(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 18828, 537] NotebookOptionsPosition[ 16591, 455] NotebookOutlinePosition[ 17030, 472] CellTagsIndexPosition[ 16987, 469] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Problema gu\[IAcute]a de dispersi\[OAcute]n", "Title", CellChangeTimes->{{3.526033317296875*^9, 3.52603332703125*^9}, { 3.7150818365908003`*^9, 3.7150818391647997`*^9}}], Cell[BoxData[{ RowBox[{"<<", "PhysicalConstants`"}], "\[IndentingNewLine]", RowBox[{"<<", "Units`"}]}], "Input", CellChangeTimes->{{3.52603179084375*^9, 3.526031792203125*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "VacuumPermittivity", "]"}]], "Input", CellChangeTimes->{{3.52620024775*^9, 3.526200250703125*^9}}], Cell[BoxData[ FractionBox[ RowBox[{"8.85418781762039`*^-12", " ", "Ampere", " ", "Second"}], RowBox[{"Meter", " ", "Volt"}]]], "Output", CellChangeTimes->{{3.526200239859375*^9, 3.526200250984375*^9}, 3.526200560796875*^9, 3.526202564390625*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "ElectronCharge", "]"}]], "Input", CellChangeTimes->{{3.526200680984375*^9, 3.52620071390625*^9}, { 3.526200753859375*^9, 3.52620075975*^9}}], Cell[BoxData[ RowBox[{"1.602176487`*^-19", " ", "Coulomb"}]], "Output", CellChangeTimes->{{3.526200685984375*^9, 3.526200714265625*^9}, 3.52620076009375*^9, 3.526202564421875*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Datos y magnitudes", "Section", CellChangeTimes->{{3.526032309984375*^9, 3.52603231478125*^9}}], Cell[CellGroupData[{ Cell["Haz", "Subsection", CellChangeTimes->{{3.5260306204375*^9, 3.52603062090625*^9}}], Cell[TextData[{ "El haz est\[AAcute] caracterizado por \ni) los iones del haz: \ part\[IAcute]culas \[Alpha], n\[UAcute]mero at\[OAcute]mico ", Cell[BoxData[ FormBox[ SubscriptBox["Z", "\[Alpha]"], TraditionalForm]]], "=2, n\[UAcute]mero de masa ", Cell[BoxData[ FormBox[ SubscriptBox["A", "\[Alpha]"], TraditionalForm]]], "=4, su Energia\nii) la corriente i y por eventualmente la secci\[OAcute]n \ A (no es dato, pero se cancela luego) \nCon esos datos uno busca el flujo de \ part\[IAcute]culas incidente NN." }], "Text", CellChangeTimes->{{3.5260306265625*^9, 3.526030670359375*^9}, { 3.526030722*^9, 3.526030890609375*^9}, {3.526031384765625*^9, 3.526031434609375*^9}, {3.5260314904375*^9, 3.526031525890625*^9}, { 3.5260334239375*^9, 3.5260334495625*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"Energia", "=", RowBox[{"55", "*", RowBox[{"10", "^", "6"}], RowBox[{"Convert", "[", RowBox[{"ElectronVolt", ",", "Joule"}], "]"}]}]}], " ", RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{"sistema", " ", "de", " ", "laboratorio"}], "=", RowBox[{"sistema", " ", "de", " ", "centro", " ", "de", " ", "masa"}]}], ",", " ", RowBox[{ "pues", " ", "la", " ", "masa", " ", "del", " ", "oro", " ", "es", " ", "mucho", " ", "mas", " ", "grande", " ", "que", " ", "la", " ", "de", " ", "las", " ", "part\[IAcute]culas", " ", "\[Alpha]"}]}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"i", "=", RowBox[{"0.5", "*", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "9"}], ")"}]}], "Ampere"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["Z", "\[Alpha]"], "=", "2"}], ";"}]}], "Input", CellChangeTimes->{{3.5260314395625*^9, 