9.6: Emission Spectrum of Iodine Vapor
- Page ID
- 370546
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This semester, you use a laser spectrometer to investigate the Molecular Spectroscopy of Iodine Vapor. In this assignment you will plot the electronic potential energy curves (Morse potentials) for the iodine molecule. A discussion of the terms used in this assignment can be found in your textbook (D. A. McQuarrie, and J. D. Simon "Physical Chemistry: A Molecular Approach", University Science Books, CA, 1997, Chapter 13, Section 13.1-13.7.
The functional form of the ground and excited state Morse potential wells for iodine molecule I2 are given by the expression
\(V(R)= {T}_{e}+ {D}_{e} {\left[ 1- {e}^{-a(R- {R}_{e}) } \right]}^{2}\)
where V(R) is the potential energy of the system (y-axis), R is the interatomic separation (x-axis) between the iodine atoms, and Te, and De, a and Re are constants. Literature values for these constants are given below.
| Constant | Ground State | Excited State |
| Te | 0 \(( {cm}^{1})\) (arbitrarily set) | 15730 \(( {cm}^{1})\) |
| De | 12244 \(( {cm}^{1})\) | 4112 \(( {cm}^{1})\) |
| a | 1.87 \({ \left(\overset{\circ}{ A}\right) }^{-1}\) | 2.00 \({ \left(\overset{\circ}{ A}\right) }^{-1}\) |
| Re | 2.67 \(( \overset{\circ}{ A})\) | 2.97 \(( \overset{\circ}{ A})\) |
- Generate a vector R that varies between 2 and 6 Å, in increments of 0.01 Å.
- For both ground and excited states, calculate V(R) for each value of R using the above expression and the constants from the table. NOTE: These constants should be used in the units given above. No conversions are necessary.
- On the same graph, plot V(R) (y-axis) versus R (x-axis), for both ground and excited states. Rescale the axes using the following axis scales:
- V(R): 0 – 22500 cm–1
- R: 2 – 6 Å
- Assemble a pdf document that contains both this assignment and the FTIR assignment into one pdf document and submit your work on Gradescope.