What type of bond would you expectr-.y1 ) ov.gws0wsl9sch z( sf for
(a) the $N_2$ molecule,
(b) the HCl molecule,
(c) Fe atoms in a solid?

Describe how the molecu1oed-5yyk;*c4( un 0fbrx ckvle $ \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 moleculvxr b 5f)l(b(ke $ \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 categoriexmcz9,ps epgx 6i ;x4+s. What are they?

  Would you expect the ul6- jgt -d;3jy x. q)ua9cr4ullc/yc molecule $ \text{H}_2^+ $ to be stable? If so, where would the single electron spend most of its time?{yes|no}

Explain why the carbon arri +p(xcv3d.tom ($ Z=6 $) usually forms four bonds with hydrogen-like atoms.

If conduction electrons are free to roam about in a metal, whyu1zqd9dyl,g:w qq2s + don't they leave the metal en:lduq +d 2 zsg9wq1q,ytirely?

Explain why the resistivity of metals increases with tempesp,71y 4tiy w);uwe cyrature whereas the resistivity of semiconductors may decrease with increasing temperatur,7escyuw; i w)p yy4t1e.

(Fig. Below) shows a "bridge-type" full-wave rectifier. Explain how the-/abxk mx7p** xa0akg current is rectified and how current flows during each half cymk * 7ag/x0x*x-akabpcle.

Compare the resistance of a pn junction diod;zwt 6qp6cj h7e connected in forward bias to its resistance when connhptz;w jc676qected in reverse bias.

Explain how a transistor could be;r54gm6veylk)74mf ;d oox e a used as a switch.

What is the main difference between n-type and p-type semiconductoeooo1:ix/zd6w452hwwr rm s )rs?

Describe how a pnp transistik1bu vq6* dp0or can operate as an amplifier.

In a transistor, the base-emitter junction and the base.437.a jgd4hsbgenro -collector junction are essentially diodes. Are these junctions reverse-biased or forward-biased in thdg4 j. .3ea h4gonr7bse application shown in (Fig. Below)?

A transistor can amplify an electroh:/ t z tj73fm6xtuts(nic signal, meaning it can increase the power of an input signal. Where does it get the energy to increash 7zm3tf:(/suxjtt t6e the power?

A silicon semiconductor is doped with phosphorus. ymi4w2w/w pf/ao 9*lqWill these atoms be donors or accl o2wq94ay/ i*pw wfm/eptors? What type of semiconductor will this be?

  Do diodes and transistors obey Ohm’s law0x5tp9oflu ea0 3v pj5? Explain. {yes|no}

  Can a diode be used to amplify 9;srbmr0:so 3anr5 d fa signal? Explain. {yes|no}

  Estimate the binding ener/snwy; dd-u/dt9x7 - c*fbkzmgy of a KCl molecule by calculating the electrostatic potenti/b;dkyd 7m*zs /-9dxn -cf tuwal 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 energyxwkz1 ttib55whmuj/b 8, ,8w z of KCl is 4.43 eV. From the result of Problem 1, estimate the contribution to the binding energy of the repelling electron clouds at bw58 ti x/zbk jm1,uw5t,z8whthe equilibrium distance $ r_0 = 0.28\ \text{nm} $. $PE_{\text{clouds}} =$    $\ \text{eV}$

  Estimate the binding energy of e*kzhqls +c)7 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 expeq7ucnl -dbf;2 2j4sf trimentally 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 to2tld7;n - jfcu42f qsb 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 text for the states in.v1zg 2.gjdqo the formation of tho q2g1j. zvdg.e $ \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.i)w:hdtz cz rp)z;m.cgq p74 $ \frac{\hbar^2}{2I} $ has units of energy.

  The so-called “characteristic rotationa rcbz0ksk6 8;wl 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 ro.3vc0ua yf)p.79eu ob1kmfp ztational 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 atom /.leu 3cixli/k)h0a .ga oev8s 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 the NaCl molecule given that three successive wa..wbji(; o+w tm ;memfvelengths for rotational transitions are 23.1 mm, 11.6 mm, and 7.71m (.+j.wfm beit; omw; mm. $r = $    $\times 10^{-10}\ \text{m}$

  (a) Use the curve of (Ft f 7q k580spc.chq5xrig. Below) 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 cryx:pj81 f nto;vyv7l;istal is 0.24 nm. What is ttjn;fp yv7v:xi81 ol;he spacing between two nearest neighbor Na ions? D =    nm

  Common salt, NaCl, has a den wnlav9r b 8-t*1wi1wcsity 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 dens1gsf/wt46o-/ot2 kg q t vul-kity is $ 1.99\ \text{g/cm}^3 $. $s$ =    nm

Explain on the basis of energy bands wzu d0* -f:ktxfhy the sodium chloride crystal is a good insulator. [Hint: Czt -:k*ufd xf0onsider the shells of $ \text{Na}^+ $ and $ \text{Cl}^- $ ions.]

