ࡱ> npmh5@vtbjbj22 0XXJ#vvvv  *& \"""---U%W%W%W%W%W%W%$'Rh){%i- "---{%vv"g %$$$-v"U%$-U%$"$$d^$ zA /"$U%%0*&$)$)$vvvv)$|--$-----{%{% $ Experimentul Stern  Gerlach. Devierea unui fascicul de atomi printr-un cmp magnetic variabil. Descrierea dispozitivului experimental. Fig. 1 Dispozitivul experimental const ntr-o surs de atomi de argint n stare fundamental, un sistem electromagnetic ce creeaz un cmp magnetic puternic variabil, _i un ecran sensibil, pe care se nregistreaz incidencele atomilor de argint (Fig. 1). Se poate observa, n urma experimentului, c fasciculul de particule nu rmne coerent, ci se scindeaz n dou subfascicule. Problema nu a putut fi explicat prin teoria clasic, ci au trebuit introduse nociuni noi, cum ar fi spinul electronic, momentul magnetic de spin, interacciunea spin-orbit. n cele ce urmeaz este prezentat explicacia acestui fenomen _i un calcul teoretic al devierii pe vertical a fasciculului. Considerente teoretice. Momentul cinetic n mecanica cuantic. Corectarea cuantificrii date de Niels Bohr momentului cinetic,  EMBED Equation.DSMT4 , a fost adus mai trziu, fundamentat de Schrdinger _i Heisenberg. Cuantificarea oricrui moment cinetic din mecanica cuantic se face dup o regul simpl:  EMBED Equation.DSMT4 , unde l este numrul cuantic corespunztor. nc o regul dat de mecanica cuantic este cea a cuantificrii unui moment cinetic rezultant. Dac avem dou momente cinetice  EMBED Equation.DSMT4  _i  EMBED Equation.DSMT4 , care se cuantific dup regulile  EMBED Equation.DSMT4 , respectiv  EMBED Equation.DSMT4 , atunci momentul cinetic rezultant,  EMBED Equation.DSMT4  se cuantific dup regula  EMBED Equation.DSMT4 , unde  EMBED Equation.DSMT4 . Momentul cinetic orbital, numrul cuantic orbital, momentul magnetic orbital, numrul cuantic magnetic. Momentul cinetic orbital se cuantific dup regula cunoscut,  EMBED Equation.DSMT4 , unde  EMBED Equation.DSMT4 . De asemenea, se cuantific _i proieccia acestui moment cinetic pe o ax preferencial (de exemplu  a unui cmp magnetic), prin formula  EMBED Equation.DSMT4 , unde ml este numrul cuantic magnetic,  EMBED Equation.DSMT4 . Corespunztor momentului cinetic orbital este un moment magnetic orbital, dat de formula binecunoscut,  EMBED Equation.DSMT4 . Dac introducem atomul ntr-un cmp magnetic  EMBED Equation.DSMT4  va aprea o energie de interacciune magnetic, dat de formula  EMBED Equation.DSMT4 . Dar  EMBED Equation.DSMT4 , _i avem  EMBED Equation.DSMT4 , unde  EMBED Equation.DSMT4  se nume_te magneton Bohr. Momentul cinetic de spin, numrul cuantic de spin, momentul magnetic de spin, numrul cuantic magnetic de spin. Spinul electronic a fost introdus fr suport intuitiv, pentru c s-a demonstrat c electronul nu poate avea o mi_care efectiv de rotacie n jurul axei proprii. Spinul electronic trebuie privit ca o proprietate intrinsec a electronului, ca _i momentul cinetic (se observ din cuantificare c momentul cinetic poate fi _i nul, ceea ce contrazice firescul). Momentul cinetic de spin se cuantific identic cu celelalte momente cinetice:  EMBED Equation.DSMT4 . n cuantificare, s este numrul cuantic de spin. S-a artat c acesta nu poate lua dect valoarea  EMBED Equation.DSMT4 . De asemenea, proieccia acestui moment cinetic pe o ax preferencial se cuantific:  EMBED Equation.DSMT4 , unde ms se nume_te numr cuantic magnetic de spin _i ia dou valori:  EMBED Equation.DSMT4 . Corespunztor momentului cinetic de spin apare un moment