Chapter 12 Review, pages Knowledge

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1 Capter 12 Review, pages Knowledge 1. (d) 2. (a) 3. (d) 4. (b) 5. (a) 6. (a) 7. (a) 8. (a) 9. (b) 10. (b) 11. (d) 12. () 13. (d) 14. True 15. False. Wen two lassial partiles approa ea oter, one partile annot pass troug te oter. 16. False. If te frequeny of a ligt soure doubles, ten te energy of ea poton from tat ligt soure will double. 17. True 18. False. Plank s onstant is independent of te metal tat is used. 19. False. Te potoeletri effet is an experiment tat demonstrates te partile nature of ligt. 20. False. Plank s onstant as units of energy-time. 21. True 22. False. As te temperature of an objet inreases, te wavelengt of maximum radiated intensity will derease. 23. True 24. True 25. False. Superonduting quantum interferene devies interpret brain wave signals and onvert tem into instrutions for operating artifiial limbs. 26. True 27. False. Two up quarks and one down quark make up a proton. 28. True 29. False. Partiles in te lepton family are fermions, not bosons. 30. (a) (v) (b) (iv) () (vi) (d) (i) (e) (iii) (f) (ii) Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-2

2 31. Te double-slit experiment an be used to sow tat matter as wave-like properties, just like it is used to sow te wave nature of ligt. To sow wave-like properties of a partile, one sends a partile beam troug te slits instead of ligt. Te partiles must ave a de Broglie wavelengt of about te widt of te slit or larger to sow te interferene effet. So, slow-moving, not ig-energy, partiles sould be used. 32. (a) Te essential features of te potoeletri effet are an inident soure of ligt, a material surfae, and an ejeted eletron. Tey are related as sketed below. Ligt of frequeny f strikes a surfae (typially metal) of work funtion W, and if te frequeny of ligt is su tat f > W, an eletron gets ejeted wit speed v. (b) Ligt wit a iger intensity does not provide more kineti energy to te eletrons beause inreasing te ligt intensity just inreases te number of potons itting te surfae; if te poton energy is less tan W, no eletron gets ejeted, regardless of te intensity. Tis is beause te poton ollisions are single events, and tus te individual poton energy must itself be large enoug to ejet te eletron. () Te kineti energy of te ejeted eletron is less tan te poton s energy beause of onservation of energy. Te eletron is attaed to te surfae wit energy W, and tus te initial energy of te system equals f W. Te final energy must be te same, and tus must be less tan f by te amount W. Understanding 33. (a) Money is quantized just like energy. We an spend money in units of a ent, but not a fration of a ent. All tings bougt and sold ave a prie in units of a ent or multiples of a ent, su as a dollar. (b) Te quantization of money is analogous to te quantization in quantum pysis. Money gets exanged in units of ents. Similarly, energy is exanged via ligt in units of potons. In te potoeletri effet, potons of energy less tan W do not remove an eletron from te metal, no matter ow many potons strike te surfae. Similarly, if we go to a store tat sells widgets for amount W, ten only ustomers wit money exeeding W an remove te widget from te store, regardless of te number of ustomers entering te store. () Answers may vary. Sample answer: Many oter tings we experiene are quantized. Brik ouses are built in units of briks. Sool progress is measured in units of redits. Wareouses are stoked in units of items. Bread is used in units of slies. Time periods are given in units of years, days, or ours. Digital loks give time in units of minutes or seonds. Companies ire work in units of people. 34. Te main differene between lassial and quantum meanis is te quantization of energy. In lassial meanis, ligt of frequeny f an ave any energy, wereas in quantum meanis, te energy of ligt must be in multiples of f. 35. (a) Te double-slit experiment wit subatomi partiles sows te pattern on te sreen building up point by point, sowing tat te impat on te sreen is partile-like. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-3

