox3e6i qbh-3ara;: 3m ejnzm+ ky 1rez3nship 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 enss 4uhmqgal 1:5)l:,kxwt2 wqergy 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 translati99pqn5p /v/kj bvt/xxonal kinetic 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 5/gspag1c9chj gi0d) 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 weakl;ek*qc ,ebe y9y bound cubic lattice, with each atom connected to six neighbors, each bond having a e;*ey e, c9bkqbinding 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 eV. When the ms*l6u:4 k m1y gikv6i7ywxms+.4onololecule is disassociated, 1.6 eV of energy is released. Draw a potential energy curvek li6y 74sx* :4.in+ymou wl1gvko6ms for this molecule.

  When EM radiation is incident on diamond, it is found that light with wavezya.qa 9k ,wywdg7bm 4fu5w55lengths shorter than 226 nm will cause the diaq k gbw uawz75,5f5da wy.y4m9mond 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 Indk/ 3 +rm4q j01csw;eoer8urR light. If the detector on the TV set is not to react ts 0r4 cn8 +/j1e; wrrk3dequmoo 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 indv(e4equ) s7f a doped silicon semiconductor, assume that the "extra" electron moves in a Bohr orbit about the arsenic ion. For thev7)d( ue4qsfis 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 radiae9z+z hi 3(vdution has wavelengths shorter than 1000 nm. For a solar cell to absorb all this, what energy gap ought theiv 3hz(d+9zeu material have? $E_g$ =    eV

  For a certain semiconductor, the longest wavelength rh4-z p1 qxd/zrg+hd5o 3si)f zadiation that can be absorbed is 1.z-gx 1szi+ofrz4 3d/hq 5hp)d92 mm. What is the energy gap in this semiconductor? $E_g$ =    $ \times 10^{-4}\ \text{eV}$

  Green and blue LEDs became availav-9 e p57wdbgrl/xu4 kble many years after red LEDs were first developed. Approximately what energy gaps would you expect to find i5bl e rw7gd9kxpu/v4 -n 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 gh5xw8q -*2 eic 5gb/b qtp+khin (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?    $\ \text{k}\Omega \leq R_{\text{load}} < \infty$