ࡱ> ')&t7 bjbjUU ":7|7| l(((((((<    $8 t< $ 6888888$ \!( \(( } ( ( 6 6(( O<  @T0 <<((((STUDIUL FLUCTUATIILOR STATISTICE IN MASURATORI RADIOACTIVE CU CONTORI GEIGE-MULLER INTRODUCERE In fizica nucleara, un numr mare de mrimi au un caracter statistic, adic msurate fiind in acelea_i condicii experimentale, rezultatele obcinute difer unele de altele. Aceste abateri sunt proprii insusi fenomenului fizic si nu se datoreaz procesului de msurare ca si in cazul altor mrimi fizice. Din aceasta categorie fac parte fenomenele ca dezintegrarea radioactiva, interacciunea radiaciei cu materia. Lucrarea de fata are ca scop verificarea caracterului statistic al fenomenului de dezintegrare radioactiva. Pentru acest lucru avem nevoie de o lege si anume de cea care implica functia de distributie a dezintegrarii radioactive. Asadar, vom avea un numar x de dezintegrari ce au loc intr-un interval de timp t. Acest x poate lua valorile 1, 2 ,3... Tot aici vom avea si o probabilitate de a avea dezintegrari care provin din  EMBED Equation.DSMT4  nuclee radioactive, probabilitate pe care o notam cu  EMBED Equation.DSMT4 . Daca p este probabilitatea de dezintegrare a unui nucleu atunci q=1-p este probabilitatea aceluiasi nucleu de a nu se dezintegra. Deci probabilitatea evenimentului compus: x nuclee se dezintegreaza si  EMBED Equation.DSMT4  raman nedezintegrate este:  EMBED Equation.DSMT4 . Aceste dezintegrari pot avea loc de nenumarate ori, de forma  EMBED Equation.DSMT4  ori si:  EMBED Equation.DSMT4 . Aceasta lege se numeste lege de distributie binomiala. Distributia Poisson: ea se aplica unor evenimente intamplatoare in care probabilitatea de aparitie este foarte mica, p<<1, in timp ce numarul de probe  EMBED Equation.DSMT4  este atat de mare incat produsul  EMBED Equation.DSMT4  ramane constant, lucru ce se intampla si in cazul nostru. In aceste conditii, dupa o serie de calcule functia de distributie a dezintegrarii radioactive are forma:  EMBED Equation.DSMT4 . Masuratorile Geiger-Muller se comporta si ele dupa aceasta relatie, unde x este numarul de impulsuri inregistrate de catre contor intr-un anumit interval de timp. MODUL DE LUCRU Executam masuratori ale fondului cosmic cu ajutorul unui contor gama obisnuit. Intervalul de timp pentru o masuratoare este cuprins intre 5 si 10 secunda, adica t. In acest fel, nu vom avea un numar de impulsuri prea mare. Vom realiza 1000 de inregistrari si apoi, variabila statistica x este, in acest caz, numarul total de impuslsuri inregistrate in intervalul de timp t. Daca ea apare de  EMBED Equation.DSMT4  ori atunci numarul total de masuratori va fi:  EMBED Equation.DSMT4  si frecventa de aparitie a unei valori este:  EMBED Equation.DSMT4 . Reprezentam grafic  EMBED Equation.DSMT4  in functie de x sub forma unei histograme. Apoi calculam valoare experimentala medie a masuratorilor facute:  EMBED Equation.DSMT4  iar P(x) se obtine conform formulei amintita mai sus si reprezinta probabilitatea teoretica de realizare a rezultatului x. Comparam grafic/in tabel  EMBED Equation.DSMT4  si P(x), valorile obtinute trebuind sa fie apropiate. 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