3 (b) Te experiment sows te pattern on te sreen to ave fringes, sowing tat te partile beam as interferene, wi is arateristi of a wave. () Te experiment wit a double slit sows te same type of result wit potons as wit massive partiles. Te partiles (massless, as wit potons, or massive, as wit oter partiles) strike te sreen in disrete lumps like partiles yet interfere like waves. Tus, tey exibit wave partile duality. 36. (a) Te relative intensity of ligt from a blakbody varies wit wavelengt as sketed below. (b) Classial pysis predits tat te intensity will inrease witout limit as te frequeny inreases, so on te grap of intensity versus wavelengt, 0 would be an asymptote were te intensity inreases very rapidly. () Te problem of te blakbody intensity inreasing infinitely was solved by Max Plank by assuming tat te energy modes (later alled potons) in te blakbody avity were quantized in units proportional to a onstant. By doing tis, e sowed tat te relative intensity vanised at te igest frequenies, and te relative intensity fit te data exatly wen equalled a onstant. Te onstant was later named Plank s onstant. 37. Answers may vary. Sample answer: Te timeline below sows tree piees of evidene tat support te partile model of ligt. 38. Te frequeny of te ligt determines weter or not potoemission will our. Te reason is tat te frequeny of ligt determines te energy of te poton, and potoemission ours troug single-poton ollisions wit te atoms. Tus, ea poton must ave suffiient energy to knok te eletron out. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-4

4 39. An eletron of energy 1 ev differs from a poton of te same energy in several ways. Te table below sows four quantities tat differ: arge, mass, momentum, and wavelengt. Partile Energy, E (ev) Carge (C) Mass, m (kg) Momentum, p (J s/m) Wavelengt, (m) poton 1 ev 0 0 E / 3.3!10 "28 / p 2.0!10 "6 eletron 1 ev!1.6 "10! !10 "31 2mE 4.3!10 "25 / p 1.5!10 "9 Te eletron as greater arge, mass, and momentum, wereas te poton as greater wavelengt. 40. An experiment sowing eletron diffration from a single slit of various widts supports te Heisenberg unertainty priniple in te following way: Wen te slit is made smaller, te unertainty in te eletron s position at te slit Δx dereases but te unertainty in te eletron s momentum along te slit-widt diretion Δp inreases. We know tat tis momentum unertainty inreases beause te position were te eletron strikes te sreen is spread out. Tus, te produt of ΔxΔp annot be made arbitrarily small. 41. Te Davisson Germer experiment in wi eletrons diffrated like a wave from a rystal supports te wave model of matter. 42. An optial mirosope annot magnify an image as mu as an eletron mirosope beause te wavelengt of visible ligt is mu larger tan tat of an eletron of te same energy. Te wavelengt of an eletron of te same energy as a poton is 1000 times smaller. A smaller wavelengt an resolve smaller distanes and tus ave greater magnifiation. 43. Te apter disusses four interpretations of quantum meanis. Applied to te double-slit experiment, tey are as follows: 1) Te ollapse interpretation says tat te partile leaves te soure as a partile, spreads out as a wave and goes troug te slit, and ten ollapses bak into a partile wen it is measured at te sreen. 2) Te pilot wave says tat te partile remains a partile, but is guided by a pilot wave tat follows te laws of quantum meanis. Te pilot wave diffrats like a wave troug te slit, but te partile is deteted at te sreen. 3) Aording to te many-worlds interpretation, an eletron goes troug bot slits, but in our universe, only one eletron reaes te sreen; te oter eletron is in anoter universe. 4) In te Copenagen interpretations, te eletron s wereabouts between te measurement points annot be determined, so it is meaningless to ask about it. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-5

5 44. Quantum ryptology differs from traditional ryptology. In quantum ryptology, any attempt to interept a message will likely be deteted beause te message is sent via polarized potons. Te sender and reeiver know te polarization, but a potential eavesdropper would not. In quantum meanis, te at of measuring a system will alter te system. Tus, te attempt at eavesdropping on te message will alter te message, and te alteration an be deteted. 45. Te main teoretial problem wit te planetary model of te atom was tat it would ontinuously lose energy troug radiation. Te atom would tus be unstable, in ontradition to observations. 46. Te development of our understanding of te atom involved te atomi models of Ruterford and Bor. Ruterford tested an earlier model of te atom in wi tere was no nuleus. His experiment sent a beam of ig-speed, positively arged partiles at a piee of gold foil and found greater defletion tan expeted. He proposed tat te atom ad a small nuleus around wi te eletrons orbited like planets around te Sun. But te model ad te teoretial problem of prediting unstable atoms (as desribed in Question 45 above). Te Bor model, proposed by Niels Bor, and later strengtened by Louis de Broglie, was te first quantum model. His model ad te eletrons orbiting wit disrete energy levels tat did not radiate and tus were stable. Potons ould radiate if tey dropped down to lower energy levels, or te atom ould absorb radiation by going to a iger level. It explained te experiments done on te ydrogen atom very well, but did poorly at explaining atoms wit many eletrons. 47. Te tree fundamental fores overed in te standard model are te eletromagneti and te two nulear fores. Tey are mediated by te bosons listed in te table below. Fundamental fore Boson eletromagneti fore poton weak nulear fore W +, W, and Z strong nulear fore gluon 48. Te standard model as two types of partiles, fermions and bosons. Te bosons mediate te fores between te fermion partiles. Te fermions ave two sub-types: leptons and adrons. Te leptons inlude te eletron family (eletron, muon, tau, plus teir neutrinos and antipartiles) and quarks. Only te quarks make up omposite partiles alled adrons. Te adrons wit two quarks are alled mesons, and te adrons wit tree quarks are alled baryons. Te most familiar baryons are protons and neutrons, te nulear partiles in atomi nulei. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-6