magnetic de spin. Apare ns o anomalie fac de momentul magnetic orbital, factorul de proporcionalitate se schimb:  EMBED Equation.DSMT4 , nu cum ne-am fi a_teptat. Proieccia momentului magnetic de spin pe o direccie preferencial se cuantific de asemenea:  EMBED Equation.DSMT4 . Interacciunea spin-orbit. Momentul cinetic total. Momentul magnetic total. Momentul magnetic efectiv. S-a introdus interacciunea spin-orbit ca o orientare a  EMBED Equation.DSMT4  n cmpul magnetic produs de mi_carea orbital ( EMBED Equation.DSMT4 ). Energia electronului n atom depinde nu doar de mi_carea n jurul nucleului, ci _i de spin. Momentul cinetic total al atomului este  EMBED Equation.DSMT4 . Acesta se cuantific dup regula cunoscut:  EMBED Equation.DSMT4 , unde  EMBED Equation.DSMT4 , deoarece  EMBED Equation.DSMT4 . De asemenea vom avea un moment magnetic total  EMBED Equation.DSMT4 . Interacciunea dintre aceste momente cinetice se manifest sub forma unei precesii a cuplului spin-orbit ( EMBED Equation.DSMT4 ), dar _i a unei precesii a lui  EMBED Equation.DSMT4  n jurul unei axe preferenciale. Componenta  EMBED Equation.DSMT4  este cuantificat dup regula  EMBED Equation.DSMT4 , unde  EMBED Equation.DSMT4 . Se mai observ c, datorit anoN     4 bdbdᰛsaMs7s+jh/CJOJQJU^JaJmHsH&h*h/56OJQJ^JmHsH"h"zCJOJQJ^JaJmHsH"h/CJOJQJ^JaJmHsH+h"zh"z5CJOJQJ^JaJmHsH(h"zh"zCJOJQJ^JaJmHsH)jh"zh"zOJQJU^JmHsHh/OJQJ^JmHsHhJpOJQJ^JmHsHh"zOJQJ^JmHsH h"zh"zOJQJ^JmHsH  dhvx"%~&z((*, $a$gd*xgd* $a$gdxgdgd xgd  $a$gd  $xa$gd"zxgd"zgd"zrtt  hhjѻ{nY@Y1jh h/CJOJQJU^JaJmHsH(h h/CJOJQJ^JaJmHsHh/6CJaJmHsH5j?h/h/CJEHOJQJU^JaJmHsH%j]#@ h/CJUVaJmHsH"h/CJOJQJ^JaJmHsH+jh/CJOJQJU^JaJmHsH5j<h/h/CJEHOJQJU^JaJmHsH%j\#@ h/CJUVaJmHsH"$RTVXpȯ~cG,5jQIh h/CJEHOJQJU^JaJmHsH7j^#@ h h/CJOJQJUV^JaJmHsH5jiFh h/CJEHOJQJU^JaJmHsH7j^#@ h h/CJOJQJUV^JaJmHsH(h h/CJOJQJ^JaJmHsH1jh h/CJOJQJU^JaJmHsH5jCh h/CJEHOJQJU^JaJmHsH7jo^#@ h h/CJOJQJUV^JaJmHsHpr "$&\^ѵ~cG,5jSh h/CJEHOJQJU^JaJmHsH7j]#@ h h/CJOJQJUV^JaJmHsH5jPh h/CJEHOJQJU^JaJmHsH7j^#@ h h/CJOJQJUV^JaJmHsH5jMh h/CJEHOJQJU^JaJmHsH7j^#@ h h/CJOJQJUV^JaJmHsH(h h/CJOJQJ^JaJmHsH1jh h/CJOJQJU^JaJmHsH@vѼlZD.D*h*h 6CJOJQJ\^JmHsH*h*hL6CJOJQJ\^JmHsH"h CJOJQJ^JaJmHsH5jnWh hLCJEHOJQJU^JaJmHsH7j _#@ h hLCJOJQJUV^JaJmHsH1jh hLCJOJQJU^JaJmHsH(h hLCJOJQJ^JaJmHsH(h h/CJOJQJ^JaJmHsH1jh h/CJOJQJU^JaJmHsH &(VXZ\jlڱڃhU:5jxahLhLCJEHOJQJU^JaJmHsH%j`#@ hLCJUVaJmHsH5jf^hLhLCJEHOJQJU^JaJmHsH%jF`#@ hLCJUVaJmHsH5jZh/hLCJEHOJQJU^JaJmHsH%j]#@ hLCJUVaJmHsH+jhLCJOJQJU^JaJmHsH"hLCJOJQJ^JaJmHsH&h*hL6OJQJ\^JmHsH<>lnprFHvxz| ֭dR,,,,,ĩז{hM:%jl#@ hCJUVaJmHsH5jȩhhCJEHOJQJU^JaJmHsH%jl#@ hCJUVaJmHsH5jӦhhCJEHOJQJU^JaJmHsH%jk#@ hCJUVaJmHsH5jhhCJEHOJQJU^JaJmHsH%jk#@ hCJUVaJmHsH"hCJOJQJ^JaJmHsH+jhCJOJQJU^JaJmHsH,,, --<->-@-B-P-R------RRRRSμμμμ{`μ^μK%jm#@ hCJUVaJmHsHU5jhhCJEHOJQJU^JaJmHsH%jol#@ hCJUVaJmHsH5jhhCJEHOJQJU^JaJmHsH%j8l#@ hCJUVaJmHsH"hCJOJQJ^JaJmHsH+jhCJOJQJU^JaJmHsH5jhhCJEHOJQJU^JaJmHsH,-dWXZYYZf\\]]`pbbhevg,idi>jBkzk $a$gd;$ $a$gd;$ $a$gdd$v $a$gdQixgdQi $a$gdQi $a$gdg $a$gd*maliei ce a aprut la proporcionalitatea dintre momentul cinetic _i cel magnetic de spin, direccia lui  EMBED Equation.DSMT4  nu corespunde direcciei lui  EMBED Equation.DSMT4 . Datorit precesiei, _i vectorii  EMBED Equation.DSMT4  _i  EMBED Equation.DSMT4 , deci _i  EMBED Equation.DSMT4  vor efectua o precesie n jurul direcciei lui  EMBED Equation.DSMT4 . Aceasta ne permite s introducem un moment magnetic efectiv al atomului, obcinut prin mediere pe mai multe perioade