Nice Try. Some Properties of Nuclei. Charge and mass Introduction: Development of Nuclear Physics. Nuclear Binding, Radioactivity

Transcription

1 SPHUI Physics Modern undersanding: he ``onion picure Nuclear Binding, Radioaciviy Nucleus Proons om and neurons Le s see wha s inside! Nice Try Inroducion: Developmen of Nuclear Physics 1896 he birh of nuclear physics Becquerel discovered radioaciviy in uranium compounds Ruherford showed he radiaion had hree ypes lpha (He nucleus) Bea (elecrons) Gamma (high-energy phoons) 1911 Ruherford, Geiger and Marsden performed scaering experimens Esablished he poin mass naure of he nucleus Nuclear force was a new ype of force 1919 Ruherford and coworkers firs observed nuclear reacions in which naurally occurring alpha paricles bombarded nirogen nuclei o produce oxygen 193 Cockcrof and Walon firs used arificially acceleraed proons o produce nuclear reacions 193 Chadwick discovered he neuron 1933 he Curies discovered arificial radioaciviy 1938 Hahn and Srassman discovered nuclear fission 19 Fermi achieved he firs conrolled nuclear fission reacor Some Properies of Nuclei ll nuclei are composed of proons and neurons Excepion is ordinary hydrogen wih jus a proon The aomic number (charge),, equals he number of proons in he nucleus The neuron number, N, is he number of neurons in he nucleus The mass number,, is he number of nucleons in he nucleus = + N Nucleon is a generic erm used o refer o eiher a proon or a neuron The mass number is no he same as he mass Noaion X where X is he chemical symbol of he elemen 7 Example: l 13 Mass number is 7 omic number is 13 Conains 13 proons Conains 1 (7 13) neurons The may be omied since he elemen can be used o deermine Charge: Charge and mass The elecron has a single negaive charge, -e (e = x C) The proon has a single posiive charge, +e Thus, charge of a nucleus is equal o e The neuron has no charge Makes i difficul o deec Mass: I is convenien o use aomic mass unis, u, o express masses 1 u = x 10-7 kg Based on definiion ha he mass of one aom of C-1 is exacly 1 u Mass can also be expressed in MeV/c From E R = m c 1 u = MeV/c 1

2 Summary of Masses Masses Paricle kg u MeV/c Proon x Neuron x Elecron x x Quick problem: proons in your body Wha is he order of magniude of he number of proons in your body? Of he number of neurons? Of he number of elecrons? Take your mass approximaely equal o 70 kg. n iron nucleus (in hemoglobin) has a few more neurons han proons, bu in a ypical waer molecule here are eigh neurons and en proons. So proons and neurons are nearly equally numerous in your body, each conribuing 35 kg ou of a oal body mass of 70 kg. N 1 nucleon kg 8 35kg 10 proons 7 Same amoun of neurons and elecrons. The Size of he Nucleus Firs invesigaed by Ruherford in scaering experimens He found an expression for how close an alpha paricle moving oward he nucleus can come before being urned around by he Coulomb force The KE of he paricle mus be compleely convered o PE 1 qq e e 1 mv k d e ke r d or k e e For gold: d = 3. x 10-1 m, for silver: d = x 10-1 m Such small lenghs are ofen expressed in femomeers where 1 fm = m (also called a fermi) mv Since he ime of Ruherford, many oher experimens have concluded he following Mos nuclei are approximaely spherical verage radius is Example: r r r o = 1. x m o Size of Nucleus l 13 has radius 15 r m Densiy of Nuclei The volume of he nucleus (assumed o be spherical) is direcly proporional o he oal number of nucleons This suggess ha all nuclei have nearly he same densiy Nucleons combine o form a nucleus as hough hey were ighly packed spheres Nuclear Sabiliy There are very large repulsive elecrosaic forces beween proons These forces should cause he nucleus o fly apar The nuclei are sable because of he presence of anoher, shorrange force, called he nuclear (or srong) force This is an aracive force ha acs beween all nuclear paricles The nuclear aracive force is sronger han he Coulomb repulsive force a he shor ranges wihin he nucleus

3 BINDING ENERGY in MeV/nucleon Nuclear Sabiliy char Isoopes Ligh nuclei are mos sable if N = Heavy nuclei are mos sable when N > s he number of proons increase, he Coulomb force increases and so more nucleons are needed o keep he nucleus sable No nuclei are sable when > 83 The nuclei of all aoms of a paricular elemen mus conain he same number of proons They may conain varying numbers of neurons Isoopes of an elemen have he same bu differing N and values X aomic number (charge), neuron number, N nucleon number,, Example: 11 C 1 C 13 C 1 C The oal energy of he bound sysem (he nucleus) is less han he combined energy of he separaed nucleons This difference in energy is called he binding energy of he nucleus I can be hough of as he amoun of energy you need o add o he nucleus o break i apar ino separaed proons and neurons Binding Energy Binding Energy Plo Iron (Fe) is mos binding energy/nucleon. Ligher have oo few nucleons, heavier have oo many. Fission Fission = Breaking large aoms ino small Fusion = Combining small aoms ino large Binding Energy per Nucleon Binding Energy Noes Excep for ligh nuclei, he binding energy is abou 8 MeV per nucleon The curve peaks in he viciniy of = 60 Nuclei wih mass numbers greaer han or less han 60 are no as srongly bound as hose near he middle of he periodic able The curve is slowly varying a > 0 This suggess ha he nuclear force sauraes paricular nucleon can inerac wih only a limied number of oher nucleons Quesion Where does he energy released in he nuclear reacions of he sun come from? (1) covalen bonds beween aoms () binding energy of elecrons o he nucleus (3) binding energy of nucleons 3