3.52603155928125*^9}, { 3.52603170128125*^9, 3.526031740515625*^9}, {3.526031868953125*^9, 3.526031884171875*^9}, {3.52603199165625*^9, 3.5260320310625*^9}, { 3.52603206321875*^9, 3.526032065890625*^9}, {3.526033455140625*^9, 3.526033522859375*^9}, {3.52620064484375*^9, 3.526200663828125*^9}, { 3.526200724765625*^9, 3.5262007358125*^9}, 3.5262022036875*^9}], Cell[BoxData[ RowBox[{"8.8119706785`*^-12", " ", "Joule"}]], "Output", CellChangeTimes->{3.526202204*^9, 3.526202564484375*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NN", "=", " ", RowBox[{"i", "/", RowBox[{"(", RowBox[{ SubscriptBox["Z", "\[Alpha]"], "ElectronCharge", " ", "A"}], ")"}], " "}]}]], "Input", CellChangeTimes->{{3.5260320598125*^9, 3.526032072296875*^9}}], Cell[BoxData[ FractionBox[ RowBox[{"1.5603774117801044`*^9", " ", "Ampere"}], RowBox[{"A", " ", "Coulomb"}]]], "Output", CellChangeTimes->{3.526200561*^9, 3.52620077753125*^9, 3.52620256453125*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Blanco", "Subsection", CellChangeTimes->{{3.52603090296875*^9, 3.52603090409375*^9}}], Cell[TextData[{ "El blanco son \[AAcute]tomos de oro. La dispersi\[OAcute]n se d\[AAcute] \ por interacci\[OAcute]n con el n\[UAcute]cleo con carga ", Cell[BoxData[ FormBox[ SubscriptBox["Z", "Au"], TraditionalForm]]], "=79 veces el m\[OAcute]dulo de la la carga del electr\[OAcute]n, \ n\[UAcute]mero de masa ", Cell[BoxData[ FormBox[ SubscriptBox["A", "Au"], TraditionalForm]]], "=197. el blanco posee un espesor: Th=\[Rho]d, \n\[Rho] es la densidad y d \ es la profundidad del blanco. Asumimos condici\[OAcute]n de simple dispersi\ \[OAcute]n: las part\[IAcute]culas son dispersadas solamente por el \ n\[UAcute]cleo m\[AAcute]s cercano que encuentran en el camino.\nSe busca el \ n\[UAcute]mero de dispersores Nd=\[Rho] d A atravezados por el haz:" }], "Text", CellChangeTimes->{{3.526030907453125*^9, 3.52603128903125*^9}, { 3.526032272734375*^9, 3.52603227509375*^9}, {3.526032475046875*^9, 3.52603253615625*^9}, {3.526032680421875*^9, 3.526032681046875*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"Th", "=", RowBox[{"0.5", " ", "*", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "3"}], ")"}]}], "*", RowBox[{"10", "^", RowBox[{"(", "4", ")"}]}], " ", RowBox[{"Kilogram", "/", RowBox[{"Meter", "^", "2"}]}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["Z", "Au"], "=", "79"}], " ", ";"}], " ", RowBox[{"(*", " ", RowBox[{"N\[UAcute]mero", " ", "At\[OAcute]mico", " ", "del", " ", "oro"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["A", "Au"], "=", "197"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{"Masa", " ", "At\[OAcute]mica", " ", "del", " ", "oro"}], " ", "*)"}]}]}], "Input", CellChangeTimes->{{3.52603129165625*^9, 3.526031292734375*^9}, { 3.52603133534375*^9, 3.5260313680625*^9}, {3.52603211921875*^9, 3.52603215525*^9}, {3.526032191921875*^9, 3.526032236453125*^9}, { 3.526200944609375*^9, 3.526200975375*^9}, {3.526201135375*^9, 3.52620124528125*^9}, 3.52620228021875*^9}], Cell[BoxData[ FractionBox[ RowBox[{"5.