  A semiconductor, bombarded with light of slowly increased freq1*xhy7xcm1u4xqw yjs4gt3n,es k2) vuency, begins to conduct when the wavelength of light is 640 s3,1x s )wjg7 mvuhxte 2yx1 n*qc4y4knm. Estimate the size of the energy gap $ E_g $. $ E_g $ =    eV

  Calculate the longest-wavelength photon that can cause an electron in silicon apqdax2 i0 h0kt*c(l8ud8ve ; ($ 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 idr 7s4 ra m/f(-a v-gg+ovv8tgn germanium is 0.72 eV. What range of wavelengths can a photon have to excite an eles g gg-vaadt74+mrv( fo vr-8/ctron from the top of 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 ard86n2qbmwh+)8 bav6f:lv wm ae $ 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 w gizkhy)oxhu/fvuv-1/- d9i9n b1 2rpd2so9oith phosphorus so that one silicon atom in on9gs-/v fbh 9zov 2dx h)i1/ uui9kdp-2y1ro $ 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 .wi.+ abuh:qx8hxo/z6q/ y vwLED radiate if made from a material with an energy gahw+hyazo//v.uq6: 8. bxx wiqp $ E_g = 1.4\ \text{eV} $? $\lambda $ =    $\mu m$

  If an LED emits light of waj* ) :fyi+mzkznk( vz2velength $ \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. Be0 c cgyk-2kaio(9z2mn low), is conneak9-(2g i 2ynkzmc oc0cted 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) i 9.yta0 uve1x oyvrq8dr32c/ xs 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 fm yp ;b1(r 6uqjl1g/ywunction 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 thhg+gmzw7o acgt, ovo7 5n/f+e / f87fye average curraev +fn /877ggc7mt o+ fgy5zhf/ ,oowent 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 lwmzypi) g* 52current only if the forward-bias voltage exceeds about 0.6 V. Make a rough estimate of the averz2 lyp*i)5mwgage 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 voltag,ltr,3dc1a4au19 w ko5inqd oe is to be rectified with a full-wave rectifier (Fig. Below), whe4ulcrk39,5wa 1oai 1qt,ondd 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 relati0jo8u6fvf .ox fo-+ebonship 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 (m 22m wdd0uxi$ \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 ener)u k-e/q/osjugy 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 separatij6 nx+ucqmxodzk 5 4*kt m;8a*on 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 with a weakly bound cubic lattice, with eacac if 4 o,mtcy(3/hozsvk41)b w 2zu7mh atom connected to tmhy 3mzbzo4),iw vs 2f/ 4cakc1o(u7six 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 activatl 7b 7rrv:x2p-x xnbgo2)zs8v ion energy of 1.4 eV. When the molecule is disassociated, 1.6 eV of energy is relx8bvsrzronbg l77x:2 v2p) - xeased. Draw a potential energy curve for this molecule.

  When EM radiation is incident on diamond, it is found that st aj3j,h *ei/y+jwz-light with wavelengths shor j3y-j,jz wat/ s+h*eiter than 226 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 px6jg sh4gz4q)w3 .pf IR light. If the detector on the TV set is not to react to visible light, could it make use of silicon as a "window" with i4p 64g3p szfjxhgq.w)ts 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, assume that tht,quc :m1c2k xrpru p3t3.. velq8d6we "extra" electron moves in a Bohr orbit about the arsenic ion. For this electron in the ground state, take into account the dielectric ttxpl, c2.uv1d m6r3qckqp8:.3ewur 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 wmqll+px u*5ze;ift9j)gv *ol9 ,tr -has wavelengths shorter than 1000 nm. For a solar cell to absorb all this, what energy gap ought the material havv5q; tjg zuf9ewi l x*)lo*9plm+-t,re? $E_g$ =    eV

  For a certain semiconductor, the longest wave.taj:mf- ku4cz /rc u0length radiation that can be absorbed is 1.92 mm. What is the en/uj.crkat f:z0c-u m4ergy gap in this semiconductor? $E_g$ =    $ \times 10^{-4}\ \text{eV}$

  Green and blue LEDs became available many years after red LEDs were first deveaxcfv - 1kr.l,loped. Approximately what energy gaps would you expect to find in green (525 nm) and in blue (465 nm)f,-vcxk lar1. LEDs?
the green $E_g$ =    eV
the blue $E_g$ =    eV

  A zener diode voltage regulator is shown in (Fm.0hw./ f1- pvfddcptig. 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?    $\ \text{k}\Omega \leq R_{\text{load}} < \infty$