Te structure of te atoms Atomos = indivisible University of Pécs, Medical Scool, Dept. Biopysics All tat exists are atoms and empty space; everyting else is merely tougt to exist. Democritus, 415 B.C. November 013 Josep Jon Tomson Tomson model (190) Te atom models Atoms are stable Teir cemical properties sow periodicity (Mendeleev 1869) After excitation tey emit ligt, and teir emission spectra is linear 1897 - electron Plum pudding Joann Jacob Balmer s empirical formula (1885): 1 1 1 R 4 n n: 3,4,5 R: Rydberg constant (R = 10 973 731.6 m -1 ) Ernest Ruterford Ruterford model (1911) Ruterford s conclusions 1. Te majority of matter is empty space!. Te positive carge is concentrated into a tiny space (nucleus ~10-15 m). 3. Electrons are revolving around te nucleus, like planets around te Sun. 1
Niels Bor Bor s model Bor s postulates: 1. Electrons in an atom can only ave defined orbits. Te formula defining te radius of te allowed orbits is: L mrv n r n n mv Stationary wave! Te conclusions of te Bor s model 1. Radius of te 1 st orbit: r 1 = 5.3 10-11 m (Bor-radius) r = 4r 1, r 3 = 9r 1.. r n = n r 1. Energy of te first orbit: E 1 = -13.6 ev (because it is bound) E E3 E n 4 9 n. Wen te electron jumps from one allowed orbit to anoter, te energy difference of te two states is emitted as a poton wit te energy of ν: v E E 1 Te proof of te Bor s model Te Frank-Hertz experiment Quantum mecanical atom model Matter wave wave function () Described by te Scrödinger s equation Atoms can absorb only precisely given amounts of energy. Te Hg atoms e.g. 4,9 ev. Te 4,9 ev is equals to te energy difference between te ground state and te first excited state of a Hg atom. Te position of te ground state electron of a ydrogen atom, around te nucleus. Te density of te spots is proportional to te finding probability of te electron. Te grap sows Ψ in te function of te distance measured from te nucleus. Probability of occurrence of an electron: Heisenberg s uncertainty principle (197) It is impossible to precisely determine te position and te of te particle at te same time. Te multiplication of te uncertainty (error) of two measurements at te same time is always iger tan / : x p x An example to te Heisenberg s uncertainty principle Te Large Hadron Collider ( LHC ) at CERN will be accelerating protons close to te speed of ligt, C, wose rest mass is Before acieving smasing protons at close to C, let's suppose tat te protons are speeding at wit a 1% measurement precision or Terefore, te uncertainty in measurement of proton velocity is and by te Heisenberg Uncertainty Principle, te uncertainty in simultaneously determining proton velocity and position is given as follows: Te relation gives a limit of principle: te multiplication of te measured uncertainty of te two quantities can not be smaller tan /. ttp://www.relativitycalculator.com/heisenberg_un certainty_principle.stml
describe values of conserved quantities in te dynamics of te quantum system. Tey often describe specifically te energies of electrons in atoms, but oter possibilities include angular, spin etc. It is already known from te Bor s atom model tat te energy of te electrons is quantized so tey can ave only one value. Te energy values are determined by te n principal quantum number. Te quantum mecanics is proved tat tere are sublevels of te given energy levels tat is wy te n principal quantum number is not enoug and more oter quantum numbers are needed. Te principal quantum number (n) It is known tat te principal quantum number defines te energy, and an energy value belongs to every n value ( n En ). Te electrons wit given n values are forming sells wic are named wit K, L, M, etc. letters. Tere can be more oter states inside a sell wic states are determined by te orbital quantum number. Bor ad predicted te positions of orbits wit amazing accuracy but did not take count tat tis is not te only position of electron, tis is te place were te electron can be found wit te igest probability. Te orbital quantum number (l) It defines te magnitude of te angular of an electron. Angular : Te angular of a body wic is revolving around an r radius orbital wit v speed is a vectored quantity. Its value is L = mvr. Its direction is perpendicular to te plane of te velocity. Te angular resulting from te movements of te electrons on teir orbital can only be: L l( l 1) were is te Planck constant and l is te orbital quantum number, wic can be an integer between 0 