What type of bond would y o4ezgn2p-t sc-h4xu,ou expect for
(a) the $N_2$ molecule,
(b) the HCl molecule,
(c) Fe atoms in a solid?

Describe how the molecule 2+9nhjx c 83 b:8gmgqd om9gou$ \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 1) 2vzx7ec :vd3ha w3k 77knc3eamjjf $ \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 divid/ j o8edp mew7,;ld;tlt lre7u3bt,bjz.2 gz5ed into four categories. What are they?

  Would you expect the molecule6h1-m8svbjnhp 7 a+(t(-dqf cd li r1x $ \text{H}_2^+ $ to be stable? If so, where would the single electron spend most of its time?{yes|no}

Explain why the carbonduq3r-x 3 x8(es+oeg z atom ($ Z=6 $) usually forms four bonds with hydrogen-like atoms.

If conduction electro x kd5 ls6swr.bv4a4e1ns are free to roam about in a metal, why don't they leave the metal es6b.ws5v ed 14xlrak 4ntirely?

Explain why the resistivity of metals increases with tempera*kxb44y;o;f5 vuw2g kzif:m xture whereas the resistivity of semiconductors may decrease with increo 4kf ;2xw* z4 xf:v;uyigmbk5asing temperature.

(Fig. Below) shows a "bridge*a., w 5p 0wr;zui:m7kbyvyfvt5 b0so -type" full-wave rectifier. Explain how the current is rectifieks wzypb ib0; 0.v:yoru,a7vf 5wm*t5d and how current flows during each half cycle.

Compare the resistance of a pnl*-)y:vl h6tbr* l3 qov* gcrq junction diode connected in forward bias to its resistance when connected in reve 3)l*by6rl*hl: co-rg vtv qq*rse bias.

Explain how a transistor could be used as ad5gn:,a xvf2g switch.

What is the main difference between n-type and p-type(+btf cn drmvc.(rw*2 semiconductors?

Describe how a pnp transistor can operate as an amplifiev d+(++ijl1g64i yop vuotu9kr.

In a transistor, the base-emitter junction u5kh b4vfi9/kand the base-collector junction are essentially diodes. Are these junctions reverse-biased or forward-biased in the applic4uk /59vfbk ihation shown in (Fig. Below)?

A transistor can amplify an el1o gw pr2. :hv:0hknusectronic signal, meaning it can increase the power of an input signal. Where does it getp: gkow n2sv:h1.0uhr the energy to increase the power?

A silicon semiconductor is doped with phosphorus. Will these ac3 exhi1 gib/8toms be donors or acceptors? What type of semiconductor will this /bhx 13gei8i cbe?

  Do diodes and transistors obel .mda. x4 q h9,lqrs xw4xjc13pzimt9, s/hi*y Ohm’s law? Explain. {yes|no}

  Can a diode be used to amplify a signal? Explain. {yes|nozj qkk;mo a9 x:k)-/jm}

  Estimate the binding energy of a KCl molefsy;d , 3 p2zrmi8at+tcule by calculating the electrostatic potential energy 8p t2 t;im3rsad+yzf,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. sz iy*2,phrnsq 4 7dx q(7uh1rFrom the result of Problem 1, estimate the contribution to the binding energy of the repelling electron cloudqrdpin xss *h1(q z,r7uh4y7 2s at the equilibrium distance $ r_0 = 0.28\ \text{nm} $. $PE_{\text{clouds}} =$    $\ \text{eV}$

  Estimate the binding energy oe62r zvb.y3zx f 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 p *)9sb e9 puowta(wke9er mole, and then the binding energy in eV per molecule is calculated from that result. What is the conversion factor in going from kcal pe wa (9*9 )wus9eboektpr 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 fj9 ro4gjppq1ioi 4w1r,1qz1that in the text for the states in the formation of thez1po14wj1rq fpgi4 io q1j,9r $ \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 quantity1q(dcjz+va6myn g+ j: $ \frac{\hbar^2}{2I} $ has units of energy.

  The so-called “characteristic rotationq sw**s8 h)oypi6j0mpn .g+-x /nagn nal 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 rotation qfi*jdn1 -on4 2ooqk csg(l6(al 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 o2i n0j6nndo ;x .wgt;yf H atoms 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 suwbg;6 xc v71y5vfr+4tlx8 h pqccessive wavelengths for r q+;lg pvv bh6trc8x51 fw4yx7otational transitions are 23.1 mm, 11.6 mm, and 7.71 mm. $r = $    $\times 10^{-10}\ \text{m}$

  (a) Use the curve of (k6e)lyc ,s50q uy1v rzFig. 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 cryst*0kwdo(i wr j6al is 0.24 nm. What is the spacing between two nearest nekjw0 irw6o*d (ighbor Na ions? D =    nm

  Common salt, NaCl, has a s -5m6y /utljxl v 4ym/ u)y5sgta3/hklh;sn;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 whose density ykvvf pvf/oiht 1s*.oku1 61( is $ 1.99\ \text{g/cm}^3 $. $s$ =    nm

Explain on the basis of energy bands why thp,xh;h ejyn)0 dvd 80je sodium chloride crystal is a good insulator. [ ev8nhh;0, )jp xd0jdyHint: Consider the shells of $ \text{Na}^+ $ and $ \text{Cl}^- $ ions.]