`", " ", "Kilogram"}], SuperscriptBox["Meter", "2"]]], "Output", CellChangeTimes->{3.526202280984375*^9, 3.5262025645625*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ SubscriptBox["M", "Au"], "=", RowBox[{ RowBox[{"(", RowBox[{ SubscriptBox["A", "Au"], "*", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "3"}], ")"}]}], RowBox[{"Kilogram", "/", "Mole"}]}], ")"}], "/", "AvogadroConstant"}]}], "\[IndentingNewLine]", RowBox[{"Nd", "=", RowBox[{"Th", "*", RowBox[{"A", "/", " ", SubscriptBox["M", "Au"], " ", RowBox[{"(*", " ", RowBox[{"Numero", " ", "de", " ", "dispersores"}], " ", "*)"}]}]}]}]}], "Input", CellChangeTimes->{{3.52603129165625*^9, 3.526031292734375*^9}, { 3.52603133534375*^9, 3.5260313680625*^9}, {3.526032279109375*^9, 3.52603228253125*^9}, {3.52620116375*^9, 3.526201174828125*^9}, 3.526201259671875*^9, {3.52620135346875*^9, 3.526201390140625*^9}, { 3.526201493203125*^9, 3.5262015876875*^9}, {3.526202327625*^9, 3.5262023345*^9}, {3.7150816784656*^9, 3.7150816914472*^9}}], Cell[BoxData[ RowBox[{"3.27126140283057`*^-25", " ", "Kilogram"}]], "Output", CellChangeTimes->{{3.52620151359375*^9, 3.52620154015625*^9}, 3.5262015911875*^9, 3.526201661359375*^9, 3.52620188275*^9, { 3.526202330703125*^9, 3.526202334796875*^9}, 3.52620256459375*^9}], Cell[BoxData[ FractionBox[ RowBox[{"1.5284623832487308`*^25", " ", "A"}], SuperscriptBox["Meter", "2"]]], "Output", CellChangeTimes->{{3.52620151359375*^9, 3.52620154015625*^9}, 3.5262015911875*^9, 3.526201661359375*^9, 3.52620188275*^9, { 3.526202330703125*^9, 3.526202334796875*^9}, 3.526202564609375*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Detector", "Subsection", CellChangeTimes->{{3.52603090296875*^9, 3.52603090409375*^9}, { 3.526032334359375*^9, 3.52603233584375*^9}}], Cell["\<\ El detector posee una secci\[OAcute]n a y est\[AAcute] ubicado a una \ distancia d de 20 cm. A esta distancia todas las part\[IAcute]culas \ dispersadas con el mismo \[AAcute]ngulo por cualquier n\[UAcute]cleo de oro \ son detectadas. El \[AAcute]ngulo de detecci\[OAcute]n es \[Theta]=5 grados.\ \>", "Text", CellChangeTimes->{{3.526030907453125*^9, 3.52603128903125*^9}, { 3.526032272734375*^9, 3.52603227509375*^9}, {3.526032343109375*^9, 3.526032455890625*^9}, 3.526032899125*^9, {3.52603294546875*^9, 3.526032974046875*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"a", "=", RowBox[{"Pi", "*", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "3"}], ")"}]}], "/", "2"}], ")"}], "^", "2"}], " ", RowBox[{"Meter", "^", "2"}]}]}], "\[IndentingNewLine]", RowBox[{"d", "=", RowBox[{"20", "*", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "2"}], ")"}]}], "Meter"}]}], "\[IndentingNewLine]", RowBox[{"\[Theta]", "=", RowBox[{"5.", "*", RowBox[{"Pi", "/", "180"}]}]}]}], "Input", CellChangeTimes->{{3.52603129165625*^9, 3.526031292734375*^9}, { 3.52603133534375*^9, 3.5260313680625*^9}, {3.52603211921875*^9, 3.52603215525*^9}, {3.526032191921875*^9, 3.526032236453125*^9}, { 3.526032606140625*^9, 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