What type of bond would you expect foruru5 /aqs)j9y
(a) the $N_2$ molecule,
(b) the HCl molecule,
(c) Fe atoms in a solid?

Describe how the moleculehm0:sxv)+qagc9i z3qv .vf(e $ \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 molecul)35netit4meh8 glk0 d e $ \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 divizie)e 18r 2xc7j2lcdpded into four categories. What are they?

  Would you expect the l5 l9:wpb4:q ifpc 6kwmolecule $ \text{H}_2^+ $ to be stable? If so, where would the single electron spend most of its time?{yes|no}

Explain why the carbx+ 3p:hw:n qvton atom ($ Z=6 $) usually forms four bonds with hydrogen-like atoms.

If conduction electrons are free to roam about4g1vohp7man5 k b8a0v in a metal, why don't they leave the metal entirelynkvo417h0 vabmp 5ga8 ?

Explain why the resistivity of metals increases with tempe- gx;t6k hw0-z3 dkkbdo l4dt.rature whereas the resistivity of semiconductors may decrease wigwh-d3-;dt .kt0 kkx4o6d l bzth increasing temperature.

(Fig. Below) shows a "bridge-ty;5 nqrx 6r.cywpe" full-wave rectifier. Explain how the current is rectified and how currentxnryc6wr5q; . flows during each half cycle.

Compare the resistance of a pn j(zpnh +comfkw( n2a-xco 17c2unction diode connected in forward bias to its resistance when connect2cx2(-wn+kc mpzhn oaof(1 c 7ed in reverse bias.

Explain how a transistor could be used as a switch.)qinhn8fi)q mp) d3-l

What is the main difference between n-type and p-type semicond ebj(l /yyu/,f.j x6zvuctors?

Describe how a pnp transistor can operate as an ampli vp5bz 9voc4o5+h m3rkfier.

In a transistor, the base-emitter junc*i l12mhrdr1 -4lsie q1db9ua5 mtro swa.- 3ktion and the base-collector junction are essent14sr.9 o i1- eti1hu2drsr* abl5md-3wlakmq ially diodes. Are these junctions reverse-biased or forward-biased in the application shown in (Fig. Below)?

A transistor can amplify an electronic signal, meaneis k28z.2y -5gt*rwjx*vxc.)aqn lz ing it can increase the power 52tg8xilz)- vz aw*yk 2.. *qxcesrjnof an input signal. Where does it get the energy to increase the power?

A silicon semiconductor is doped9** w vnl)oneywp+1. lfczz1k with phosphorus. Will these atoms be donors or acceptors? What type of semiconductor wi1*l.nzkv)1 9z+ owynw*fcl pe ll this be?

  Do diodes and transistha 34eprhb :rnx( rb0*ors obey Ohm’s law? Explain. {yes|no}

  Can a diode be used to amplify a signal5nwxs.c( 0,0k run+yaa5opae? Explain. {yes|no}

  Estimate the binding energy of a KCl molecule by calculating tyt e)u+h35 viz1v1dyg he electrostatic potential energy when the iy315 euy +)zhvvdt 1g$ \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. From the result of Probvs9qy035eke olem 1, estimate the contribution to the binding energy of the repee9s 5 ykv3e0oqlling electron clouds at the equilibrium distance $ r_0 = 0.28\ \text{nm} $. $PE_{\text{clouds}} =$    $\ \text{eV}$

  Estimate the binding energy of tcw)2g dxs8tjbe 2.u) uhe $ \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 /p ozplrzm9,6er mole, and then the binding energy in eV per molecule is calculated from that result. What lz9 morpz6,/ pis 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 8v51 sdf copnlgf*q 4/similar to that in the text for the states in the formation of the /nv fo45gdcq f*8spl1 $ \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 quantitoza9 gq gpe5,c9:d33;hdoirwy $ \frac{\hbar^2}{2I} $ has units of energy.

  The so-called “characteristic rotational enerlki9yib+t 0al 8a1 mz2gy,” $ \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 rotationmo+uu9*3l*h;hlqj drgr m3b) 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 of H atoms in the 1uegva *x-o/j 7q,pic $ \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 b13p 9vtijwthb bp4gx j+ 9(d4given that three successive wavelengths for rotational transitions are 23.1 mm, 11.6 mm, and 7.71 mm hptbwgb9j9itv(4 bdjx3+14p . $r = $    $\times 10^{-10}\ \text{m}$

  (a) Use the curve of (Fig. Below) izq1i+9ln -dk9y* eupm+go4a5zgc93kg -f zpto 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 crys1va -z9 16zrukkif hj:tal is 0.24 rz9k 1i: fuj6v hzka1-nm. What is the spacing between two nearest neighbor Na ions? D =    nm

  Common salt, NaCl, has a density nqx+lw,i49cj 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 KC4od eoew)znhz. ( fz0)l whose density is $ 1.99\ \text{g/cm}^3 $. $s$ =    nm

Explain on the basis of energy bands why the sodium chloride u c1gu36xqn4xcrystal is a good insulator. [Hint: Consin6xqu3 ucgx 14der the shells of $ \text{Na}^+ $ and $ \text{Cl}^- $ ions.]

