Structure of atom nucleus

Transcription

1 Philosophers / scieniss Timeline Srucure of aom nucleus risoeles Dalon J.J.Thompson Bohr Schrödinger Pauli Biophysics lecures Ocober József Orbán Biophysics Deparmen hp://biofizika.aok.pe.hu/en/ Pierre, Marie Curie Teller Fermi Einsein and Szilárd hp:// omicsrucure/omictimeline/omictimeline.hm hp://library.hinkques.org/79/exs/imeline/imeline.hml Yukawa Democrius The word aom has he origin: aomos (aomos), a Greek word meaning uncuable (indivisible). Thompson s aomic model (9) The aomic models from he viewpoin of he nucleus elecrons Discovery of he elecron. The plum-pudding model. There is no nucleus menioned. The posiive charge is spread in a large volume. Ruherford model (9) a experimenal seup a-paricles Posiively charged nucleus exiss and he elecrons move in he subsance. euron and proon are no menioned! R =. -5 m Wha does an aom consis of? ccording o Bohr s model (9): egaively charged elecrons e - cloud Posiively charged nucleus proon and neuron were no known! Spaial connecion beween he nucleus and elecron: i can no appear everywhere in he subsance, jus close o he nucleus! (maximum ~ - m) Discovering he aomic nucleus Is he nucleus indivisible? Is i he final indivisible paricle? Is here any oher paricle in he nucleus? Wha is he role of hese paricles? 5

2 Chadwick s inerpreaion (9) Collision of Be and α-paricle new paricle is emied. Same mass as a proon bu wihou any elecric charge. Be He C 9 He named his new paricle neuron. neuros (greek; neural) n Heisenberg and Tamm (9) James Chadwick (obel-prize in physics 95) They developed a new nuclear model which includes neurons, as well. ew meaning is brough o aomic number! C mass number () = -; proon number () neuron number or aomic number (charge) From he simples: Hydrogen aom aom engineering p One proon, nohing more! H R H aom - m; R H nucleus -5 m More complex aom, like He (aomic number = ) Size? The charged proons repel each oher because of he elecrosaic Coulomb force. Why is ha paricle needed? 7 8 The real He aom: aomic number =, mass number = p and n The presence of neurons does no explain he sabiliy (elecrically neural)! Bu hey demonsrably sabilize he nucleus. Some glueing effec should appear! Sronger han he elecric repulsion! eurons also ake par in creaing his force which is no based on elecric charge! Wha is ha force??? He 9 Defici of mass binding energy The mass of composie nuclei is always less han he oal mass of is componens (separaed proons and neurons). The missing mass value is linearly proporional o he binding energy. Energy is disengaged (released), while a nucleus is consruced from free nucleons. m ( m m ) m E mc p n nuc mass-energy equivalency rule of Einsein (uclear) Binding energy: is he required energy o remove one nucleon from he nucleus of an aom. (c: speed of ligh) uclear force Srong ineracion Compensaes he repulsion of elecric charges. high inensiy (srong) shor range of ineracion ( -5 m) aracion only (always) independen of elecric charge neurons are also included! in p-p, p-n, n-n ineracions he same magniude of force is creaed! uclear models

3 Binding energy per ucleon (MeV) Increase of nucleon number - effecs Increasing: nucleon number mass (number: ) radius of aom volume of aom surface of aom r ~ ; V ~ r ~ surface ~ r ~ Liquid drop model (LDM) incompressible nuclear fluid Observaions:. Each of he nucleons is bound wih (almos) he same binding energy. (E B neuron = E B proon!). Toal binding energy of he nucleus is proporional o he number of nucleons ().. The volume of he nucleus is linearly proporional o he number of nucleons (). Hofsaeder (menioned on previous slide) Same effec(s) as in he case of liquid drops! E B nonlinear! This concludes ha: he densiy of nucleus is equal for any kind of aom a any poin in he nucleus! 5 LDM. size-independen densiy incompressibiliy, 5. spherical form,. nucleons inerac only wih heir closes neighbours. Based on macroscopic properies (experimenal daa). Explains: binding energy, mass, sabiliy of nuclei. Model (95): creaed by Carl von Weizsäcker based on he calculaions of Hans Behe. E B a LDM - Behe-Weizsäcker (semi-empirical) mass formula: Memorise: E B E volume E surface E Coulomb E Pauli E The binding energy is a sum of differen energies. Terms explained by classical physics: ucleons move (exis) in he poenial field of he neighbouring nucleons: volume energy ucleons on he surface (ouer side) have less neighbours surface energy Elecrosaic energy (charged proons presen) Coulomb-energy ani Hund! Wha does ha mean??? hp://en.wikipedia.org/wiki/liquid_drop_model 7 hp://en.wikipedia.org/wiki/behe-weizs%c%cker_formula LDM Oher erms explained by quanum heory: One nucleons binding energy as a funcion of aomic number Pauli (asymmery) energy (fermions) E p E n ani-hund (pairing) energy Parameers (a,,,, ) are experimenally deermined semiempirical model! Pauli s Exclusion principle: forbidden o occupy he same quanummechanical sae. ni-hund law: ucleons - wih differen spins - like o fill he same energy level. 8 Maximum: beween 55-! The fi is almos good! Bu...! The raio of surface and volume (energies) changes! (r /r = /r) Effec of Coulomb force increases! omic number (aomic mass uni) The model predics:! i 9

