/1/15 Physics 1 April 1, 15 Ovrviw of topic Th constitunts and structur of nucli Radioactivity Half-lif and Radioactiv dating Nuclar Binding Enrgy Nuclar Fission Nuclar Fusion Practical Applications of Nuclar Physics Elmntary Particls Unifid Forcs and Cosmology Th Constitunts and Structur of Nucli Z = atomic Numbr N = Nutron Numbr A = Mass Numbr A = Z + N Th Atomic Mass Unit, AMU It is an quivalnc btwn th notation that 1 proton or 1 nutron has a mass of 1 (i.. 1 hydrogn atom has a mass of 1 amu) 1 amu= 1.66 x 1-7 kg.g. Carbon -1 1 6C Prcis Masss of particls Particl Mass (kgx 1-7) Mass(MV/c ) Mass (amu) Charg (C) Proton 1.6763 x 1-7 938.8 1.776 +1.6 x 1-19 Nutron 1.6799 x 1-7 939.57 1.8665 Elctron 9.19 x 1-31.511.585799-1.6 x 1-19 Nuclar Siz and Dnsity To obtain an stimat for th siz of a nuclus, Ruthrford did a simpl calculation using th consrvation of nrgy H considrd th cas of a particl of charg +q and mass m approaching th nuclus of charg +Zwith a spd v. H assumd th approach was had-on At som distanc, d, from th cntr of th nuclus, th incoming particl coms to rst instantanously, bfor turning around. Th radius of th nuclus is lss than d 1
/1/15 Th incoming particl movs on a lin that passs through th cntr of th nuclus. Far from th nuclus, th particl s spd is v. Th particl turns around (coms to rst simultanously) a distanc d from th cntr of th nuclus W can find th distanc, d, by applying nrgy consrvation. In particular, th initial nrgy of th systm is th kintic nrgy of th particl, ½ mv, assuming th particl approachs th nuclus from infinity. Th final nrgy is th lctric potntial nrgy, which whn w st kintic and potntial qual to ach othr w can solv for d 1 kq1q Ek = mv = U = d k( Z) q 1 E final = = mv d kzq d = 1 ( mv ) whr is th lmntary charg Conclusion Using this rsult, Ruthrford found that for an alpha particl (hlium nuclus) approaching a gold nuclus in on of his xprimnts, th distanc of closst approach was 3. x 1-1 m W arrivd, from this, that th radius of a nucli diffrs from diffrnt atoms It is givn by: r = (1. x 1-15 m)a 1/3 Nuclar Stability W know that lik chargs rpl ach othr; but what of th protons in a nuclus, don t thy rpl ach othr Ys! Thr is a forc of about 3N btwn two protons if sparatd by 1 frmi [1 fm] (x 1-15 m) Th attractiv forc that holds a nuclus togthr is calld th strong nuclar forc. This forc has th following proprtis Th strong forc is short rang, acting only to distancs of a coupl fm Th strong forc is attractiv and acts with narly qual strngth btwn protons and protons, protons and nutrons, and nutrons and nutrons Nuclar Stability Th strong nuclar forc has no ffct on lctrons which mans it has no ffct on th chmical proprtis of an atom It is th comptition btwn th rpulsiv lctrostatic forcs and th attractiv strong nuclar forcs that dtrmins whthr a givn nuclus is stabl This comptition is illustratd in th blt of stability
/1/15 Blt of Stability Notic th dviation btwn th 1:1 ratio of nutrons to protons Nutrons ar usd as a form of nuclar glu Thy sparat protons which othrwis would tar apart th nuclus Radioactivity An unstabl nuclus dos not last forvr-soonr or latr it braks down by mitting on particl or anothr It also may rarrang its nuclons (nuclar particls) to lowr its intrnal nrgy, thus mitting high nrgy (Gamma Dcay,γ) Th dcayof a nuclus dscribs this procss. Th dcay of a nuclus mans th mass of th systm is lowring and thrfor nrgy is rlasd E= m c Particls Alpha (α) particls which ar th nucli of a hlium atom H A bta(β - ) particl is simpl a high nrgy lctron Pntrating Powr Alpha rays can barly pntrat a sht of papr Bta rays can pntrat a fw mm of aluminum Gamma rays can pntrat svral cm of lad Positrons ar particls ar th sam mass as an lctron but th opposit charg (β + ) It is th antiparticlof an ordinary lctron Alpha (α) Dcay Alpha dcay occurs whn a nuclus jcts a hlium nucli ( H ). This is vry common dcay and has th smallst amount of pntrating powr 38 9 U 3 9 Th + H Sampl 1: What product is formd whn radium 6 undrgos alpha dcay 6 A 88 Ra Z X + H 6 = A + A = 88 = Z + Z = 86 Thn w look at th Priodic tabl and find th atomic numbr of 86 radon(rn) 6 88 Ra 86Rn+ H 3