  A semiconductor, bombarded with light of slowly increased frequency, begins to c ur9io(y:f8 gsonduct when the wavelength of gy o rs(fi9u8:light is 640 nm. Estimate the size of the energy gap $ E_g $. $ E_g $ =    eV

  Calculate the longest-wavelength photon that can ca0fk(vy m:2wxs use 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 1pu kj3 6((fj9angfxre zz s5:germanium is 0.72 eV. What range of wavelengths can a photon have to excite an electron from the top of the valence band i9jxnzerpj a ((fs3f ug:61 z5knto 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 areitn4 53ejd w234 poykj $ 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 do:dgm1oa3 hi)4;z ww wjped with phosphorus so that one silicon atoawmoj1hw dz)3i:4gw ;m 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 LED radiate if made from a maz,v;qg y;-(zlr)ns ij terial with an energy gagr,nyj;-q;(iz sz lv)p $ E_g = 1.4\ \text{eV} $? $\lambda $ =    $\mu m$

  If an LED emits light of waveleng0y,h0h5qv jozti(d :nth $ \lambda = 650\ \text{nm} $, what is the energy gap (in eV) between valence and conduction bands? $e_g$ =    eV

  A silicon diode, whose curre)n ; .ed3icua.; wvxwynt-voltage characteristics are given in (Fig. Below), is connected in series with a bat ;.y3.uaevxww d;i)nctery 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 :w:jvul,.os f 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 function of currenth,e4k2n+i6ytt hh1/vkg c q2 p, for $ V > 0 $, for the diode shown in(Fig. Below).

  An ac voltage of 120 V rms is to be rectny/pq/pd1c f vo5/,2gucvrt.ified. Estimate very roughly the average current tnrc./p1pv fy gqv/co25/ud ,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 current only if the forward-bias voltage exce 1af9 eaq,/z;f.zuuyjgv 5 3g5eg,jlleds about 0.6 V. Maa g5yfz1le9fa;gejjvuq , ,./g5u3z lke a rough 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 rectified with a full-wav +vgo(hvzwn1 unrmox)*-k3b 1 e rectifier (Fig. Below), 1 v(h-*)omwbg 3oruznk1+x vnwhere $ 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 ruo4c)obo9t(y)x 88uhq3 o0qjwedf 4velationship 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 ofllv89k*n4qygu+.z o,j ;ilqe yw3p) t 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 energy of an atom or moleclkiylhjq w qh1d8el h )17j .p, rp4;-wuwh:u:ule 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 KF6o;dr6 ngyimaq;d .h(wr*)ly , the separation 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)-o3(mnmu e( qw ses-p cubic lattice, with each atom connected to six neighbors, each bond having a binding ensepm q(o --3nsu) ew(mergy 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 e0k36ka5l wf tthe molecule is disassociated, 1.6 eV of energy is released. Draw a potent0 alwkt35ek6f ial energy curve for this molecule.

  When EM radiation is incident on diamonoi,pb1 cfx7 ,u u56rssd, it is found that light with wavelengths shorter than 226 nm will cause the diamond to conduct. What is the energy gap between the valence band and t, 5 u6birs1cfsuo,7pxhe conduction band for diamond? $E_g$ =    eV

  A TV remote control emits IR light. If wo /dj8an, ttf5ja40ithe detector on the TV set is not to reactwtj j08 adf5,oa4n i/t 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 that t6xr oc 10gdjul2 zb81rz .tg 38t5kul jk8*qcbhe "extra" electron moves in a Bohr orbit about the arsenic ion. For5 jjr z b.6x2*c1t8 tkrkguo80dl8 l3bgucq 1z 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 shorter t-vayu /3wl- hphan 1000 nm. For a solar cell to absorb all this, what energy ga3hv l-/uwy-pap ought the material have? $E_g$ =    eV

  For a certain semiconductor, the m/cn0 .qaj30 bqfv-mjlongest wavelength radiation that can be absorbed is 1.92 mm. What is qj-0 mfa03bcj/ mn .qvthe energy gap in this semiconductor? $E_g$ =    $ \times 10^{-4}\ \text{eV}$

  Green and blue LEDs becamj-,xckoa2mji) (j/qae available many years after red LEDs were first developed. Approximately what energy gaps would you expect to find in green (525 nm) and in blue (aijjxom ,jc2a(q-/ k)465 nm) LEDs?
the green $E_g$ =    eV
the blue $E_g$ =    eV

  A zener diode voltage regulator is showi,f5esgq :mk (n 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?    $\ \text{k}\Omega \leq R_{\text{load}} < \infty$