Phy207_Final_Spr07

Phy207_Final_Spr07 - Physics 207 Final Exam Spring 2007...

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Unformatted text preview: Physics 207 Final Exam. Spring 2007 Problem 1 (25 points) Photons with energy 4.70 eV shine on an aluminum surface. The energy required to eject an electron from the aluminum is 4.20 eV. (3) What is the wavelength of the photons? (5 points) (b) What is the kinetic energy of the fastest electrons that are ejected? (5 points) (c) What is the kinetic energy of the slowest electrons that are ejected? (5 points) (d) What is the stopping potential for this situation? (5 points) (e) What is the longest photon wavelength that can eject electrons from aluminum? (5 points) ox) E4: “‘0 = [1; “'9 )\ z l1Es : ié-éw’opfi)(v’w°6} = ($70,911) ( i .6)! “inf/W) L) Ei :i‘iK +W a Ek I E‘- ‘W: (9,706U—“i.1o€£/) :@ Wit-d I“! b“ {we ele than -"—‘— fioox 4;,“ng- kmeJ'W W’fiY I. can MN 0% PM we “ti- "3‘ E 1 EL: F i-t elet'i'n-A S 0 9y r [Mir 159'“ ax. C) 5(swP5'L Eif’c‘F’O’l (09¢? RH hating Nata/W OM. 4-11! and Jugi» bawdy {PAL/*8 Aimmrqu—Dfik :@ Inti.‘ A) ‘7. "‘79 (Flu kthéil'c (MA/5y afl pSfQ‘LPd P/Pc-Loifll may: [‘3 (onlzrwf-(oi Lu w-quflwu FAQ/3y and U1» fleck“ 5‘0’95 __ E g x lo Usiflo “- kw 7— ,1':D,iq;: ii '50 Ti 0,; LL'7er-‘ffiogl/ (i _ I; F.- g : — . Ofi/ _‘S_O ,9 M Jfl 6) .. in c. __ [2311/ 4 ’ T“ - O tw n WNW, fifi”? firing bawriy FjWCJ‘pg ,, 14 n Han-y? (We?) .____ 7 >‘maxg '__C: i t ’* 9} -rfi ) Lf—J W Tm.) w) Linc/o my Place your answers here (a) Photon Wavelength=fl_—F____—W (4) {L\ V:--“:.. n-hnm- nrnilflnn‘l :Jnn‘I-nll nlWAna— Physics 207 Final Exam, Spring 2007 Problem 2 (25 points) An electron is trapped in a one-dimensional infinite potential well that is L=3OU pm wide. (it) Find the ground state energy and energies of first two excited states. (6 points) (b) What is the wavelength of light emitted at electron transition from the second excited to the first excited levels? (3 points) (c) What is the mathematical expression for the wave fimction of an electron in the first excited state? Recall that the normalization factor for all wave function in a one-dimensional infinite potential well is A = (/2/L . Why is A important? (4 points) (d) Sketch the probability density (not the wave fiinction) for the electron in the first excited state. In which pan(s) xumcly in the well is it most unlikely to detect an electron in the first excited state? (6 points) (e) What is the probability that one can detect the electron in the first excited state in an interval between x = 0.5L and x e 0.75L? You should be able to determine this probability by carefiilly looking at the plot you made in part (d) but you can also calculate the answer, for which the following relation could I: . be helpfiJl: Isinz (ta/)4}; = l[fl— Sln 2C? . (6 points) a ,L c 2 4 a v A I L (I -4, “itsrawi- % L1 '1 :. (“we-“Ml 11 2:6,.7MD‘MSFH.” 9U. "‘ —‘€—(”l.llflo"1‘)(’Soorro~lt}1 ' ' ' 'L 1 h_.._.._._ - -. _ F _ — - , ,, _-. “5r: ' a?“ '1 ‘l "e. ’°..‘..‘:?‘..£::?i:lt-‘6 End _ h} [L '51" :[Qo’gfiu'o‘lt‘j 37.7195: (f C 4YmL __...w 5) GE 1 Emu: — Elsi : (C'Oero’hj —?.¢%”e"q_5) I 53-53% )1: bf :[Jlg‘ir‘w‘mi 4?:(6 1°16 ‘35. W...— M J? gli/x a“)? @7qu slatted/two” x} ‘1 X n _ . __-I . A“: [E l‘g I‘Mftw in“ ‘f‘ grg/‘gfie H's if'r'} Std/f JrMA-L 4.x“, Fwd!