4 Quesion Which elemen has he highes binding energy/nucleon? Quesion Neon (=10) Iron (=6) Iodine (=53) Which of he following is mos correc for he oal binding energy of an Iron aom (=6)? 9 MeV 3 MeV 70 MeV 50 Mev For Fe, B.E./nucleon 9MeV 56 6 Fe has 56 nucleons Toal B.E 56x9=50 MeV Binding Energy Einsein s famous equaion E = m c Big Problem: binding energy Proon: mc = 938.3MeV Neuron: mc = 939.5MeV dding hese, ge MeV Calculae he average binding energy per nucleon of 93 1 Nb Using aomic mass unis Deueron: mc =1875.6MeV Difference is Binding energy,.mev M Deueron = M Proon + M Neuron Binding Energy Calculae he average binding energy per nucleon of Given: m Nb = u m p = u m n = u 1u=931.5 MeV c =931.5 MeV/u Find: E b =? In order o compue binding energy, le s firs find he mass difference beween he oal mass of all proons and neurons in Nb and subrac mass of he Nb: Number of proons: N p 1 Number of neurons: Mass difference: m 1m 5m m p n Nb Thus, binding energy is N mc u931.5MeV u 93 Nb 1 Eb 8. MeV nucleon 93 n u u u u Radioaciviy Radioaciviy is he sponaneous emission of radiaion Experimens suggesed ha radioaciviy was he resul of he decay, or disinegraion, of unsable nuclei Three ypes of radiaion can be emied lpha paricles The paricles are He nuclei Bea paricles The paricles are eiher elecrons or posirons posiron is he aniparicle of he elecron I is similar o he elecron excep is charge is +e Gamma rays The rays are high energy phoons

5 B field ino screen Types of Radioaciviy Radioacive sources a paricles: He nuclei b paricles: elecrons deecor aluminum g phoons (more energeic han x- rays) Barely penerae a piece of paper Can penerae a few mm of Can penerae several cm of lead The Decay Processes General Rules When one elemen changes ino anoher elemen, he process is called sponaneous decay or ransmuaion The sum of he mass numbers,, mus be he same on boh sides of he equaion The sum of he aomic numbers,, mus be he same on boh sides of he equaion Conservaion of mass-energy and conservaion of momenum mus hold lpha Decay When a nucleus emis an alpha paricle i loses wo proons and wo neurons N decreases by decreases by decreases by Symbolically X Y H e X is called he paren nucleus Y is called he daugher nucleus lpha Decay -- Example Decay of 6 Ra Ra Rn He Half life for his decay is 1600 years Excess mass is convered ino kineic energy Momenum of he wo paricles is equal and opposie Bea Decay During bea decay, he daugher nucleus has he same number of nucleons as he paren, bu he aomic number is one less In addiion, an elecron (posiron) was observed The emission of he elecron is from he nucleus The nucleus conains proons and neurons The process occurs when a neuron is ransformed ino a proon and an elecron Energy mus be conserved Bea Decay Elecron Energy The energy released in he decay process should almos all go o kineic energy of he elecron Experimens showed ha few elecrons had his amoun of kineic energy To accoun for his missing energy, in 1930 Pauli proposed he exisence of anoher paricle Enrico Fermi laer named his paricle he neurino Properies of he neurino ero elecrical charge Mass much smaller han he elecron, probably no zero Spin of ½ Very weak ineracion wih maer 5

6 Symbolically X Y e 1 X Y e Bea Decay 1 is he symbol for he neurino is he symbol for he anineurino To summarize, in bea decay, he following pairs of paricles are emied n elecron and an anineurino posiron and a neurino Gamma Decay Gamma rays are given off when an excied nucleus falls o a lower energy sae Similar o he process of elecron jumps o lower energy saes and giving off phoons The excied nuclear saes resul from jumps made by a proon or neuron The excied nuclear saes may be he resul of violen collision or more likely of an alpha or bea emission Example of a decay sequence The firs decay is a bea emission The second sep is a gamma emission B C * e C* C g The C* indicaes he Carbon nucleus is in an excied sae Gamma emission doesn change eiher or a: example b: example Decay Rules 1) Nucleon Number is conserved. ) omic Number (charge) is conserved. 3) Energy and momenum are conserved. g: example U Th a P P g * 0 0 recall He a 1) 38 = 3 + Nucleon number conserved ) 9 = 90 + Charge conserved n p e nii-neurino needed o conserve energy and momenum. Pracice nucleus undergoes a decay. Which of he following is FLSE? 1. Nucleon number decreases by. Neuron number decreases by 3. Charge on nucleus increases by a decay is he emission of He a decreases by decreases by (charge decreases!) U Th He 38 3 Ex b Pracice 3 The nucleus Th undergoes b 90 decay. Which of he following is rue? 1. The number of proons in he daugher nucleus increases by one.. The number of neurons in he daugher nucleus increases by one. decay is accompanied by he emission of an elecron: creaion of a charge -e. 3??? 3 0?? X e 0 90Th 91Pa e In fac, n p e e inside he nucleus, and he elecron and neurino escape. Decay Which of he following decays is NOT allowed? 1 3 U Th a Po Pb He C Ng K p e = = = = = <> = =