6 Analysis and Appliation 49. Given:! max 625 nm m Required: T Analysis: Use Wien s law, rearranged to find T.! max 2.90 " 10#3 m $ K T T 2.90 " 10#3 m $ K! max Solution: T 2.90!10"3 m # K $ max 2.90!10"3 m # K 6.25!10 "7 m T 4640 K Statement: Te orange blakbody as a temperature of 4640 K. 50. (a) Te temperature 37.0º C equals K. (b) Given: T K Required: max Analysis: Use Wien s law:! max 2.90 " 10#3 m $ K T Solution:! max 2.90 " 10#3 m $ K T 2.90 " 10#3 m $ K 3.10 " 10 2 K! max 9.35 " 10 #6 m 6 Statement: is m or 9.35 µm. 51. Given: E m 2 ; p mv; E f ; f Required: relation found by Compton, ppoton 2 Analysis: From E m, assume tat a poton of energy E as an effetive mass of E m. So (at non-relativisti speeds) te momentum of su a mass would be mv, or 2 E p v. But from Einstein, E f for a poton. Putting tis relation into te expression 2 f for p gives p v. 2 Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-7

7 Setting v and ten using f gives f p 2 p Solution: p Statement: Using Einstein s relation for te rest mass energy and poton energy, Compton ould derive de Broglie s relation between momentum and wavelengt, p. 52. Given: Two data points are given: one for ligt of wavelengt, te oter wit wavelengt 2. Te atual wavelengt is not important. But notie tat tis orresponds to a data point using ligt of frequeny f and frequeny 2f. We will use frequeny instead of wavelengt to avoid a onversion step in te potoeletri equation. From E f W, we ave te two results: 1) 1.0 ev f W 2) 3.0 ev 2f W Te above are our givens. Required: W Analysis: Subtrat twie te first equation from te seond equation. 3.0 ev 2f! W 2(1.0 ev) 2f! 2W Subtrat te bottom equation from te top, and simplify. 3.0 ev 2.0 ev 2f 2 f W ( 2 W ) 1.0 ev W Solution: W 1.0 ev Statement: Te work funtion W equals 1.0 ev. 53. Te first metod determines te work funtion diretly and is sketed in Figure 2 of Setion Te metal plate is set parallel a sort distane from a seond plate. Bot plates are in a vauum and onneted by a voltage soure to make a iruit. Turn up te voltage until a urrent rosses te gap between te plates. Multiply tis minimum voltage by te arge of an eletron to get te work funtion. Te seond metod uses te potoeletri effet. You an use te same two plates, but spaed far enoug apart tat ligt an sine on one of tem. Ten, inrease te frequeny of te ligt until a urrent rosses te gap. Multiply tis minimum frequeny by Plank s onstant to get te work funtion. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-8

8 54. (a) Given:! 3.20 "10#7 m; W 1.95 ev 3.12 "10 19 J; 3.0 "10 8 m/s; 6.63!10 "34 J #s Required: E Analysis: Use te potoeletri effet equation and onvert frequeny to wavelengt. E f W E W Solution: E! W % 3.0 "10 8 m/s ( (6.63"10 #34 J $ s ) & ' 3.20 "10 #7 m ) * 3.12 "10 19 J "10 #19 J (two extra digits arried) E 3.10 "10 #19 J Statement: Te kineti energy of te ejeted eletron is 3.10!10 "19 J. (b) Given: E 3.096!10 "19 J Required: voltage V needed to stop te eletron from reaing te plate Analysis: An eletron rossing a voltage V would aquire a kineti energy of ev. E Tus, V. e Solution: V E e 3.096!10"19 J 1.60!10 "19 C V 1.93 V Statement: An applied voltage of 1.93 V would stop te ejeted eletrons. 55. Given: E 1.7 ev 2.72!10 19 J ; W 4.52 ev 7.23!10 19 J ; 3.0!10 8 m/s; 6.63!10 "34 J #s Required: Analysis: Use te potoeletri effet equation, rewritten to obtain : E f W E W E+ W E + W Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-9

