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# s7 - l 615 PHYS 260 Problem Set 7 1 The HERA colliding beam...

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Unformatted text preview: l) 615 PHYS 260 Problem Set 7 1. The HERA colliding beam accelerator in Hamburg, Germany was built to look for structure in the quarks that are found inside the proton. This was done by scattering high energy electrons off protons. (Similar experiments at lower energies at revealed the presence of quarks inside the proton.) In HERA a beam of electrons collided head—on with a beam of protons. Each electron had total energy of 27 GeV and each proton had total energy of 820 GeV. (a) using four-vectors, calculate the centre—of—mass energy of these collisions. (The centre—of—mass energy is the total energy available for new particle production in a frame where there is no net momentum, ie where the colliding particles have equal and opposite momentum.) (b) again usingifouﬂvectors, calculate the energy required of an electron hitting a stationary proton’ that would give the same centre—of-mass energy. (This is called ’ﬁxed target’ mode.) (c) what would be the de Broglie wavelength of such an electron? This gives an indicatiOn of the ' minimum size of the structure that one could hope to resolve. Macaw“ MMWW i’ 1A<ZZa )0ng Xaéumd/e’h cassd ‘51» WW 1429.. PGZW Doodl%c:éufk 7t. 4W£§mu _ 7,3».2. : ,é>._,o)0,tl€a,/Q ’ L l P9 (0 O 0114+ Eefycla<d0ﬁh 0, 33.:5ws/CA 3 FW +2.» mWwwé’b 4- ‘ «realism 5% 'i'" (iis um Raﬁ P} 42a. Pp. vwncw ma amp 2% Cit A4 41‘4va Must; but W ma}; afpwm’hafﬂm {ilk'é AMEN Mﬁso wt ,0“: abémifu E: ‘ C.” lc‘l‘ 13)) c) If ‘ékm 5cm; wvg+BLde<émmsad ﬁagugdw" WWJL WWWM Cf Dec/+615: I}; (9:11 o 0 U3: E E3, <09 9,0, (INC—3 ﬁﬁm mug «AW c4 SW Nut/{S h (E; i P} CWEC) d (MPG) “' 2E ESE/Y“? mgw A; : U V 2;, m /sza 300 /2 MW .1») m : 430W? GOA/“m £43.23 iK2k/PM "pm-e, 43xm4- cw , , =43 xwﬁw 2. In the Davisson—Germer experiment, at what angle would the reﬂected electron beam appear if the accelerating voltage had been 105 V instead of 54 V? H 4123 MW lbs Mix .5“;on S4 46L» m, ‘ were We; Wot be Wg ev.‘ ‘ P“? >\ '—‘ @110th . iQosw may“- lac}? ?? mm «JV ’ " ’1]; Wlté‘“<w WWW SCAMS LS A: (\$30139 ' M‘EL :OILS,W:0.1I5 ,rxmm ‘ or , 3w;g w/w a w m lee l 0; mm 1 h ‘34" ‘ 0410 wees-ML. M We we Mme/mil» 'wwgbwte 34" 3. In order for an electron to be conﬁned to a nucleus, its de Broglie wavelength would have to be less than 10‘14 m (a) what would be the kinetic energy of an electron conﬁned to a region of this size? (b) on the basis of this result, would you expect to ﬁnd an electron in a nucleus? Explain. 69 “VP PC- kc/x‘x 3% 124/11.” {03% 7, my AM. it: g3; (33 m. 3 e w 5) Fa m wCufrte/L to L3. LWLA. LL» mm“; 5153 665M W33 Wt .122 £3:s ”(LLL‘QA‘LIN m ‘ £3 I<+U.<D SWKS r/Z4Mcv M<a11¢mv Fat 0» Cmsw 4;;on OL— 4“?) OLE/A ML {u /4I‘t% r cgﬁ‘ﬁ» {at (A. wtﬁm mot 33;, L5 “62;. *éc‘iaLC/W W_€é@ fL 12 .29 h L L 7. WLW {mﬂmAzloéwW W443i Mix L F 13% ,QJ/ Mac/Vi} L I? (fix/36,1122 3:0 SAN)” “ 'L2L M =139x 2;? a“, iLs/L 379M) £373.30 076an For nsL 0LO§LI€ ijmwé ignL =Lz Lch-lZALeL/ ,3 I M Le. W {/24 mev ”+433: H , L ...
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s7 - l 615 PHYS 260 Problem Set 7 1 The HERA colliding beam...

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