(************** 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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Assume ", StyleBox["r", FontSlant->"Italic"], " = 127 pm, ", StyleBox["k", FontSlant->"Italic"], " = 516 N/m, ", StyleBox["J", FontSlant->"Italic"], " = 10, ", StyleBox["n", FontSlant->"Italic"], " = 0." }], "Text"], Cell[CellGroupData[{ Cell["Solution to Part A", "Subtitle"], Cell[TextData[{ "Rotation energy.", StyleBox["\n\n", FontWeight->"Plain"], Cell[BoxData[ FormBox[ RowBox[{ StyleBox[\(E\_J\), FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox["=", FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox[\(hbar\^2\/\(2\ \[Mu]\ r\^2\)\ J\ \((J + 1)\)\), FontWeight->"Plain"]}], TraditionalForm]]], "\n\n(", StyleBox["Note: exact masses for isotopes are given in Engel, inside back \ cover.)", FontWeight->"Plain"] }], "Text", FontWeight->"Bold"], Cell[CellGroupData[{ Cell[BoxData[{ \(m1H\ = \ 1.0078\ amu\ \((1.6605\ 10\^\(-27\)\ kg/ amu)\)\), "\[IndentingNewLine]", \(m35Cl\ = \ 34.9688\ amu\ \((1.6605\ \(10\^\(-27\)\) kg/amu)\)\), "\[IndentingNewLine]", \(\[Mu]\ = \ \(m1H\ m35Cl\)\/\(m1H + m35Cl\)\)}], "Input", CellLabel->"In[83]:="], Cell[BoxData[ \(1.6734519`*^-27\ kg\)], "Output", CellLabel->"Out[83]="], Cell[BoxData[ \(5.806569240000001`*^-26\ kg\)], "Output", CellLabel->"Out[84]="], Cell[BoxData[ \(1.626574073167559`*^-27\ kg\)], "Output", CellLabel->"Out[85]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(J\ = \ 10\), "\[IndentingNewLine]", \(r\ = \ 127\ \(10\^\(-12\)\) m\), "\[IndentingNewLine]", \(hbar\ = \ 1.0546\ 10\^\(-34\)\ kg\ m\^2/s\), "\[IndentingNewLine]", \(Erot\ = \ \(hbar\^2\/\(2\ \[Mu]\ r\^2\)\) J \((J + 1)\)\)}], "Input", CellLabel->"In[86]:="], Cell[BoxData[ \(10\)], "Output", CellLabel->"Out[86]="], Cell[BoxData[ \(\(127\ m\)\/1000000000000\)], "Output", CellLabel->"Out[87]="], Cell[BoxData[ \(\(1.0546`*^-34\ kg\ m\^2\)\/s\)], "Output", CellLabel->"Out[88]="], Cell[BoxData[ \(\(2.3316155121697914`*^-20\ kg\ m\^2\)\/s\^2\)], "Output", CellLabel->"Out[89]="] }, Open ]], Cell[TextData[{ "Vibration energy.\n\n", Cell[BoxData[ FormBox[ RowBox[{ StyleBox[\(E\_n\), FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox["=", FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], RowBox[{ StyleBox["h", FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox["\[Nu]", FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], RowBox[{"(", RowBox[{ StyleBox["n", FontWeight->"Plain"], StyleBox["+", FontWeight->"Plain"], StyleBox[ FractionBox[ StyleBox["1", FontWeight->"Plain"], StyleBox["2", FontWeight->"Plain"]], FontWeight->"Plain"]}], StyleBox[")", FontWeight->"Plain"]}]}]}], TraditionalForm]]], " = ", StyleBox["hbar ", FontWeight->"Plain"], Cell[BoxData[ \(TraditionalForm\`\(\@\(k\/\[Mu]\)\) \((n\ + \ 1\/2)\)\)], FontWeight->"Plain"] }], "Text", FontWeight->"Bold"], Cell[CellGroupData[{ Cell[BoxData[{ \(k\ = \ 516\ kg/s\^2\), "\[IndentingNewLine]", \(n\ = \ 0\), "\[IndentingNewLine]", \(Evib = hbar \((\@\(k\/\[Mu]\))\) \((n\ + \ 1\/2)\)\)}], "Input", CellLabel->"In[90]:="], Cell[BoxData[ \(\(516\ kg\)\/s\^2\)], "Output", CellLabel->"Out[90]="], Cell[BoxData[ \(0\)], "Output", CellLabel->"Out[91]="], Cell[BoxData[ \(\(2.9699264854251764`*^-20\ kg\ m\^2\ \@\(1\/s\^2\)\)\/s\)], "Output", CellLabel->"Out[92]="] }, Open ]], Cell[TextData[{ StyleBox["Comparison with ", FontWeight->"Bold"], StyleBox["kT", FontWeight->"Bold", FontSlant->"Italic"], StyleBox[".", FontWeight->"Bold"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(kT\ = \ 1.3807\ 10\^\(-23\)\ \((kg\ \(m\^2\) \(s\^\(-2\)\) K\^\(-1\))\) 300\ K\)], "Input", CellLabel->"In[98]:="], Cell[BoxData[ \(\(4.142100000000001`*^-21\ kg\ m\^2\)\/s\^2\)], "Output", CellLabel->"Out[98]="] }, Open ]], Cell[TextData[{ StyleBox["Comment.", FontWeight->"Bold"], " ", StyleBox["kT", FontSlant->"Italic"], " is substantially smaller than the vibration energy. This means quantum \ behavior can be expected in terms of vibration energy exchange with the \ surrounding environment and most molecules will be in the ground vibration \ state at room temperature. The comparison with rotation energy seems less \ meaningful because we are considering a highly excited state of the molecule \ (", StyleBox["J", FontSlant->"Italic"], " = 10).\n\n", StyleBox["Part B.", FontWeight->"Bold"], " What is the period of rotation? vibration? How many times does the \ molecule rotate during a single vibration?" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Solution to Part B", "Subtitle"], Cell[TextData[{ "Rotation period. 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