9 Solution:! E +W % 3.0 "10 8 m/s ( (6.63"10 #34 J $ s ) & ' 2.72 "10 19 J "10 19 J ) *! 2.0 "10 #7 m Statement: Te wavelengt of te ligt is 2.0! 10 7 m. 56. (a) Aording to te grap in Figure 3, te potosyntesis proess is using te red and te blue-violet parts of te spetrum. So, assuming tat most of te absorption of ligt is due to potosyntesis, ten very little green gets absorbed by te plant. If te ligt does not get absorbed, ten te ligt gets sattered bak into our eyes, making te plant appear green. (b) Pure green ligt produes a very low reation rate beause te plot sows little potosyntesis at wavelengts orresponding to green. () Given: T 5300 K Required: max Analysis: Use Wien s law,! max 2.90 " 10#3 m $ K. T Solution:! max 2.90 "10#3 m $ K T 2.90 "10#3 m $ K 5300 K! max 5.5"10 #7 m Statement: Te ligt from an inandesent bulb at 5300 K produes ligt of maximum wavelengt 5.5!10 "7 m or 550 nm, wi lies in te middle of te green, were te rate of potosyntesis is lowest. Te amount of potosyntesis will depend on ow mu offpeak intensity lies in te red and te blue-violet (a) Given: V min 5.65 V; e C Required: W Analysis: To get te work funtion W, multiply te minimum voltage V by te eletri arge e. W ev min If we use te units of ev, ten te work funtion is numerially te voltage. Solution: W ev min (1.60! 10 "19 C)(5.65 V) W 9.04! 10 "19 J Statement: In eletron-volts, te work funtion is 5.65 V. In joules, te work funtion is 9.04!10 "19 J. (b) Aording to Table 1, te metal wit tis work funtion is platinum. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-10

10 58. (a) Given: W Cu 8.17! 10 "19 J; W Pb 6.81! 10 "19 J; 6.63! 10 "34 J # s Required: f 0, te tresold frequenies for Cu and Pb Analysis: Use te potoeletri effet equation, rewritten to obtain f wen E 0. E f W 0 f0 W f W 0 W f0 W Solution: f0 For opper f ! 10"19 J 6.63! 10 "34 J #s For lead f 0 f ! Hz 6.81! 10"19 J 6.63! 10 "34 J #s f ! Hz Statement: Te frequeny for opper is sligtly iger tan tat for lead. Te values sould be lose to te values dedued from te grap. (b) Te lines in te grap ave te same slope beause tey arise from te equation E f W, wi as te slope of, a universal onstant. 59. (a) Given: W 7.47!10 "19 J 4.67 ev; 6.63!10 "34 J #s Required: f 0, te tresold frequeny for Fe W Analysis: f0 Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-11

11 Solution: f 0 W 7.47! 10"19 J 6.63! 10 "34 J #s f ! Hz Statement: Te minimum frequeny of ligt to ejet eletrons from iron is Hz. 15 (b) Given: f Hz Required: energy of eletron ejeted from iron, E Analysis: Use te potoeletri effet relation, E f W. Solution: E f W (6.63! 10 "34 J # s )(7.9! s "1 ) (7.47! 10 "19 J) E 4.5! 10 "18 J $ 1 ev ' (4.5! 10 "18 J) % & 1.60! 10 "19 J ( ) E 28 ev Statement: Te ejeted eletron as a kineti energy of 4.5! J or 28 ev. 60. (a) Given: W 8.17!10 "19 J ; E 2.1 ev 3.36!10 19 J; 6.63!10 "34 J #s Required: frequeny of te ligt, f Analysis: Use te potoeletri effet equation, rewritten to obtain f. E f W E + W f E+ W f Solution: f E +W 3.36!10"19 J !10 "19 J 6.63!10 "34 J #s f 1.7!10 15 Hz Statement: Te frequeny of te inident ligt is 1.7! Hz. (b) Ligt of frequeny 1.7! Hz is ultraviolet. 61. Given:! 580 nm 5.80 " 10 #7 m; 6.63 " 10 #34 J $ s Required: momentum of te poton, p Analysis: Use te relation p. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-12