and n-1. Example: n = ; l = 0 (s state): L = 0 l = 1 (p state): L Te orbital quantum number (l) It defines te magnitude of te angular of an electron. Its value is L = mvr. Its direction is perpendicular to te plane of te velocity. Sample calculation: Te Moon: Mass = 7.344 10 kg Average orbital speed = 1.05 km/s Distance from Eart (average) = 384 400 km Angular =? kg m /s, vagy N m s Te magnetic quantum number (m) It defines te direction of te angular of an electron. Tat is wy te angular can be set only in given directions. Te projection of te angular on te direction of te outer magnetic field can only be: L z m were m is te magnetic quantum number wic values are wole numbers between -l and +l. Tis determines te direction of te angular definitely. How can it define te angular : Example: if n = ; l = 0, 1; m = -1, 0, +1 Zeeman effect I Wen an atom turns from an initial iger energy level to a stationary level wit lower energy ten te energy difference can be emitted as a poton. Tis may gives a line in te visible spectrum. In te presence of an external magnetic field, tese different states will ave different energies dueto aving different orientations of te magnetic dipoles in te external field, so te atomic energy levels are split into a larger number of levels and te spectral lines are also split. Te rate of split is proportional to te applied magnetic field. Te new lines appear symmetrically on te rigt and on te left side of te original line. Tis is te so-called Zeeman effect (normal Zeeman effect). 3
Te spin quantum number (s) It defines te value of te spin angular of te electron. It is imagined as te electron (like te Eart) not just revolving around its orbit but it is spinning around its own axis. Te electron s own angular s can only be: S s( s 1) were s is te spin quantum number. Te spin quantum number can only be ½. It does not defines oter sublevels. Te magnetic spin quantum number (m s ) It defines te direction of spin angular of an electron. Te projection of te angular on te direction of te outer magnetic field (z) can only be: S z m were m s is te magnetic spin quantum number wic is ½ or -½, so te spin (owned angular ) can be set only in two directions. s Zeeman effect II As an atom is placed into a magnetic field eac of its fine structure lines furter splits into a series of equidistant lines wit a spacing proportional to te magnetic field strengt. Te Stern-Gerlac experiment For some atoms, te spectrum displays a more complex pattern of splittings. Tat is te so-called anomalous Zeeman effect. In tese cases, it is found tat te number of Zeeman sub-levels is actually even rater tan odd. Tis cannot be explained witin te normal Zeeman teory. However, it suggests te possible existence of an angular like quantity. Te proximate proof for te evidence of spin angular was found by te Stern-Gerlac experiment. Te Stern-Gerlac experiment involves sending a beam of particles troug an inomogeneous magnetic field and observing teir deflection. Te particles passing troug te Stern-Gerlac apparatus are deflected eiter up or down by a specific amount. Tis result indicates tat spin angular is quantized (it can only take on discrete values), so tat tere is not a continuous distribution of possible angular momenta. Te Stern-Gerlac experiment Conclusions: 1 st Te experiment proves tat te angular is quantized. nd Wy is te beam deflected into two beams? if l=0 => m=0 => no deflection if l=1 => m=0, 1 => deflects into tree beams (tat is wy a two-beam deflection can not caused by direction of te angular ) Pipps and Taylor reproduced te effect using ydrogen atoms in teir ground state in 197. 195 Ulenbeck and Goudsmit formulated teir ypotesis of te existence of te electron spin. 19 Te Einstein-de Haas effect A freely suspended body consisting of a ferromagnetic material acquires a rotation wen its magnetization canges. Because of te cange of te external magnetic field mecanical rotation of te ferromagnetic material is appened associated wit te mecanical angular, wic, by te law of conservation of angular, must be compensated by an equally large and oppositely directed angular inside te ferromagnetic material. 4
Quantum number Symbol Quantized value Values Principle n Energy 1,,3 Orbital l Value of angular 0,1 n-1 ttp://dilc.upd.edu.p/images/lo/cem/quantum/quantum.swf Magnetic m Direction of angular -l, -l+1 0 l-1, l Spin s Value of own angular Magnetic spin m s Direction of own angular ½ ½, +½ 5