Atom

1. Atom • Base character of atoms follows from experiments: • Atom is indivisible in some physical processes • Atom is electrically neutral in base state • Mass of atoms is in the range of • 10-25 - 10-27 kg. • Dimensions of atoms are approx. 10-10 m.

3. Rutherford experiment • Final intensity ofelectricfieldisapproximately 1013 V/m for Thompson model. In thesescond case plus chargeislocated in a smallnucleus in the centre of atom and calculated intensity ofelectricfield on thesurfaceofnucleuswillbe 1021 V/m whichis 108times more then in theformer case. • Experimentalresultofthis diference consists in factthat majority of alfa particlesisdeflected (turned) onlyatsmallangles but 1/8000 ofparticlesisdeflectedwithanglehigherthen 90o . Ifwetry to explainthisdifference by superpositionof independent deflections, theresultwillbe probability 10-3500 , whatis in thedisagreementwithexperimentalresuts.

4. Bohr model of atom • Atoms are in stationary states, their energy is constat, no adsorption, no emission of energy, energies which correspond with stationary states creates discrete sequence. These energies are controlled by quantum rules. • Atom can adsorbe and emit energy only in quantum and only during the pass from one stationary state to another one. For quantum of radiation is valid: • hn = Ei –Ef • h=Planck constant

5. Quantum mechanics model of atom • Everyparticleisrepresented by wavefunction, whichdepends on position and time. Square ofamplitudeoffunctiondeterminesthe probability offindingtheparticlewithgivenproperties in time and place. • Animprotantrequirementisprincipleofcorrespondence, itmeansthattheresultsofquantummechanicsmustbethesame in macro as resultsofclassicalmachanics. • 3 dimensionaltimeSchrodingerequationwhichisapplicableforsolution non-relativisticproblemsis in agreementwithexperiments in rangeofitsusability. • Wecanconsiderit as succesfulexpessionofphysicalpostulate. • This equation cannot be derived from any other physicallaworprinciple. Thisequationdoes not meanincreaseofthenumberofpostulatesbecauseof in agreementwiththecorrespondenceprinciplethe second Newton lawcanbederivedfromthisprinciple. The second Newton lawisthepostulate in clasicalphysics. • .

6. quantum model of atom • Solution of Schredinger equation gives the same relation as Bohr solution for hydrogen atom. The existence of quantum numbers follows from this solution including rules for theirs valid values. • Main quantum num. n=1,2,3,......... • Orbital quantum num. l=0,1,2,....(n-1) • Magnetic quantum num. ml=0,1,2,3, ……, l

7. Model of atom • We are used to mark the momentum stage by letters as follows: • l= 0 1 2 3 4 5 6 • s p d f g h i • This „code“ was created from english names of empiric clasification of spectral serie :(sharp, principal, diffuse, fundamental ). Stages of electrons are marked by combination of number n and letter (s,p,d,f) representing orbital momentum. • The same system of indication (nomenclature) is used for atom nuclei in the range of energy (shell) model of atom nucleus.

8. Model of nuclei • Atomic nuclei (kernels) are composed from protons and neutrons which are called nukleons because of the same charecteristics (excluding electromagnetic properties.

9. Table 1. Characteristics of nukleons

10. Nuclear forces – short range forces • Nuclear forces have short range (reach), they have an impact on each other (between nucleons) on distance shorter than aprox. 1,5x10-15m, at first, if we are approaching two nucleons, they are very intensive attachment forces, in the range of distances shorter than 0,4x10-15m the nuclear forces are changed into intensive detachment forces. • Nuclear forces display fullness, it means that nucleon can be in interaction only with the limited number of other nucleons, this attribute has consequences in binding energy of nuclei. • Nuclear forces are charge independent, Jaderné síly jsou nábojově nezávislé, nuclear interactions proton – neutron, neutron-neutron are the same, interaction proton – proton is different only by electorstatic interaction. • Nuclear forces are spin dependent. Interaction between two nucleons with parallel spins (J=1) is different from interactions with antiparallel spins (J=0). Energy of stage of  J=1 (triplet ) is lower then energy of  J=0 (singlet) (viz fig). • Nuclear forces has tenzor character. Properties of two nucleons systems shows fact that the nuclear forces are dependant on angle between directions of spins and direction between nucleons.

12. Potencial of nuclear forces – short range forces

13. Potencial of atom nuclei • Thedivisionofelectriccharge in nucleiisaprox. Spheric ( thisis not validfornucleiwithnucleonnumbers 150A180 and for A>225 – these nuclei are called as deformated). • Nuclearforces are charge independent and itispossible to assumethatthespacedivisionofneutronswillbethesame as protons, itmeanswecanassumethatthenuclei are sphericexceptthedeformatednuclei. • Potencialofnuclearinteractionis in these cases as wellspheric. • Thereisa big increaseofthenuclearinteraction intensity on thenucleisurface.. • Densityofnuclearmassinsidethenucleiisvarying very little, insidethenucleithe intensity offorcesbetweennucleonsissmallansthereforethepotentialwillbeapproximatellyconstant. • Electrostaticalinteractionactsforchargedparticlesoutsideofnuclei. Thisinteractioncanbecharacterized by Coulomb potential.

14. Potential of nuclei

15. Energy levels of nuclei • Nucleonshave spin 1/2, on oneenergylevelcanbeonly limited maxnumberofnucleons (Pauli law – principle)  • Everysystemof N neutrons and Z protons has onelevelwhich has minimum energy, thisis base stageofnuclei • Otherlevelscorrespondwithhigherenergies, excitedstates. Theenergydifferenceisexcitationenergyofnuclei Ei-E0 = • Everylevelischaracterized by spin.