12 Solution: p! 6.63 " 10#34 J $s 5.80 " 10 #7 m p 1.1" 10 #27 kg $ m/s Statement: Te poton s momentum is 1.1! 10 "27 kg # m/s. 62. (a) Given: p 2.03!10 "24 kg #m/s; 6.63!10 "34 J #s Required: te poton s wavelengt, Analysis: p p Solution:! p 6.63"10 #34 J $s 2.03"10 #24 kg $m/s "10 #10 m (two extra digits arried)! 3.27 "10 #10 m Statement: Te X-ray wavelengt is 3.27! 10 "10 m or nm. (b) Given:! "10 #10 m; 3.0 "10 8 m/s Required: te poton s frequeny, f Analysis: f Solution: f! 3.0 "10 8 m/s "10 #10 m f 9.19 "10 17 Hz Statement: Te frequeny is 9.19!10 17 Hz. 63. Given: E 6.40 ev 1.024!10 18 J; 3.0!10 8 m/s Required: momentum of te poton, p E Analysis: Use te relation p. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-13

13 Solution: p E 1.024!10 18 J 3.0!10 8 m/s p 3.41!10 "27 kg #m/s Statement: Te momentum of te poton is 3.41! 10 "27 kg # m/s. 64. Altoug we do not diretly experiene quantum meanial effets in our everyday lives, we use many eletroni devies tat rely upon quantum meanis to operate. Moreover, te proesses we observe in our everyday lives, inluding te very at of seeing, rely upon quantum meanis. 65. To detet diffration effets, te slit widt sould be less tan or equal to te wavelengt of te impinging wave. So, we will assume a maximum slit widt equal to te eletron s wavelengt and use de Broglie s expression for te wavelengt. As 4 ev is a low energy for an eletron, we will use te lassial expression for te momentum. Given: E 4 ev 6.4! J; m 9.11! 10 "31 kg; 6.63! 10 "34 J #s Required: Analysis: First, find te eletron s momentum using p 2mE, ten use de Broglie s relation,! p. Solution: p 2mE 2(9.11!10 "31 kg)(6.4!10 "19 J) p 1.08!10 "24 kg #m/s (two extra digits arried)! p 6.63 " 10 #34 J $s 1.08 " 10 #24 kg $ m/s! 6 " 10 #10 m Statement: Te slit widt sould be at most 6! 10 "10 m or 0.6 nm. 66. Given: m 9.11! 10 "31 kg; v 5.80! 10 6 m/s; 6.63! 10 "34 J # s Required: te de Broglie wavelengt, Analysis: As te speed of te eletron is mu less tan, use te lassial momentum p in de Broglie s relation. p mv Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-14

14 Solution:! p 6.63" 10 #34 J $s (9.11" 10 #31 kg)(5.80 " 10 6 m/s)! 1.25 " 10 #10 m Statement: Te eletron s wavelengt is 1.25! 10 "10 m or nm. 67. (a) Given:! nm 2.20 " 10 8 m; m 9.11" 10 #31 kg; 6.63 " 10 #34 J $ s Required: speed of te eletrons, v Analysis: As te speed of te eletron is mu less tan, use te lassial momentum p in de Broglie s relation, but rewrite to determine v.! p! mv v m! Solution: v m! 6.63 " 10 #34 J $ s (9.11" 10 #31 kg)(2.20 " 10 8 m) v " 10 6 m/s (one extra digit arried) 6 Statement: Te eletron s speed is m/s. (Tis is mu less tan, wi justifies our use of lassial momentum.) 6 31 (b) Given: v m/s; m kg Required: te eletron s kineti energy, E 1 2 Analysis: As te speed is non-relativisti, use te lassial kineti energy, E mv. 2 Solution: E 1 2 mv2 1 2 (9.11! 10"31 kg)(3.308! 10 6 m/s) 2 E 4.984! 10 "18 J (one extra digit arried) # 1 ev & 4.984! 10 "18 J $ % 1.60! 10 "19 J ' ( E 31.2 ev 18 Statement: Te eletron s kineti energy is J or 31.2 ev () Given: E J ; e C Required: voltage, V, to aelerate te eletrons Analysis: Te energy equals te eletroni arge times te voltage. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-15

