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.

Rutherford experiment Final intensity of electric field is approximately 1013 V/m for Thompson model. In the sescond case plus charge is located in a small nucleus in the centre of atom and calculated intensity of electric field on the surface of nucleus will be 1021 V/m which is 108 times more then in the former case. Experimental result of this diference consists in fact that majority of alfa particles is deflected (turned) only at small angles but 1/8000 of particles is deflected with angle higher then 90o . If we try to explain this difference by superposition of independent deflections, the result will be probability 10-3500 , what is in the disagreement with experimental resuts.

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

Quantum mechanics model of atom Every particle is represented by wave function , which depends on position and time. Square of amplitude of function  determines the probability of finding the particle with given properties in time and place. An improtant requirement is principle of correspondence, it means that the results of quantum mechanics must be the same in macro as results of classical machanics. 3 dimensional time Schrodinger equation which is applicable for solution non-relativistic problems is in agreement with experiments in range of its usability. We can consider it as succesful expession of physical postulate. This equation cannot be derived from any other physical law or principle. This equation does not mean increase of the number of postulates because of in agreement with the correspondence principle the second Newton law can be derived from this principle. The second Newton law is the postulate in clasical physics. .

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

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.

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

Table 1. Characteristics of nukleons Proton Neutron Mass 1,64252x10-24 g , (1836*me) 1.6726485x10-27 kg 1.00894u, tj. 1,00894 x 1,6605655x10-24 g 1.6749543x10-27kg Charge +e, 1.6021892x10-19C Spin 1/2 Half life 11,7 min ,  decay Lifetime >6x1037 s 918 (14) s

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.

Potencial of nuclear forces – short range forces

Potencial of atom nuclei The division of electric charge in nuclei is aprox. Spheric ( this is not valid for nuclei with nucleon numbers 150A180 and for A>225 – these nuclei are called as deformated). Nuclear forces are charge independent and it is possible to assume that the space division of neutrons will be the same as protons, it means we can assume that the nuclei are spheric except the deformated nuclei. Potencial of nuclear interaction is in these cases as well spheric. There is a big increase of the nuclear interaction intensity on the nuclei surface.. Density of nuclear mass inside the nuclei is varying very little, inside the nuclei the intensity of forces between nucleons is small ans therefore the potential will be approximatelly constant. Electrostatical interaction acts for charged particles outside of nuclei. This interaction can be characterized by Coulomb potential.

Potential of nuclei

Energy levels of nuclei Nucleons have spin 1/2, on one energy level can be only limited max number of nucleons (Pauli law – principle)  Every system of N neutrons and Z protons has one level which has minimum energy, this is base stage of nuclei Other levels correspond with higher energies, excited states. The energy difference is excitation energy of nuclei Ei-E0 = Every level is characterized by spin.

Energy levels of nuclei Spin of nuclei with even nucleon number is integral, spin of nuclei with odd nucleon number is half-integral because of spin of nucleons is half. Magnetic dipol momentum and electrical quadrupole moment belongs every energy level of nuclei. All excited stages are non-stable and nuclei is passing into stage with lower energy mostly by photon radiation (gama ray,  photon). If the excitation energy is higher then binding energy Ex of some particle X, this particle can be released – radiated from the nuclei. The nuclei is changed in this case into other one (the example is alpha decay = radiation of  - particle 2He4). Mean lifetime  (alternatively width of level r= h/ ) characterizes the rate of decay of nuclei excited stages. Mean lifetimes for various excited stages are very divergent, from 10-15s up to  minutes (which is called as izomer stage of nuclei).

Binding energy of atom nuclei Exact determination of nuclei mass is equivalent to determination of binding energy. With known mass of electron me and atom maX , for mass of nuclei is valid mX : mX=mAx-Zme Mass of atoms and nuclei are frequently quoted in mass units u, where u is equal 1/12 of mass of isotope carbon 6C12, it means : 1u=1,6605x10-27kg. Mass of nuclei is frewquently expressed as well in energy units (as the resting energy) on the base of relativistic equatin E=mc2. The unit in this case is 1u=931,478 MeV.

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.

Binding energy per one nucleon

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.

Stability of nuclei

Stability of nuclei

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

Models of nucleus Drop Shell Statistical

Drop model

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

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

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.

Radioactivity Radioactivity is connected with the most inner part of atoms and it is not possible to affect it by any outer force. The radioactive ray (particles) were divided into three groups after behaviour in magnetic field. Plus charged particles - alpha , later identified as nuclei 2He4. Minus (negatively) charged particles beta identified as electrons. Particels which are not affected by magnetic field – gama – fotons, electromagnetic ray with very short wave length (approx. 10-13 m and shorter)

Displacement law

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

Successive (combined) decay

Combined decay

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:

Decay b

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

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)

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

Cross section (or sensitivity factor)

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:

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

Stabilita jader nukleony jsou vázány jadernými silami jen se svými nejbližšími sousedy. Protože elektrostatické odpuzování protonů působí v celém jádře, existuje určitá hranice schopnosti neutronů bránit roztržení velkých jader. Touto hranicí je izotop vizmutu 83Bi209, který je nejtěžším stabilním nuklidem. Všechna jádra s vyšším atomovým nebo protonovým číslem jsou nestabilní a rozpadají se samovolně emisí jedné nebo více částic , což je heliové jádro 2He4. Pokud výsledné jádro má přebytek neutronů nebo protonů přechází na jádro s vyšší vazebnou energií pomocí emise elektronů ( rozpad - ) nebo pozitronů (rozpad + ). Zmíněnou linií stability se rozumí křivka izotopů s nejvyšší vazebnou energií v souřadnicích Z –N. Jádra nalevo od oblasti stabilních jader vykazují aktivitu + a jádra vpravo aktivitu -.

Stabilita jader Po dosazení jednotlivých hmotností (m(C14)=14,003235 u dostaneme energii 105,282 MeV. Druhá soustava se 14 nukleony je izotop dusíku 7N14, který má hmotnost 14,003068u. Vazebná energie tohoto izotopu je 104,656 MeV. Tedy rozdíl vazebných energií (626 keV) je dostačující na vytvoření elektronu s klidovou energií 0,51 MeV. To se projeví rozpadem jádra 6C14 na jádro 7N14 a elektron. Poločas tohoto rozpadu byl stanoven na T1/2 =5568 let. Pomocí rozpadu tohoto izotopu se stanovuje stáří některých nálezů původně živých organismů. Druhým příkladem bude samotný neutron. Jeho hmotnost a hmotnost protonu vyjádřené v jednotkách u jsou mp=1,007277u a mn=1,008664u. Rozdíl hmot je 0,001387u. Energie, která odpovídá tomuto rozdílu je 1,193 MeV. Tato hodnota je opět dostatečná na vytvoření elektronu. Lze tedy očekávat, že volný neutron se bude rozpadat na proton a elektron a bude tedy nestabilní. Radioaktivita neutronu byla zjištěna experimentálně a poločas rozpadu byl změřen na 10,8 minuty.