/1/15 Bta (β) Dcay This is th nxt highst nrgy of dcay. It occurs whn a nutron braks apart into a proton and a high nrgy lctron which is shot out of th nuclus I X+ 131 131 53 5 1 n p+ 1 1 1 1 Gamma (γ) Dcay Consists of high nrgy photons. It changs nithr th atomic numbr nor th mass numbr of th nuclus and is rprsntd by a gamma symbol with no mass or charg. It rprsnts th nrgy lost whn th nuclus rarrangs itslf into a mor stabl arrangmnt Gamma dcayoccurs bcaus th nuclus is at too high an nrgy. Th nuclus falls down to a lowr nrgy stat and, in th procss, mits a high nrgy photon known as a gamma particl. Hr's a diagram of gamma dcay with hlium-3: Positron Emission A positron is th xact sam mass as an lctron but has a positiv charg An Exampl: 11 6 C 5B+ 11 1 Elctron Captur This occurs whn an lctron hits a proton, turning that hit proton into a nutron. 11 6 C+ 1 11 5 B Radioactiv Dcay Sris Considr an unstabl nuclus that dcays and producs a daughtr nuclus which is also unstabl This crats a dcay sris Hr is th dcay of uranium-38 Can w labl alpha and bta dcays on this?
/1/15 Activity Th rat at which nuclar dcay occurs is calld th activity of th matrial Th Curi, Ci, is qual to 3.7 x 1 1 dcays/s 1 Ci is th activity of 1g of radium W usually run into µci 1 bcqurl= 1 Bq= 1 dcay/s (SI UNIT) Half-lif and Radioactiv Dating Th phnomnon of radioactiv dcay, through fundamntally random in its bhavior, has crtain proprtis that mak it usful as a typ of nuclar clock W can us th dcay constant, λ(unit: s -1 ) N = N λt N = amount lft N t = tim that has past(s -1 = original amount ) Half-lif Th half-lif, t 1/, of a givn typ of radioactiv nuclus is th tim rquird for th numbr of such nucli to dcras by a factor of ; that is, for th numbr to dcras from N o to ½ N to ¼ N o and so on t 1 =.693 λ R = λn 1 t = ln λ λt R R = R λt N = N.693t t 1/ t1/ t = ln.693 N N Whr R is th rat and R o is th initial rat Whr N is th amount and N o is th initial amount 5
/1/15 Exampl: Ag of an Icman Early in th aftrnoon of Spt. 19,1991, a Grman coupl hiking in th Italian Alps noticd somthing brown sticking out of th ic 8 to 1m ahad. At first thy took th objct to b a doll or som rubbish. As thy got closr, howvr, it bcam apparnt that th objct thy had discovrd was th body of a prson trappd in th ic, with only th top part of th body xposd It was a Icman who had bcom ntombd in th ic. Th C-1 activity whn found was.11 Bq, compard to th.31 Bqof frsh C-1. How old is h? Nuclar Binding Enrgy An alpha particl consists of two protons and two nutrons. Dos it follow that th mass of an alpha particl is twic th mass of a proton addd to twic th mass of a nutron? Mass of nuclus = ( x protons) + ( x nutrons) NO, thr is a mass diffrnc which can b attributd to th Einstin quation, E = mc 6
/1/15 Nuclar Fission Scintists Otto Hahn and Fritz Strassmandiscovrd in 1939 that a uranium nuclus can split apart into two smallr nucli. This can happn to various larg nucli This is calld nuclar fission This rlass nrgy at about MVfor vry singl nuclus brokn down Nuclar Fission This occurs whn a slow nuclus is absorbd by a Uranium-35 nuclus. This incrass th mass numbr and lavs it in an xcitd stat 1 35 36 * n+ 9U 9U Th nuclus bcoms distortd in its xcitd stat and braks into two daughtr nucli Chain Ractions Sinc fission ractions giv off mor than on nutron on avrag, ach of thos nutrons can start anothr fission procss. This is calld a chain raction Nuclar Fusion Whn two lightnucli combin to form a mor massiv nuclus, th raction is rfrrd to as a nuclar fusion. This ncourags nrgy to b rlasd (from binding nrgy) This nds to occur at a drastically high tmpratur. Whn that tmpratur is rachd w say that th thrmonuclar fusion raction is taking plac 7