a vectorului  EMBED Equation.DSMT4 . Notm acest moment magnetic efectiv cu  EMBED Equation.DSMT4  (figura 2). Acest moment magnetic efectiv poate fi calculat. Observm c:  EMBED Equation.DSMT4 . Cosinusurile respective le vom obcine din teorema cosinusului aplicat n triunghiul respectiv al momentelor cinetice:  EMBED Equation.DSMT4 , respectiv  EMBED Equation.DSMT4 . Vom folosi urmtoarele identitci:  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4 . Acum putem scrie:  EMBED Equation.DSMT4 , sau, dup simplificri _i aducerea la acela_i numitor:  EMBED Equation.DSMT4 . Acum folosim faptul c  EMBED Equation.DSMT4  _i pentru celelalte momente cinetice analog, deci vom avea expresia lui  EMBED Equation.DSMT4  doar n funccie de numerele cuantice respective:  EMBED Equation.DSMT4 . Dac n formula de mai sus notm cu  EMBED Equation.DSMT4 , vom avea  EMBED Equation.DSMT4 . Vectorial, putem scrie:  EMBED Equation.DSMT4  Coeficientul g se nume_te factor Land de proporcionalitate a momentului magnetic efectiv fac de momentul cinetic total. binnd cont de expresia magnetonului Bohr, putem scrie _i o formul alternativ a momentului magnetic efectiv:  EMBED Equation.DSMT4 , expresie care seamn ca form cu cele ale  EMBED Equation.DSMT4  sau  EMBED Equation.DSMT4 . Atomul, plasat ntr-un cmp magnetic suficient de mic astfel nct s nu strice cuplajul spin-orbit, va avea o energie suplimentar de interacciune magnetic:  EMBED Equation.DSMT4 , unde  EMBED Equation.DSMT4 . Explicacia scindrii fasciculului de atomi de Ag Stern _i Gerlach au folosit atomi de Ag pentru faptul c au doar un singur electron pe ultimul strat, _i acesta este oarecum ecranat de celelalte straturi. Similaritatea cu atomul de Hidrogen este foarte mare. Atomii de Ag erau n stare fundamental. Explicacia o vom da prin analogie cu atomii de Hidrogen n stare fundamental. Atomul de hidrogen n stare fundamental are numerele cuantice  EMBED Equation.DSMT4 . n acest caz, factorul Land are valoarea  EMBED Equation.DSMT4 . Energia de interacciune magnetic va avea urmtoarele valori posibile:  EMBED Equation.DSMT4 . n cmp magnetic variabil, energia potencial de interacciune magnetic este variabil _i d na_tere unei force (este forca care mparte fasciculul n dou). Matematic, aceast forc este dat de relacia binecunoscut:  EMBED Equation.DSMT4  n formula de mai sus EMBED Equation.DSMT4  sunt versorii celor trei axe ( EMBED Equation.DSMT4 ). Cum cmpul n experiment variaz puternic doar pe direccia z, pe celelalte dou fiind constant, formula de mai sus se simplific:  EMBED Equation.DSMT4  Dar  EMBED Equation.DSMT4  _i  EMBED Equation.DSMT4 . Iat c asupra atomilor accioneaz force proporcionale cu gradientul cmpului magnetic, n dou sensuri. O parte din atomi vor avea  EMBED Equation.DSMT4  _i o parte vor avea  EMBED Equation.DSMT4 , de aceea se mparte fasciculul de atomi n dou. Dac lungimea sectorului cu cmp magnetic variabil este x _i distanca pe care atomii se mi_c liber (distanca de la electromagnet pn la ecran) este D, atunci se arat u_or c devierea fasciculului are formula:  EMBED Equation.DSMT4  Iat cum am putut explica scindarea fasciculului de atomi de Ag cu ajutorul analogiei cu modelul atomului de Hidrogen. Experimentul Stern-Gerlach este de referinc n evolucia mecanicii cuantice, confirmnd presupunerile fizicienilor cu privire la spinul electronic _i interacciunea spin-orbit. 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