15 E ev E V e Solution: V E e 4.984! 10"18 J 1.60! 10 "19 C V 31.2 V Statement: Te voltage needed to aelerate te eletrons is 31.2 V Given: m kg; m kg; v v ; v e p e p e Required:! e /! p Analysis: Use te de Broglie relation for bot eletron and proton and simplify. Beause te speeds are mu less tan, we an use te lassial momentum (but te result is te same even if we use te relativisti momentum). e mv e e p mv p p e mv e e p mv p p Now we an anel te s and bot vs (beause bot vs are equal). m e p m p e Solution:! e! p m p m e 1.67 "10#27 kg 9.11"10 #31 kg! e 1800! p Statement: Te ratio of te eletron to te proton wavelengt equals te inverse ratio of teir masses, wi is 1800, so te ratio of te de Broglie wavelengts of a proton and of an eletron bot moving at is 1 : Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-16

16 69. Answers may vary. Sample answer: In te early 1900s, experiments involving te bombardment of atoms and nulei by various partiles sowed tat nulei were made of protons and neutrons. For a sort time, eletrons, protons, and neutrons were tougt to be te fundamental partiles of all matter. However, tis onjeture was soon disproved by osmi ray studies, ollision experiments, and nulear deay experiments by various researers. Te resear sowed tat protons and neutrons were made of smaller partiles alled quarks. Protons, neutrons, and teir anti-partiles belong to te adron group. It is assumed adrons are divisible. Eletron and positrons belong to te lepton group. It is assumed tat leptons are elementary partiles tat are not divisible. Wit te disovery of tese new partiles, te standard model of elementary partiles beame te urrent teory of fundamental partiles and te fores tat interat wit tem. Partile pysis resear is readily applied to te nulear power tenology. Understanding ow nulear fission works and te energy reated is due to te teories of partile pysis. Evaluation 70. Answers may vary. Sample answer: I tink Niels Bor made te largest ontribution to quantum meanis for several reasons. One, is atomi model, in aurately explaining te spetrum from ydrogen, gave a uge impetus to te development of quantum meanis. He also did mu oter work on various tenial results in quantum meanis. Two, e developed te orrespondene priniple, te idea tat te results of quantum meanis sould approa tose of lassial pysis as te quantum numbers beome large. Tree, is idea of omplementarity proposed tat quantum meanis allows omplementary ways of viewing a system, so tat we an view te double-slit experiment as exibiting wave-like or partile-like beaviour. Four, Bor ontributed greatly to te ideas beind te Copenagen interpretation. Finally, e nurtured many younger sientists wo would later go on to make signifiant ontributions to quantum meanis. 71. A brigt ligt bulb produes a different spetrum of radiation tan te Sun, and tus our skin responds to te two spetra differently. Te Sun is mu otter tan a ligt bulb, and tus from Wien s law, produes more ig-energy, ig-frequeny radiation. Te iger-energy radiation an damage te skin wen lower-energy radiation does not, even wen te iger-energy radiation as mu lower intensities. Te reason is related to te potoeletri effet. Te iger-energy ultraviolet (UV) radiation may dislodge an eletron from some tissue material, as it does for a metal in te potoeletri effet, and tis proess damages te tissue. Su damage will not our for low-energy radiation. 72. (a) Te ompleted table is below. Wavelengt (nm) Frequeny of ligt (Hz) Kineti energy of ejeted eletrons (J) ! ! ! ! ! ! ! ! ! ! Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-17

17 Given:! 600 nm 6.0 " 10 7 m; 3.0 " 10 8 m/s Required: frequeny, f Analysis: Use te general relation for waves, applied to ligt and written to obtain f. f f Solution: f! 3.0 " 108 m/s 6.0 " 10 7 m f 5.0 " Hz Statement: Tis frequeny value is listed in te table above, along wit tose for te oter wavelengts. (b) f! 3.0 "108 m/s 440 nm # % $ 1"10 9 nm 1 m & ( ' f "10 14 Hz () From inspetion of te plot, te x-interept is approximately 6.1!10 14 Hz. (d) From inspetion of te plot, te slope is approximately 6.4! 10 "34 J/Hz or 6.4! 10 "34 J # s. (e) At te lowest frequenies, te potons do not ave enoug energy to ejet an eletron. 73. Te term mediate is appropriate as a desription of wat bosons do in partile pysis. A mediator stands between and ommuniates between two parties. In tis sense, te bosons mediate te fore beause tey lie between te partiles and onvey te one partile s position to te oter partile, wi tells te oter partile ow to respond and vie versa. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-18

