Collg Physcs Studnt s Manual Chaptr 33 CHAPTER 33: PARTICLE PHYSICS 33. THE FOUR BASIC FORCES 4. (a) Fnd th rato of th strngths of th wak and lctromagntc forcs undr ordnary crcumstancs. (b) What dos that rato bcom undr crcumstancs n whch th forcs ar unfd? (a) From Tabl 33.1, w know that th rato of th wak forc to th lctromagntc 13 Wak 1 11 forc s 1. In othr words, th wak forc s 11 Elctromagntc 1 ordrs of magntud wakr than th lctromagntc forc. (b) Whn th forcs ar unfd, th da s that th four forcs ar just dffrnt manfstatons of th sam forc, so undr crcumstancs n whch th forcs ar unfd, th rato bcoms 1 to 1. (S Scton 33.6.) 33.3 ACCELERATORS CREATE MATTER FROM ENERGY 7. Suppos a W cratd n a bubbl chambr lvs for 5 5. 1 s. What dstanc dos t mov n ths tm f t s travlng at.9c? Snc ths dstanc s too short to mak a track, th prsnc of th W must b nfrrd from ts dcay products. Not that th tm s longr than th gvn W lftm, whch can b du to th statstcal natur of dcay or tm dlaton. Usng th dfnton of vlocty, w can dtrmn th dstanc travld by th W n a bubbl chambr: d vt 8 5 16 (.9)( 3. 1 m/s)( 5. 1 s) 1.35 1 m.135 fm 3
Collg Physcs Studnt s Manual Chaptr 33 33.4 PARTICLES, PATTERNS, AND CONSERVATION LAWS 13. Th s ts own antpartcl and dcays n th followng mannr: γ γ. What s th nrgy of ach γ ray f th s at rst whn t dcays? If th s at rst whn t dcays, ts total nrgy s just E mc. Snc ts ntal momntum s zro, ach γ ray wll hav qual but oppost momntum.. p p, so that p p, or p p. Snc a γ ray s a photon: E p c. f y1 y y1 y Thrfor, snc th momnta ar qual n magntud th nrgs of th γ rays ar qual: E 1 E. Thn, by consrvaton of nrgy, th ntal nrgy of th quals twc th nrgy of on of th γ rays: m c. Fnally, from Tabl 33., w can E dtrmn th rst mass nrgy of th, and th nrgy of ach γ ray s: m c E ( 135 MV c ) c 67.5 MV γ γ 19. (a) What s th uncrtanty n th nrgy rlasd n th dcay of a du to ts short lftm? (b) What fracton of th dcay nrgy s ths, notng that th dcay mod s γ γ (so that all th mass s dstroyd)? (a) Usng h Δ EΔt, w can calculat th uncrtanty n th nrgy, gvn th 4 lftm of th from Tabl 33.: h ΔE 4Δt 34 6.63 1 J s 6.8 1 17 4 (8.4 1 s) 19 1V J 1.6 1 19 3.9 V J (b) Th fracton of th dcay nrgy s dtrmnd by dvdng ths uncrtanty n th nrgy by th rst mass nrgy of th found n Tabl 33.: 33
Collg Physcs Studnt s Manual Chaptr 33 ΔE m 3.956 V 8.9 1 6 c ( 135. 1 V c ) c. 6 So th uncrtanty s approxmatly.9 1 prcnt of th rst mass nrgy. 33.5 QUARKS: IS THAT ALL THERE IS? 5. Rpat th prvous problm for th dcay mod Ω Λ K. (a) From Tabl 33.4, w know th quark composton of ach of th partcls nvolvd n ths dcay: Ω ( sss) Λ ( uds) K ( us). Thn, to dtrmn th chang n strangnss, w nd to subtract th ntal from th fnal strangnss, rmmbrng that a strang quark has a strangnss of - 1: ΔS S [ 1 ( 1) ] ( 3) 1 f S 1 1 1 (b) Usng Tabl 33.3, w know that B 1, 3 3 3 1 1 1 1 1 Bf 1, so th baryon numbr s ndd consrvd. Agan, 3 3 3 3 3 usng Tabl 33.3, th charg s: 1 1 1 1 1 1 Q q q, and Q q q q, so f 3 3 3 3 3 3 3 3 charg s ndd consrvd. Ths dcay dos not nvolv any lctrons or nutrnos, so all lpton numbrs ar zro bfor and aftr, and th lpton numbrs ar unaffctd by th dcay. (c) Usng Tabl 33.4, w can wrt th quaton n trms of ts consttunt quarks: ( us) or s u u d ( sss ) ( uds).snc thr s a chang n quark flavor, th wak nuclar forc s rsponsbl for th dcay.. (a) Is th dcay Σ n possbl consdrng th approprat consrvaton laws? Stat why or why not. (b) Wrt th dcay n trms of th quark consttunts of th 34