7 Decay The Decay Consan Which of he following are possible reacions? (a) and (b). Reacions (a) and (b) boh conserve oal charge and oal mass number as required. Reacion (c) violaes conservaion of mass number wih he sum of he mass numbers being 0 before reacion and being only 3 afer reacion. The number of paricles ha decay in a given ime is proporional o he oal number of paricles in a radioacive sample N N λ is called he decay consan and deermines he rae a which he maerial will decay The decay rae or aciviy, R, of a sample is defined as he number of decays per second N R N Decays per second, or aciviy Sar wih 16 1 C aoms. Radioaciviy N N decay consan fer 6000 years, here are only 8 lef. No. of nuclei presen How many will be lef afer anoher 6000 years? 1) 0 ) 3) 8 Every 6000 years ½ of aoms decay The decay curve follows he equaion N N e The half-life is also a useful parameer The half-life is defined as he ime i akes for half of any given number of radioacive nuclei o decay T 1 0 Decay Curve ln Unis The uni of aciviy, R, is he Curie, Ci 1 Ci = 3.7 x decays/second The SI uni of aciviy is he Becquerel, Bq 1 Bq = 1 decay / second Therefore, 1 Ci = 3.7 x Bq The mos commonly used unis of aciviy are he mci and he µci Decay Funcion 1 N() N e N 0 0 ime 7

8 Pracice The half-life for bea-decay of 1 C is ~6,000 years. You es a fossil and find ha only 5% of is 1 C is undecayed. How old is he fossil? 3,000 years 6,000 years 1,000 years 0 years: 100% remains 6,000 years: 50% remains 1,000 years: 5% remains Radioaciviy Quaniaively Decays per second, or aciviy Survival: No. of nuclei presen a ime decay consan N () N e Insead of base e we can use base 1/: 1 where Half life e N N 0 T No. we sared wih a =0 1/ 1 Then we can wrie N() N0e N0 No. of nuclei presen Radioaciviy Example The half-life for bea-decay of 1 C is 5730 years. If you sar wih 1000 carbon-1 nuclei, how many will be around in 90 years? 1 N() N e N N( ) N T 1/ N N0e ) 1000e 6.5 Carbon Daing Uses of Radioaciviy Bea decay of 1 C is used o dae organic samples The raio of 1 C o 1 C is used Smoke deecors Ionizaion ype smoke deecors use a radioacive source o ionize he air in a chamber volage and curren are mainained When smoke eners he chamber, he curren is decreased and he alarm sounds Radon polluion Radon is an iner, gaseous elemen associaed wih he decay of radium I is presen in uranium mines and in cerain ypes of rocks, bricks, ec ha may be used in home building May also come from he ground iself Binding Energy Which sysem weighs more? 1) Two balls aached by a relaxed spring. ) Two balls aached by a sreched spring. 3) They have he same weigh. M 1 = M balls + M spring M = M balls + M spring + E spring /c M M 1 = E spring /c Kg 8

9 Srong Nuclear Force Q Values (nice o know) cs on Proons and Neurons Srong enough o overcome Coulomb repulsion cs over very shor disances Two aoms don feel force Energy mus also be conserved in nuclear reacions The energy required o balance a nuclear reacion is called he Q value of he reacion n exohermic reacion There is a mass loss in he reacion There is a release of energy Q is posiive n endohermic reacion There is a gain of mass in he reacion Energy is needed, in he form of kineic energy of he incoming paricles Q is negaive Problem: nuclear reacions Li H e n 7 Deermine he produc of he reacion: 3? Wha is he Q value of he reacion? Deermine he produc of he reacion: 7 X 1 3 Y 0 Wha is he Q value of he reacion? Given: reacion Find: Q =? I is easier o use aomic mass unis raher han kg. In order o balance he reacion, he oal amoun of nucleons (sum of -numbers) mus be he same on boh sides. Same for he -number. Number of nucleons (): 7 X 1 X 10 Number of proons (): 3 Y 0 Y 5 Thus, i is B, i.e. The Q-value is hen n 7 10 Li He B u.00603u u u Mev / u Q m c m m m m c.79mev Li H e? n Li He B n Summary Nuclear Reacions Nucleon number conserved Charge conserved Energy/Momenum conserved a paricles = He nucleii b - paricles = elecrons g paricles = high-energy phoons Survival: N () N0e Decays Half-Life is ime for ½ of aoms o decay 9