18 Reflet on Your Learning Answers may vary. Sample answers: 74. I found te wave partile duality most interesting beause it seems mu different from oter pysis, wi seems more rigid and one-sided. Also te potoeletri effet was nie to learn about beause it elped me to better understand ow ligt interats wit matter. I would like to learn more about tese topis in more advaned lasses. 75. I would use examples and analogies, not abstrat onepts. For example, I would talk about te two-slit experiment and te potoeletri effet. I would ompare te eletron in a box to a marosopi ball in a box. For te standard model, I would talk about ow boson partiles mediate a fore, but first I would like to learn ow a partile auses an attrative fore. 76. I do not need to onsider quantum meanial effets in navigating troug my daily life. But I sometimes reflet on ow quantum meanis an seem so strange yet allow researers and engineers to devise wonderful new devies as well as older devies tat I use regularly. For example, I use omputers regularly, and te workings of a miroip rely upon quantum meanial priniples. Resear 77. (a) In 1927, Clinton Davisson and Lester Germer onfirmed de Broglie s matter wave ypotesis by sowing tat a beam of eletrons will satter from a rystal surfae and produe a diffration pattern, just like X-rays of te same wavelengt. Tis onfirmed te wave-like nature of eletrons. Te diffration effet ours beause te surfae of a rystal as a periodi arrangement of atoms, mu like a diffration grating exept wit a mu smaller spaing. (b) Te setup of Davisson and Germer involved a low-energy eletron beam tat was aimed at a nikel surfae, te entire setup being in a vauum so te eletrons would not get sattered by gas moleules. Tey also ad a detetor tat olleted te sattered eletrons over a small angular region. Tey ould ange te relative angle between te inident and sattered eletrons, te angle between te surfae and inident beam, and te eletron-beam energy. In tis way, tey ould establis tat te eletrons diffrated from te surfae like waves. 78. (a) In te 1920s, Edwin Hubble disovered tat te oter galaxies in te universe were moving away from us, as well as from ea oter, and te speed inreased wit teir distane. (b) In 1965, Arno Penzias and Robert Wilson disovered te uniform mirowave bakground radiation from spae. Te wavelengt indiated a termal bakground to te universe of 3.5 K. Tey made te disovery inadvertently wile testing teir mirowave antenna for ommuniation appliations. () Bot te motion of te galaxies disovered by Hubble and te mirowave bakground radiation disovered by Penzias and Wilson support te big-bang ypotesis of te origin of te universe. In an expanding universe, all galaxies would be moving away from ea oter, like dots on te surfae of an inflating balloon, and te average temperature of te universe would derease, like te temperature of an expanding gas. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-19