16. Energy levels of nuclei • Spin ofnucleiwithevennucleonnumberisintegral, spin ofnucleiwithoddnucleonnumberishalf-integralbecauseof spin ofnucleonsishalf. Magneticdipolmomentum and electricalquadrupole moment belongseveryenergylevelofnuclei. • Allexcitedstages are non-stable and nucleiispassingintostagewithlowerenergymostly by photonradiation (gama ray,  photon). Iftheexcitationenergyishigherthenbindingenergy Ex ofsomeparticle X, thisparticlecanbereleased – radiatedfromthenuclei. Thenucleiischanged in this case intootherone (theexampleisalphadecay = radiationof - particle 2He4). • Meanlifetime (alternativelywidthoflevel r= h/ ) characterizestherateofdecayofnucleiexcitedstages. Meanlifetimesforvariousexcitedstages are very divergent, from10-15s up to minutes (whichiscalled as izomer stageofnuclei).

17. Binding energy of atom nuclei • Exactdeterminationofnucleimassisequivalent to determinationofbindingenergy. Withknownmassofelectronme and atommaX,formassofnucleiisvalidmX : • mX=mAx-Zme • Massofatoms and nuclei are frequentlyquoted in massunits u, where u isequal 1/12 ofmassof isotope carbon 6C12, itmeans : 1u=1,6605x10-27kg. • Massofnucleiisfrewquentlyexpressed as well in energyunits (as therestingenergy) on the base ofrelativisticequatin E=mc2. The unit in this case is 1u=931,478 MeV.

18. Binding energy of atom nuclei • Binding energy of nuclei is difference of nuclei mass and sum of nucleon masses expressed in energy units. • Binding energy EB(A,Z) of nuclei ZXA is defined as energy which is needed for division of nuclei into nucleons with kinetic energy equal 0.

19. Binding energy per one nucleon

20. Vazebná energie • Z grafu je také vidět, že složením (jaderná syntéza) lehkých jader lze získat energii, která odpovídá rozdílu vazebných energií lehkých jader a výsledného jádra. Takto lze získat i několik MeV na jeden nukleon reagujících jader. • V případě těžkých jader dochází k poklesu vazebné energie na jeden nukleon, to znamená, že jejich rozdělením (rozštěpením) můžeme získat energii. Tak rozštěpením jádra s A=200, které má EBs přibližně 7MeV, na dvě jádra s A rovno přibližně stu se dostáváme do oblasti středně těžkých jader, kde EBs8 MeV, je tedy rozdíl vazebných energií na jeden nukleon přibližně 1MeV. Energie získaná rozštěpením jednoho těžkého jádra je E200MeV.

21. Stability of nuclei

22. Stability of nuclei

23. Stability of nuclei • Binding energy is measure of nucleus stability. • .

24. Models of nucleus • Drop • Shell • Statistical

25. Drop model

26. Shell model of nucleus • Similarly as with atoms with explicit number of electrons (2, 10, 18, 36, 54 a 86) there are nuclei with explicit number neutrons or protons (2, 8, 20, 28, 50, 82 a 126) in which the nuclear structure is more stable. • Numbers 2, 8, 20 ... Are called as magic numbers. ) • Spheric distribution of electric charge, it means - these nuclei are spheric

27. Nuclear changes • If we know structure of nuclei we can explain many phenomenas which are connected with nuclei changes.

28. Radioactivity • 1896 Henri Becquerel find that uranium salts create non visible radiation which cause that photographical desk became black. Two years later the same behaviour was identified on radium and polonium and called as radioactivity.

29. Radioactivity • Radioactivityisconnectedwiththe most inner part ofatoms and itis not possible to affectit by anyouterforce. Theradioactiveray (particles) weredividedintothreegroupsafterbehaviour in magneticfield. • Plus chargedparticles - alpha , lateridentified as nuclei 2He4. • Minus (negatively) chargedparticles beta identified as electrons. • Particelswhich are not affected by magneticfield – gama – fotons, electromagneticraywith very shortwavelength (approx. 10-13 m and shorter)

30. Displacement law

31. Statistics of radioaktive decay – laws of decay Definition of half-life Between activity and change of amount of active nuclei ther is relation

33. Successive (combined) decay

34. Combined decay

37. Decay a • It is possible determine the energy from known masses of particles, original and new nuclei • Kinetic energy released during emission of various particles by heavy nuclei Q is determined by relationship:

39. Decay b

40. Decay g • Spectrum  ray is characteristical for every nucleus and it means that it can be used for identification of nuclei

42. Nuclear reactions • Elastic scatter (dispersion) X(a,a)X • Non – elastic scatter X(a,a‘)X‘ • Reaction with nuclear change X(a,b)Y • Fragmentation X(a,b1,b2,b3……)Y • Fission X(a,f)

43. Laws of consrevation in nuclear reactions • Law of Charge Conservation • Law of conservation of nucleon number (mass number is constant) • Law of energy conservation (sum of rest energies and kinetic energies is constant) • Law of conservation of momentum

44. Cross section (or sensitivity factor)

45. Cross section (sensitivity factor) • y=  N • Yield = s.f. * intensity of particles * density of interacting nuclei Coef.  is called cross section of reaction and is defined by this equation • Dimension analyses:

50. pro A, pro která platí přibližně 30A160, je vazebná energie připadající na jeden nukleon EBs=8,5 MeV s maximálně 5% odchylkou