(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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", FontWeight->"Plain"], Cell[BoxData[ FormBox[ StyleBox[\(E\_l\), FontWeight->"Plain"], TraditionalForm]]], " ", StyleBox["goes as ", FontWeight->"Plain"], StyleBox["l", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["(", FontWeight->"Plain"], StyleBox["l", FontWeight->"Plain", FontSlant->"Italic"], StyleBox[" + 1), so ", FontWeight->"Plain"], Cell[BoxData[ \(TraditionalForm\`E\_0\ = \ 0\)], FontWeight->"Plain"], StyleBox[".", FontWeight->"Plain"], StyleBox["\n\n", FontWeight->"Plain"], "Part B.", StyleBox[" What is the smallest quantum of energy that can be absorbed by \ this molecule in a rotational excitation?", FontWeight->"Plain"] }], "Text", FontWeight->"Bold"] }, Open ]], Cell[CellGroupData[{ Cell["Solution to Part B", "Subtitle"], Cell[TextData[{ "The transition from ", StyleBox["l", FontSlant->"Italic"], " = 0 to ", StyleBox["l", FontSlant->"Italic"], " = +1 (or -1) is the smallest energy transition for a 3D rigid rotor. The \ transition energy is \[CapitalDelta]E = ", Cell[BoxData[ \(TraditionalForm\`\(hbar\^2\/\(2\ I\)\) \(l(l\ + \ 1)\)\)]], " where ", StyleBox["l", FontSlant->"Italic"], " = 1 and ", Cell[BoxData[ \(TraditionalForm\`I\ = \ \[Mu]\ r\^2\)]], ". (", StyleBox["Note:", FontWeight->"Bold"], " Exact masses for atomic isotopes are listed in Engel, inside back \ cover.)" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(r\ = \ 91.7\ 10\^\(-12\)\ m\), "\[IndentingNewLine]", \(m1H\ = \ \((1.0078\ amu)\) \((1.661\ 10\^\(-27\)\ kg/ amu)\)\), "\[IndentingNewLine]", \(m19F\ = \ \((18.9984\ amu)\)\ \((1.661\ 10\^\(-27\)\ kg/ amu)\)\), "\[IndentingNewLine]", \(\[Mu]\ = \ \((m1H\ m19F)\)\/\(m1H\ + \ m19F\)\), \ "\[IndentingNewLine]", \(Irot\ = \ \[Mu]\ r\^2\)}], "Input", CellLabel->"In[24]:="], Cell[BoxData[ \(9.17`*^-11\ m\)], "Output", CellLabel->"Out[24]="], Cell[BoxData[ \(1.6739558000000004`*^-27\ kg\)], "Output", CellLabel->"Out[25]="], Cell[BoxData[ \(3.15563424`*^-26\ kg\)], "Output", CellLabel->"Out[26]="], Cell[BoxData[ \(1.5896313078305727`*^-27\ kg\)], "Output", CellLabel->"Out[27]="], Cell[BoxData[ \(1.3367034808103426`*^-47\ kg\ m\^2\)], "Output", CellLabel->"Out[28]="] }, Open ]], Cell[TextData[{ "Now combine ", StyleBox["I", FontSlant->"Italic"], " (\"Irot\") with ", Cell[BoxData[ FormBox[ RowBox[{\(hbar\^2\), " ", "to", " ", "obtain", " ", RowBox[{ StyleBox[ RowBox[{"\[CapitalDelta]", StyleBox["E", FontSlant->"Italic"]}]], StyleBox[".", FontSlant->"Plain"]}]}], TraditionalForm]]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(hbar\ = \ 1.0546\ 10\^\(-34\)\ \((kg\ \(m\^2\) s\^\(-2\))\) \((s)\)\), "\[IndentingNewLine]", \(\[CapitalDelta]E\ = \ hbar\^2\/Irot\)}], "Input", CellLabel->"In[29]:="], Cell[BoxData[ \(\(1.0546`*^-34\ kg\ m\^2\)\/s\)], "Output", CellLabel->"Out[29]="], Cell[BoxData[ \(\(8.320328150307266`*^-22\ kg\ m\^2\)\/s\^2\)], "Output", CellLabel->"Out[30]="] }, Open ]], Cell[TextData[{ "The smallest quantum is 8.32 \[Times] ", Cell[BoxData[ \(TraditionalForm\`\(\(10\^\(-22\)\)\(\ \)\)\)]], "J." }], "Text"] }, Open ]] }, Open ]] }, FrontEndVersion->"5.2 for Microsoft Windows", ScreenRectangle->{{0, 1280}, {0, 951}}, WindowSize->{729, 651}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, Magnification->1.5, StyleDefinitions -> "ArticleModern.nb" ] (******************************************************************* Cached data follows. 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