CH342 Handin Homework 2

Transcription

1 CH34 Handin Homework 1. What are the quantum numbers for the energy levels that are involved in the lowest energy electronic transition for the molecule: C=C-C=C-C=C-C=C. Base your answer on the particlein -the-box model.. (a). Calculate the wavelength of the light absorbed in Problem 1. Assume the bonds are equivalent and the bond length is 1.39 Å. (b). Calculate the energy in cm Sketch the wavefunctions for the potentials shown on the next page.

2 tch-a-sketch use this function as a start V x V use this function as a start x Ohio Arts

3 Spectral Deconvolution and nergy level Diagrams The electronic energy level diagram for a typical molecule is shown in Figure 1. Molecules have many possible excited states. Absorption transitions in the UV/Visible portion of the spectrum correspond to transitions from the ground electronic state to the various excited electronic states. The closely spaced horizontal lines represent the different vibrational states of the given electronic state. These diagrams are called Jablonski diagrams. third excited state second excited state first excited state absorbance ground state Figure 1. Typical electronic energy level diagram. The assignment is to construct such a diagram, carefully and to scale, for bromothymol blue. The UV/Visible absorption spectrum for bromothymol blue in given in Figure. A λ (nm) Figure. UV/Visible absorption spectrum for bromothymol blue in water.

4 xample Problem: Here is an example that will help you draw the energy level diagram from your spectrum. A typical example spectrum is given in Figure Absorbance w ave le ngth (nm ) Figure 3. xample spectrum The first step is to convert the wavelengths to energy units or units like cm -1 that are directly proportional to energy, Figure 4. Then each transition is resolved by approximating each transition as a simple Gaussian peak. This process is often done by least squares fitting programs, which in this context is called spectral deconvolution. For the purposes of this exercise, the deconvolution process can just be done by eye with a pencil. Often the actual number of transitions is not completely clear, but you do the best you can with the information available. ach transition is to a different electronic state. For each electronic state the electrons are in different sets of molecular orbitals Absorbance (cm -1 ) Figure 4. Spectrum with the wavelength axis converted to wavenumbers (cm -1 ). The process of drawing the energy level diagram can be illustrated simply by rotating the absorbance spectrum on its side and using the spectral transitions to delineate the energy levels

5 into bands. It is common for the transitions to overlap. Table 1 provides the energies that are needed for this process from Figure 4. The wavelengths or wavenumbers at the start and end of each band are read by eye directly from the deconvoluted spectra. The resulting energy level diagram is shown in Figure 5. Table 1. The start and end of each band are read from the deconvoluted spectrum. The values are approximate and are often read in nm from the original spectrum and converted to wavenumbers. Transition Start of absorption band nd of absorption band λ (nm) cm-1 λ (nm) cm-1 First excited state Second excited state Third excited state Fourth excited state (cm-1) nergy (cm-1) A bsorbance ground state Figure 5. The process for drawing the energy level diagram can be illustrated by picturing the spectrum tilted on its side. The different excited state bands are offset for clearity (they are all singlet states if the ground state is a singlet). In this example, the original spectrum was converted to a plot of absorbance versus wavenumber. In actual use, the start and end wavelengths are often read directly from the

6 spectrum plotted versus wavelength. The intermediate step of converting the spectrum to a wavenumber axis is useful for demonstrating the relationships involved, but the conversion is not necessary in practice. ach electronic transition is really a set of transitions to different vibrational states of the same electronic state. The set of vibrational transitions to a given electronic state form a band of states given by the width of the electronic transition. The vibrational bands are often drawn as a series of lines, Figures 1 and 5. These lines correspond to the different vibrational transitions. For our current purposes, the spacing between the lines is arbitrary since the wavenumber resolution in solution UV/visible spectra is usually not sufficient to discern the vibrational lines. For homework purposes, the process of deconvoluting a spectrum can be done by hand with a pencil. No complicated calculations are necessary. However, if you don t have some prior experience, the process of determining the number of transitions and their widths can be difficult. Two xcel spreadsheets are available on the PChem Homework Web page to help you explore the deconvolution process. The deconvolution can be done on spectra as a function of wavelength or as a function of wavenumber. These spreadsheets do Gaussian deconvolution for a spectrum plotted as a function of wavelength. Try the xcel spreadsheet example: to test your skills. On the PC, the following message will appear in xcel below the top icon bar. Click on Options : In the subsequent Security dialog box, click on nable this content and then click OK : On the Mac, a single dialog box will appear in which you click on nable Macros. In the spreadsheet, use the up and down arrows to change the center, width, and area settings for each absorption band to get a good fit. You can judge the fit by looking at the difference spectrum in the bottom plot. You will only need five components to fit this example spectrum, even though six are available. The best parameter values are listed below, so that you can check your work. 1 This example spectrum is actually calculated from overlapping Gaussians, so the fit can work out to be perfect, which is not possible with experimental spectra. The spectrum for bromothymol blue in Figure is also available loaded into the same spreadsheet on the Homework Web page:

7 You then need to convert the start and end wavelengths to wavenumbers before constructing your energy level diagram. Use the following table to organize your measurements. Transition Start of absorption band nd of absorption band λ cm-1 λ cm-1 First excited state Second excited state Third excited state Fourth excited state Fifth excited state 1. Parameters to fit the example spectrum in Figure 3: cmp 1 cmp cmp 3 cmp 4 cmp 5 center nm width nm area