4 Binding energy per ucleon (MeV) Wha s wrong wih he liquid drop model? omic shell model (SM) magic numbers: or =, 8,, 8, 5, 8, These nuclei are more sable han he LDM predics. Quanum mechanics (QM) can inerpre he behavior of he elecrons in he elecron shell. Cerain properies of he nucleus show periodiciy. omic number (aomic mass uni) The phenomenon is similar o he magic numbers of he elecron shells:, 8,8, Halogens have more sable elecron srucure because of closed e - -shells! Reason: These aoms conain closed (filled) aomic shells. Tha phenomenon is no aken ino accoun in he LDM! Is QM able o describe he behavior of he nucleons, oo? nalogy of elecron- and aomic shells! Wha can we do? Is here a beer model? omic shell model (sphere symmeric) Barle, Elsasser, 9: independen paricle model Jensen and Göpper-Mayer, 99: aomic shell model The nucleons Schrödinger equaion s wih quanized parameers (energy, angular momenum, magneic momenum, spin) characerise he aomic shells. (spin value: ½, hence Pauli s-principle is valid) oms wih closed aomic shells are more sable! proons and neurons separaely fill heir own energy levels Radioaciviy Types of radiaion Ineracion of radiaions wih maer Universiy of Pecs, Deparmen of Biophysics ocober József Orbán Is he radioaciviy a naural process? Yes, since he Big Bang... Binding energy per nucleon as a funcion of mass number Fe 5 Wha induces he ransmuaion? The insabiliy of he nucleus! Wha kind of uilizaion do you know? uclear power plan, aom bomb, diagnosics, herapy

5 Ways o reach Sabiliy a-decay» a-radiaion Fission Fusion X X X X a He : aom number : proon number Ra Rn 88 8 a uclear reacors, aomic bomb sars Maximal exi speed: 5 m/s (.5 c) Line specrum (characerisic) hp://oureach.anf.csiro.au/educaion/senior/cosmicengine/sun_nuclear.hml hp:// U, m, Ra, Rn , 8 Po -decay» -radiaion -decay» -radiaion egaive -decay Experimen: Curie 9 Theory: Enrico Fermi, 9 n p X e X e Maximal exi speed: 8 m/s (. c) Coninuous specrum (anineurino) e 7 55 Cs elecron 7 5 Ba e Posiive -decay p n e X - isoopes isoopes X e e H, C, a Cs, , 9 C a, posiron I e e K Elecromagneic radiaion (-phoon) -radiaion Side effec of a- or -radiaion! Radioaciviy Wha ype of deecors are used o deec radioacive radiaion? f> 9 Hz, and E> kev Creaed a energy ransiions of nucleus, from excied sae o ground sae. Propagaes a ligh speed Line specrum (characerisic) 7 a, 9K, 55Cs, I 5 -phoon elecron Ba Ba 7m m: measable sae a Wilson-ype cloud chamber Geiger Müller couner Scinigraph Why do we need so many ypes of deecors? They inerac differenly wih maer. hp://en.wikipedia.org/wiki/cloud_chamber 5

6 Radiaions base of comparison civiy () Exernal influence no required Physical and chemical environmen has no influence Ionisaion (physics) Chemical and biological effecs Physical properies: civiy Life ime Specrum Peneraion deph and LET (linear energy ransfer) Radioacive ransmuaion is a random process! umber of ransmuaing nuclei in sec. ransmuaion = decay Uni: Becquerel Bq = ransmuaion/sec (ps). enion! Radioacive decomposiion does no mean ha he aom disappears! Do no use disinegraion for he process! Sable isoope Radioacive isoope Daugher aom Old uni: Curie. ( Ci =,7 Bq) hp://en.wikipedia.org/wiki/radioacive_decay Law of decomposiion - aciviy Half life (ime) mean lifeime () : number of radioacive nuclei a he begining () : number of remaining radioacive nuclei a any momen Decay consan (): Characerises he rae of decomposiion. Defines he probabiliy of ransmuaion of one nucleus. () Mean lifeime (): Reciprocal of he decay consan. umber of remaining radioacive nuclei () () / () /e T / ( ) () ( ) () T elapsed ime e ( ) () ( ) () e T T ln T e,t