“ élflvfi/ {S rovffr'i'ly h_IVM4fl?P# —-——9 +4“! di/olbfifjih'4/ LL19 €I€c{,ou1 Somewhat/r 11‘ liar (ANN/(#34 1",! 1 Sifita‘ix 2? A) 4+ m I w Frey/‘— . 6):.0 n+><::0;,SL/L H—“Zr. "Fl X 3 X:L_ x 0 xti ¥=0 H Z ISL. 36'— ’ .I r V “mt ) 6') @(-§"— 1/: X (5 figL): ’LLf ( f 9’ ioiai 4”“ “W4” ("’1 V' S " r7$L _ ._ ’L .1 ’l __ l , _ I I L _ g :Sln h EU {if-L_%H(({EI,7§L§}-§§'€L_§ihk?.§}g L/ H led wi— _. .. _1_ L! ‘ ' ' 31‘. = Place your answers here (3) Es: E first mired = s E second mind = _________________ Physics 207 Final Exam Spring 2007 Problem 3 (25 points) Consider a square oorr (two dimensional infinite potential well) with widths Lx = Ly =L=20.0 nm. (a) What is the energy of the lowest energy state for a single electron in the corral? (4 points) ([1) What is the energy of the second lowest energy state for a single electron in the corral? (4 points) (c) What is the energy of the third lowest energy state for a single electron in the corral? (4 points) (d) What is the energy of the lowest degenerate (more than one state with the same energy) level? How many different states make up this degenerate level? (4 points) Four electrons are added to the corral. Include electron spin and recall that electrons obey the Pauli exclusion principle (e) Make a diagram showing which levels the electrons occupy for the lowest energy state of the four electron system in the corral? What is the energy of this state? (4 points) (I) Make a diagram showing which levels the electrons occupy for the second lowest energy state of the four electron system in the corral? What is the energy of this state? (5 points) __ __._. ._.n_._n., I 0*) Emmi: E (mod-amiss! : '4ku QMLFL K1} ._, 'd E -ew.;_--....,:{,___j .L _ o— 1 ‘ h I .— F I K" L 1 (platens xLi-quwmw ML t S) q E’tml ": L‘q (fills) e“ @W‘Lq (st fl) E1“; 1" lESrmfio’l l 3) EU‘L lav-(5f e X 9 1‘3 _ fin w 14 1-. or 42— - 155W 4- I 5.5+ +1613; afield“ Ext ‘3 Place your answers here := M-fl/ (a) E(lowest) = (4) n \ HIAl'Ii u .\ I11 Physics 207 Final Exam, Spring 2007 Short Problem S] (15 points) The equation of a traveling transverse wave is y z (2.5 mm) sin[(25 m")x + (400 s") z] (a) Calculate the speed and direction in which the wave propagates? (6 points) (b) Sketch wave at t= 0. (4 points) INA! (“441,6 mm “4|. ole Amo‘ W mm L! 91391 (c) Calculate the maximum speed along the y—direction (transverse speed) of particles in the wave. (5 points) ‘ In —)( Ala-ctr», '1 Fl. _._J Physics 207 Final Exam, Spring 2007 Short Problem 32 (15 points) A point source emits sound waves isotropically (equally in all directions) at fi'equency 3 kHz with an average power of 133 W. (a) What is the wavelength of the sound waves? (3 points) Tfi Ihé"§ource‘?"f4~p0i‘rrts§ (c) What is the intensity of sound 1.2 m away flow the source? (4 points) lye sou . (d) What is the sound level in dB 1.2 m away from the source? (4 points) _ (-5 M A— s] «Ox; '1; up ><— 5:: H5 3 /s j Mme 76 By forbl/S if I A: Cm ( 9A1 * “1 I W A 2 Win" L —-’L '- éE—F —— 127.1(1) “if-{:13 A7— ‘47:- ([,’_LM\L Lew—m Final Exam Short Problem S3 (15 points) An unpolarized ollirriate laser beam (non-diverging with circular cross section) with average power 45 beam radius of 2.5 mm is incident on a series of two polarizers. The polarizer axis of polarizer is in the vertical direction, while P2 is rotated by 30° from vertical. (3) What is the intensity In of the laser beam before it goes through any polarizers? What is the initial electric field E0? (5 points) (b) After the light passes through P1, what are the intensity I; and electric field E}? (5 points) ((1) After the light passes through P2, what are the intensity 12 and electric field E2? (5 points) 30° / l/_ _ - “' # V/ol .