  A semiconductor, bombarded with l0 0ren0 b xdcz4cx)fe/;vqblg zv6+7light of slowly increased frequency, begins to conduct whe x0 n0gzbld6lf 7;e+4vq0rc/e )zbcxvn the wavelength of light is 640 nm. Estimate the size of the energy gap $ E_g $. $ E_g $ =    eV

  Calculate the longest-wavelength photon that can cause at)2x b1,d-8szsy y bnbn 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 ge16r v (mtq+k4 siqbpifg0v2o3rmanium is 0.72 eV. What range of waveis3io2 + v(vpmbfq61k0 4trgq lengths can a photon have to excite an electron 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 areiif*ohvq0 kh b 13 f1dlis3yk0;e )o(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 with9d kvo*s4xo1vd0 v ,uy phosphorus so that one silicon atom in* 0osu4v9vk1ov yd d,x $ 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 willfz,z5ag+ie e4lt 42c11dlz oe an LED radiate if made from a material with an energy gap1c zza1zof44 ,it 5ede2gel+ l $ E_g = 1.4\ \text{eV} $? $\lambda $ =    $\mu m$

  If an LED emits light of wavely ssn3*6x(/h3p urbifength $ \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 charact lfh-jqbik xr4qb+9;. eristics are given in (Fig. Below), is connected in serie;.4x i fk9bbr jl-qqh+s 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 iz tkq.8lmr ;k;n 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 acblxhd tqx+ ,,i,6*dp s a function 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 rouguh/ai)k 0:9f3q9+amk6re g/5ki bpbpo6xap hhly the average current i9 f:9b i+r/hb5aegpkk 6)xi 0uh 3mp6aokq/ pan 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 forward-biac (lrje.c 4pogz7a1x *s voltage exceeds about 0.6 V. Make a rough estima .cc4eg1x(rop*zla7j te 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 rectified with a full-wave rectifier (Fi*4ms-bn(u eedg. Below), mnb (eus4 -*dewhere $ 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 relat )gduw;9s2h7yzyt u9c ionship 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 energffzxe7iz 4* rlb;rzp0 n2x9o+y 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 kinetic energ)ka1ezvhxtbgv,dx: l /u*0z-. .ww xby 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 h5a9,e(v/ ju jee8; ji v32eo gonfv3kis 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 eachyb 2c(yfnlj) fi/o1v3 atom connected to sixnjy v3clyfb1/ o)2if( 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 h mgn )gijt-69nave an activation energy of 1.4 eV. When the molecule is disassociated, 1.6 eV of energy is released. Draw a potential energ6j)nt-nm gig9 y curve for this molecule.

  When EM radiation is incident on diamond, it is fo l6oez9.cev 9jund that light with wavelengths shorter than 226 nm wveoj.9 96l zceill 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 emits3o c5bdot05oh IR light. If the detector on the TV set is not to reacoo35 ch0 odbt5t to 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, assume tha g8 71u7nah/hbtfg0k*oocin ;t the "extra" electron moves in a Bohr orbit about the arsenic ion. For this electron in the ground state, take into account the dielectrio1on/ba t*0;n kgh7u fch 7i8gc 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 radiatiod7uu)f0 arg ,tn has wavelengths shorter than 1000 nm. For a solar cell to absorb all this, what energy gap ought the material haveftud,u g0ar7) ? $E_g$ =    eV

  For a certain semiconductor, the longest wavelength o/lcclg:++ cmradiation that can be absorbed is 1.92 mm. Wha: ocl cmc+g/+lt is the energy gap in this semiconductor? $E_g$ =    $ \times 10^{-4}\ \text{eV}$

  Green and blue LEDs became available many years afvz+9/ caaq4 d dvm)vd7ter red LEDs were first developed. Approximately what energy gaps would you expect4 qdcav97dzv/d+vm) a 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 regulator is shown in (Fig. Belh;ykuc j)onw.pvzb003 yy- al q96eu6ow). 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?    $\ \text{k}\Omega \leq R_{\text{load}} < \infty$