What type of bond would y-hh6o lyeuk0;o w a)*aou expect for
(a) the $N_2$ molecule,
(b) the HCl molecule,
(c) Fe atoms in a solid?

Describe how the molecule yu 7hpk3-b pm,h( 5l2jsyf9en$ \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);amo7 htjmipw9,t;n $ \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 dividedp 0c;u7h b r-a:-lu:gk4fu3l v1pny fi into four categories. What are they?

  Would you expect the moleculede 5x,ru50 edu:,p faq $ \text{H}_2^+ $ to be stable? If so, where would the single electron spend most of its time?{yes|no}

Explain why the carb 7ozxgu/dp5z:(bpmu5us25h x on 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 leavvrixs6.im 0yzb 4 qvj 5.)f;qie the met6iqxi. s40 b;rqjvy. 5z mvfi)al entirely?

Explain why the resistivity of metals inc;*ect +i(usjwreases with temperature whereas the resistivity of semiconductors may decrease with increasing t; i+jcusw(t*e emperature.

(Fig. Below) shows a "bridge-type" fue 3qrsn8/s8u g4ioke l)sa9k 3ll-wave rectifier. Explain how the current is rectified and how current flows duge) uoskl9ssei 8 38rn/a3qk4ring each half cycle.

Compare the resistance of a pn junction diode co:ft9/ah jypx( *w ix,. j-pjcannected in forward bias to its resistafyc9/*x : pw(,x-hpjjjt a. aince when connected in reverse bias.

Explain how a transistor cou*x d90 2yajfq5r2 zninld be used as a switch.

What is the main difference between n d/0+bpske rni5vy; +e vrrx6oo)..os-type and p-type semiconductors?

Describe how a pnp transistor ca bc7iagv 9jekn()27y un operate as an amplifier.

In a transistor, the base-emilq0d*1fm*tu dtter junction and the base-collector junction are essentially diodes. Are these junctions reverse-biased or forward-biased in th1mf*q uddlt0 *e application shown in (Fig. Below)?

A transistor can amplify an electronic signal, meaninoc*rm;jh1wdp4k n m6 1g it can increase the power of an input signal. Where does i64;dcjh*ok mn1pr mw 1t get the energy to increase the power?

A silicon semiconductor is doped with phosphorus. Will these atoms be donorsclo z x*/3 h6pveecdm99b h:a- or acceptors? What type p6zvb :l9e h9he-xc*d 3maoc/of semiconductor will this be?

  Do diodes and transistors obey Ohm’s law? Explai:eu 9vs g mjb9n)vv/i4n. {yes|no}

  Can a diode be used to amplify a signal? Expla;ng3 qo l nvt)nu5)o -*cej*vtin. {yes|no}

  Estimate the binding energy of a KCl molecule by calculating the electrofhxu))w7ju fh-3 ju*o.zzke 9static poo * 3-7ffj).xh)whzu uke9j zutential energy 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 4.4l tdg5z7f)8 aq;d j,sm )zib+o3 eV. From the result of Problem 1, estimate the contribution to tf+7d dt,) la)zjq85m o;zsigbhe 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 energy of th 61kkp 1)e0gcgaxdud, e $ \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 3jw1t m8; 0vbd*(pa(urbzld bmeasured experimentally in kcal per mole, and then the binding energy in eV pe1;0wrzmp tab(l j3bddv8 * (ubr 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 p) js56oeut-z text for the states in the formation of ) u- zetj5sp6othe $ \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 quantitz5gi15*qv-god l eom.,b8 amgy $ \frac{\hbar^2}{2I} $ has units of energy.

  The so-called “characteristic rotational ek , vj(j/qzc2lnergy,” $ \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 zit c4g8l.8 j an(me)j/0etodenergy, $ \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 the q c rmqm1h -gxc)e**u0 m+ cx::imtik:g, i0pb$ \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 wavhj3*n v)5wnk 7utw5l-y ge1v helengths for rotational transitions are 23.1 mm, 11.6 mm, andu)1ye3- n55* wv7whtj klghvn 7.71 mm. $r = $    $\times 10^{-10}\ \text{m}$

  (a) Use the curve of (Fig. Below) to estimate the stiffmv6z r(bej x.gm)tx72 ness 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 nfeaq9as*nwza 5u2wy;6u;c6qbx+ o 7 ueighbor” Na and Cl ions in a NaCl crystal is 0.24 nm. What is the spacing bezs qc yu u;6nu;ba6wfx9e 7+5 2*oqaawtween two nearest neighbor Na ions? D =    nm

  Common salt, NaCl, hl+u(5c +jqcv,l/v .jo atdv, tas a density 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 who0 k sd6hf*nh2zse density is $ 1.99\ \text{g/cm}^3 $. $s$ =    nm

Explain on the basis of energy bands why the sodium chloride crystal is nm5atbf/eqz 8ao21b+ a good insulator. [Hint: a+bt8nm2o/za bfq5e 1Consider the shells of $ \text{Na}^+ $ and $ \text{Cl}^- $ ions.]