— _L. "if -__—_ 3 1)) Tr ' Ll_° I WW0 14m aways @1619 “Low: Odie 7é0" t: :: JETHj _ “h”? “" /°fl h Meow"? fo—FI'JWcaTal—‘I ._. _____,___ _ I I ‘h I.“ ‘— U 2". ELEV/ML [:31 0i V/ m "kiwi 1 Rue/Fm H V? H . . . __ E0 Final Exam Short Problem S4 (15 points) A thin lens with focal length f=~10 cm is used to produce an image of an 8 cm tall object that is 15 cm to the lefi of the lens as shown in the figure below. Tick marks in on the optical axis of the figure indicate 5 cm increments. (a) Draw 2 principal rays in the figure below to graphically determine the location and appearance of the resulting image. (6 points) (1)) Calculate the position of the image relative to the lens (how far to left or right of the lens). (5 points) (c) Calculate the height of the image. Is it real or vi n 31. Is it upright or inverted? (4 points) Uta; inqj i CD “40‘ W105"- myS v1.4 «(Jenn/V f @hSQtIr-S Lin-“ought {‘W‘dijf (M>O / and “(30 W6“ Illa Ayah!) Final Exam Short Problem SS (15 points) The wavelength of yellow light in the glass with index of refraction 1.52 is 388 nm. Find (a) Speed of the light in glass. (?i points) . ‘ a (c) Wavelength of the light in air. (3 points) (d) What is the range of angles (minimum and maximum) with respect to the surface normal for which this light within the glass will be totally internally reflected (TIR) when striking the glass-air interface. (6 points) q __ _______ a) "1/5: .9 -: 3”” : lfil’Hiocé‘n/sf. m r ______J flfll__ gg’r (“Jo 5w (Ff-Ewan? w mm i» saw“, mom“, 1.5m is Many New") Ffflleotrd Final Exam Short Problem 86 (15 points) Monochromatic light of wavelength 441 nm is incident on a single narrow slit. On a screen, the distance between the econd difi'ractlo 'nimum and the central maximum is 1.50 m, and the angle of diffraction 6 of the second minimum is 043°. (:1) What is the distance of the screen fiom the slit? (4 points) (b) What is the width ofthe slit? (4 points) (c) What is the ratio of the intensity at the point 2.0 cm away from the central maximum to the intensity at the central maximum? I (7 points) in J Wu H i not In itfiow t, ) ok- Mable )x ok:T[ &:(L'q/"=— 7/“ S’Mé ' T «a A: Q} __ ’LWWHO'W 5M9 Sim-(3f?) :(|I|%X/O‘L{M C) 97- _...r 0 - . a“ 1': lion __ .s ._ --____._1_,_iiz‘”‘ i W a} 41, #53»! my '3 0L : Tl (1.19, rag-“q 5”} (gamma-2,1,5} WI“! Ht {0" a M I kgt): IM (Sim ['gqsfljl k20.9—05— rad 0.50’3md 5"" (at) " E.“ aaflltcs 1:01th a Place vnur answers here: '-n.__ -—-—-._h ...
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This note was uploaded on 04/03/2008 for the course PHY 207 taught by Professor Berim during the Spring '08 term at SUNY Buffalo.

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Phy207_Final_Spr07 - Physics 207 Final Exam Spring 2007...

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