Collg Physcs Studnt s Manual Chaptr 33 partcls. (a) From Tabl 33.4, w know th quark composton of ach of th partcls nvolvd n th dcay: Σ ( dds) n( udd ) ( ud ). Th charg s consrvd at - 1. Th baryon numbr s consrvd at B1. All lpton numbrs ar consrvd at zro, and fnally th mass ntally s largr than th fnal mass: m > mn m ), so, ys, ths dcay s possbl by th consrvaton laws. ( Σ (b) Usng Tabl 33.4, w can wrt th quaton n trms of ts consttunt quarks: dds udd ud or s u u d 37. (a) How much nrgy would b rlasd f th proton dd dcay va th conjcturd racton p? (b) Gvn that th dcays to two γ s and that th fnd an lctron to annhlat, what total nrgy s ultmatly producd n proton dcay? (c) Why s ths nrgy gratr than th proton s total mass (convrtd to nrgy)? wll (a) Th nrgy rlasd from th racton s dtrmnd by th chang n th rst mass nrgs: ( ) ( ) ( ) ΔE mc Σ mc f m p m m c Usng Tabl 33., w can thn dtrmn ths dffrnc n rst mass nrgs: ( 938. 3 MV c 135. MV c. 511MV c ) c 8 8 MV 83 MV Δ E. (b) Th two γ rays wll carry a total nrgy of th rst mass nrgy of th : γ ΔE m c 135. MV Th postron/lctron annhlaton wll gv off th rst mass nrgs of th postron and th lctron: γ ΔE m c (.511MV) 1. MV So, th total nrgy would b th sum of all ths nrgs: E ΔE ΔE Δ 938.8 MV Δ tot E 35
Collg Physcs Studnt s Manual Chaptr 33 (c) Bcaus th total nrgy ncluds th annhlaton nrgy of an xtra lctron. So th full racton should b ( p ) 4γ. 33.6 GUTS: THE UNIFICATION OF FORCES 43. Intgratd Concpts Th ntnsty of cosmc ray radaton dcrass rapdly wth ncrasng nrgy, but thr ar occasonally xtrmly nrgtc cosmc rays that crat a showr of radaton from all th partcls thy crat by strkng a nuclus n th atmosphr as sn n th fgur gvn blow. Suppos a cosmc ray partcl havng an nrgy of avragng 1 1 GV convrts ts nrgy nto partcls wth masss MV/ c. (a) How many partcls ar cratd? (b) If th partcls ran down on a 1. - km ara, how many partcls ar thr pr squar mtr? (a) To dtrmn th numbr of partcls cratd, dvd th cosmc ray partcl nrgy by th avrag nrgy of ach partcl cratd: 1 cosmc ray nrgy 1 GV # of partcls cratd 5 1 nrgy partcl cratd c (. GV c ) 1 (b) Dvd th numbr of partcls by th ara thy ht: 5 1 partcls 1 partcls m 5 ( 1 m) 1 4 partcls m 49. Intgratd Concpts Suppos you ar dsgnng a proton dcay xprmnt and you can dtct 5 prcnt of th proton dcays n a tank of watr. (a) How many klograms of watr would you nd to s on dcay pr month, assumng a lftm of 1 y? (b) How many cubc mtrs of watr s ths? (c) If th actual lftm s 1 33 y, how long would you hav to wat on an avrag to s a sngl proton dcay? (a) On avrag, on proton dcays vry 1 y 1 1 months. So for on dcay vry month, you would nd: 36
Collg Physcs Studnt s Manual Chaptr 33 1dcay N 1 1 1 1 months/dcay N month 1 protons Snc you dtct only 5% of th actual dcays, you nd twc ths numbr of protons to obsrv on dcay pr month, or know that on N 4 1 protons. Now, w H O molcul has 1 protons (1 from ach hydrogn plus 8 from 3 th oxygn), so w nd 4 1 H O. Fnally, snc w know how many molculs w nd, and w know th molar mass of watr, w can dtrmn th numbr of klograms of watr w nd. 3 1mol. 18 kg 5 ( 4 1 molculs ) 7. 1 kg of watr 6. 1 (b) Now, w know th dnsty of watr, 3 molculs mol 3 ρ 1 kg/m, so w can dtrmn th 3 1m V mρ 7. 1 kg 7. 1 m 1 kg 5 3 volum of watr w nd: ( ) 3 (c) If w had 7. 1 m of watr, and th actual dcay rat was 1 33 y, rathr than 1 y, a dcay would occur 1 tms lss oftn, and w would hav to wat on avrag 1 months to s a dcay. 37