  A semiconductor, bombarded withv2wb ;fub/ktm a.m+xg c/ )p)k light of slowly increased frequency, begins to conduct when the wavelength of light is 640 nm. Estimbtbfm.;gum/ vk )w2a/) pkcx+ate the size of the energy gap $ E_g $. $ E_g $ =    eV

  Calculate the longest-wavelength photon that can cause an electron in silicv 4o51jeocpc(z o58s xy,cd )zon ($ 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 i i-2c -cyf0ahkn germanium is 0.72 eV. What range of wavelengths can a photon have to excite an electron from the top of thhcyk-c- af20ie 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 are ussczw 7+f1o7$ 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 dopbn3.ojp, 11 nmq j4mrhed with phosphorus so that one silicon at.njnhj 4m p1br3mq1o ,om 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 L( fvr1hxo*pk ;ED radiate if made from a material with an energy gap kv o phr1x;f*($ E_g = 1.4\ \text{eV} $? $\lambda $ =    $\mu m$

  If an LED emits lightf9j a55fn ke -smu gul*r34m/z 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 given in:(tdj/zg)m(1g jaamnok/f. i (Fig. Below), i gitzkja .am((1g/ :n md/f)ojs 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 connectoob1y* d*plxhf02y,zed 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 function of current,1pgecc3 w dl no5qe-vi0 e1p7) for $ V > 0 $, for the diode shown in(Fig. Below).

  An ac voltage of 120 V rms is to bebs5)xqw 5s e0m.xc,iyt(,;si d/whuz rectified. Estimate very roughly the average current in the output r /s5h wy0i x5;me)t(z, cdbqiws,s.uxesistor $ 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-bia;x 9z2x4*0m,qjggea*1uoi v/ l rnkmxs voltage exceeds about 0.6 V. Make a rou/u ;o*l aj0eikmrmgq xx*1, n24gxv 9zgh 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 rem(j0nry;+thl)mweyul 3-j8g ctified with a full-wave rectifier (Fig. Below), whe8n wre)tl( jj-gmy3hm;uy l0+re $ 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 relationship d+wp jg cdlz)0: 8xus+fzt5)f 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 enq7 8(wz y6ffku:1bvhc:vfl oo ,uj/g ,ergy 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 kinetit b7wpist96o5 p isu;*c 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 about 0.27 f/fjzs.+nm-t b9s 2ivnm.
(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 ladzzb)8 s+(m*6axwj oa ttice, with each atom connected to six neighbors, each bond havings j(dazow*zmb+6x 8)a 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 energy of 1.4 eV. When the 3 0vd,ac ,lnl1em x-nspl:c9 vf r15vamolecule is discl150n l:d,r1s vvlma -c xp93,evnfaassociated, 1.6 eV of energy is released. Draw a potential energy curve for this molecule.

  When EM radiation is incident on diamond, it is found that light with waveam7wxin52v/ t z -hts12g+ xealengths shorter than 226 nm will cause the diamond to conduct. What is the energy gap between the valence band and the conduction band for diamond? 2 ag -/hvxi2n+xmt5ws7e a1zt$E_g$ =    eV

  A TV remote control emits IR light. If the detector on the TV set is y 8q4 mjuz.0uer.htd+not to react to visible light, could it make use 48 +eujh.uqt zmr.dy0of 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 qk nk* o8b:d9zin a doped silicon semiconductor, assume that the "extra" electron moves in a Bohr orbit about the arsenic ion. For this electron in the gb n8kod :qk*9zround 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 shorter than 1,wct(7gng huw0efs.0000 nm. For a solar cell to absorb all this, what energy u0n0,( ggw fh 7w.cestgap ought the material have? $E_g$ =    eV

  For a certain semiconductor, the longesix a sacndvbr22: *45nt wavelength radiation that can be absorbed is 1.92 mm. What is the energy gap in this cinnavs4xrab52: d *2semiconductor? $E_g$ =    $ \times 10^{-4}\ \text{eV}$

  Green and blue LEDs became available many yewe)*s t,n+q ywars after red LEDs were first developed. Approximately what energy gaps w+s,)twnew yq*ould you expect to find in green (525 nm) and in blue (465 nm) LEDs?
the green $E_g$ =    eV
the blue $E_g$ =    eV

  A zener diode voltage re;b kwhcnc,y(( yq3oecj z i0.1gulator is shown in (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?    $\ \text{k}\Omega \leq R_{\text{load}} < \infty$