19 (d) Pysiists ave suggested tat only quarks, leptons, and bosons existed at te origin of te universe. As te universe expanded and ooled, adrons formed, ten small nulei su as ydrogen and elium, and ten ligt atoms. 79. Answers may vary. Sample answers: (a) Experiments and ideas about te potoeletri effet ame from men su as Heinri Hertz, Aleksandr Stoletov, Josep (J. J.) Tomson, Pilipp Lenard, and Max Plank. (b) Solar potovoltai ells operate on te priniple of te potovoltai effet, wi is similar to te potoeletri effet. In te latter, te eletrons are dislodged from te surfae, wereas in te potovoltai effet, te eletrons move to a iger energy level in te material. In te solar ell, te material is a semiondutor layer tat as been doped to ave exess eletrons on one side and missing eletrons ( oles ) on te oter side. Tis doping provides a way for te potovoltai-generated eletrons to move one way in a iruit, tus allowing te solar ell to produe eletriity. Altoug potovoltai ells, even solar ells, preeded Einstein s work on te potoeletri effet, modern solar ells rely on te priniple of te quantum teory of semiondutors, wi grew out of Einstein s early impetus to quantum teory via is teory of te potoeletri effet. 80. Answers may vary. Sample answers: (a) Gravity posed a problem for Einstein in two senses of te word. One, e wondered wy gravitational mass was te same as inertial mass. It seemed to be a oinidene in pysis. He argued tat it was not a oinidene, tat instead tey were te same ting. Tis led to te idea tat gravity produed urvature in spae. And tis urvature led to te seond problem wit gravity: te matematis of urved spae-time was very diffiult. (b) In trying to develop a teory tat unifies gravity wit te standard model, pysiists ave partiular diffiulty wit time and quantum unertainty. Time is absolute in quantum meanis, but relative in general relativity. Wit quantum unertainty in position, or spae, te relativity of time an lead to preditions tat massive objets like blak oles an appear everywere. 81. Answers may vary. Sample answers: (a) Wen one tries to separate te quarks in a proton or neutron, te required fore beomes so strong tat new partiles are reated, tat is, quark anti-quark pairs, tat produe oter quark omposites su as mesons and oter adrons. Te strong nulear fore beomes stronger at larger separations instead of weaker, as in te more familiar fores of eletromagnetism and gravity. (b) Wen protons or neutrons are ollided at ig energy, te onstituent quarks start to separate and ten produe new quark anti-quark pairs as desribed in (a) above. () One annot separate two quarks for te same reason as desribed in (a) above. 82. Answers may vary. Sample answers: (a) Riard Feynman ontributed to our understanding of quantum meanis in various ways. One, e developed a pat-integral approa to quantum meanis tat is useful for some problems. Two, in parallel to te work of Julian Swinger and Sin-iiro Tomonaga, e developed te teory of quantum eletrodynamis. And, oter tan solving oter problems in quantum meanis, e produed a series of letures and popular books tat ontained topis in quantum meanis. (b) A Feynman diagram is useful to pysiists beause it onveys in a simple piture a omplex matematial operation. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-20

20 83. (a) A CCD works on priniples similar to te solar ell (see Question 84b), but wit speial iruitry to ollet and transport te poto-generated eletrons in an orderly fasion. (b) CCDs ave been useful to astronomers beause tey an detet lower levels of ligt tan film and ave less noise. 84. (a) Russel Ol made te first semiondutor type of solar ell in Tey were first used on satellites in (b) Te essential part of a solar ell is a speial region inside te semiondutor (usually silion) tat is similar to tat in an LED. One side as been made to ave eletron arge arriers, and te oter side to ave missing eletrons, wi at as oles tat arry positive arge aording to te quantum teory of semiondutors. At te boundary, te eletrons and oles ombine, forming te speial region alled te depletion region. Te depletion region does not ave many arge arriers, but te ombining of te eletrons and oles reates an eletri field and tus a voltage. But to generate power, te depletion region needs arges tat an flow. Tese arges are produed by te potovoltai effet, wi is similar to te potoeletri effet; briefly, an inident poton travels into te depletion region and auses an eletron to move up to a iger energy level in wi it an ondut. Te eletron ten gets pused by te eletri field troug te iruit, generating eletriity. () An array onsists of many ells. (d) Oter pysis onepts at work in a solar ell are in te fields of optis and eletriity. 85. (a) Te radiation emitted from a small ole in a larger avity nearly approximates a perfet blakbody. Blak velvet lot is also a good blakbody. (b) Blakbody radiation is useful for measuring te temperature of objets remotely. For example, te ear termometer is a useful appliation. Astronomers rely on blakbody radiation to estimate te temperature of distant objets. Blakbody radiation is also a ooling meanism in wi a body ools by radiating eat to te surroundings. 86. (a) Synrotron radiation in general is radiation from arged partiles travelling in a irular pat. Travelling in a irular pat means tat te partiles are ontinuously aelerating inward, and any aelerating arge must radiate aording to lassial eletrodynamis. Te name synrotron radiation arises beause te partile aelerators typially used for tis radiation are synrotrons in wi te partiles are igly relativisti. Te radiation is usually X-rays. (b) Eletrons ave several advantages for generating synrotron radiation. Eletrons are easy to produe and eletrons lose a greater fration of teir kineti energy during bending aeleration tan larger partiles su as protons. () Synrotron radiation as many appliations. Some general uses inlude potolitograpy, tomograpy, and spetrosopy. Copyrigt 2012 Nelson Eduation Ltd. Capter 12: Quantum Meanis 12-21