3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy March 1, 2015

Transcription

1 3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy March 1, 2015 We ll use a CCD spectrometer to collect the UV and visible spectrum of dinitrogen. A strong electric field populates excited electronic states, and we re detecting the visible light as the N 2 molecules relax from these states to lower energy excited states. In particular, we ll be observing transitions of the second positive band, from the C to the B excited electronic states (see schematic in Figure 1). The transitions between these electronic energy states are complicated by transitions between the vibrational and rotational energy levels within those states. We ll be able to resolve the vibrational states in our spectra (we ll leave rotational transitions for IR spectra in the next experiment). Analyzing our spectra, we ll be able to derive microscopic information about the characteristics of these two excited states of nitrogen (Figure 1, inset). Over the next two weeks, we ll calculate the fundamental vibrational frequencies and the anharmonicity constants for the two excited states of N 2. In the first week of lab we will 1) calibrate our spectrometer using the known emission lines of Hg, 2) identify and classify the clusters of peaks and identify the transitions for the peaks in the clusters, 3) determine the wavelengths of peaks in overlapping peaks in the spectrum, and 4) determine vibrational splitting in each of the electronic states using Deslandres tables. For now we will assume that our spectra will be due to energy level diagrams similar to those shown in Figure 1. We ll assign peaks based on this assumption. Next week we ll more fully discuss the energy levels in anharmonic oscillators 1 and we ll fully analyze our assigned peaks to characterize the potential energy the excited electronic states impart on the nuclei in N 2. 1 v = 0 State C Energy Δv = v = 0 State C 2 1 v = 0 State B v = 0 Bond length State B Figure 1. A schematic of the two electronic energy states with superimposed anharmonic vibrational energy levels. Transitions of the same v = v v will have similar wavelengths creating the grouped band structure observed in molecular spectroscopy. See ref [1] for more detail of the N 2 spectrum. Inset: We can use pairs of transitions between the electronic states to calculate the vibrational spacing. Here 3 pairs of electronic transitions could be used to calculate v C (0 1).

2 3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy 2 Notation Transitions occur from vibrational states in the C energy state to vibrational states in the B energy state. The wavenumber of a transition will be written: ν v v = ( ( ) E el,c + E v,c) Eel,B + E v,b where v is the vibrational quantum number for the C state and v is the vibrational quantum number for the lower B state. E e,c is the electronic energy of state C and E v,c is the energy of vibrational state v in state C. Terms for state B are similarly defined. We ll think mostly about these transitions in the following ways: We can simplify reading the emission spectrum because transitions with the same change in vibrational quantum numbers are in grouped bands. We can get the same difference in vibrational quantum number of v = 1 from the following transitions: ν 4 3, ν 3 2, ν 2 1, and ν 1 0. Transitions between vibrational levels in a single state are giving by differences in observed transitions: The transition between the first excited and ground vibrational states in state C would be ν C (0 1) = ν 1 0 ν 0 0. These types of calculations are helped with a Deslandre table described below. Procedure We ll collect two spectra this week using the same instrumentation as we did for the H and Na emission spectra. You ll want an emission spectrum for Hg and N 2 with particular focus on the peaks in the range. Be careful: Hg emits in the UV, so avoid looking at the Hg lamp and avoid leaving the lamp on and uncovered. Even if you can t see UV radiation, it can still hurt you. Table 1. Franck-Condon factors ( 10 4 ) for N 2 vibrational transitions in the second positive system 3. ṿ. v Calibration Determine the wavelength of the following mercury peaks 2 : , , , , and nm. Do a linear fit of literature wavelength (λ) versus the your measured wavelength (λ m ): λ = mλ m + b and use this to correct your measured wavelengths in all steps below.

3 3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy 3 Band Locations Identify the bands on your spectra and start to assign v (upper, C state) and v (lower, B state) quantum numbers. Tabulate the quantum numbers and the calibrated wavelength. Be careful of garbage peaks near v = 3 and 4. McQuarrie s 1 st edition figures and on pages may be a BIG help 3. The correct, approximate band head wavelengths are 300, 315, 340, 360, 380, 405, 435, and 465 nm. Use these values to help assign the wavelengths that you find on your spectrum. More help in assigning the transitions can be found by using the transition probability as an estimate of relative peak height 4. Within a single system of 2 electronic states, the transition probability between vibrational levels depends on the degree of overlap between the wavefunctions of the two states. This overlap is captured in the Frank-Condon factors, a set of which are given in Table 1. If worse comes to worst, literature values of emission lines for nitrogen 5,6 can be used. Our CCD spectrometer doesn t quite have the resolution to make it clear, but you may have noticed that the peaks have a characteristic shape: gradually rising from the blue and steeply dropping off to the red. This is due to overlap and smearing of many closely-spaced rotational peaks for each v v transition. This shape due to the rotational fine structure of vibrational transitions is called a band head. The peak for the vibrational transition is masked in this smear, and Shoemaker 7 suggested that you use the sharp rise before the band head, not the peak center in assigning a band s wavelength. Because we can t fully resolve the band head for each peak, you may choose not to take that approach, just be consistent. See the N 2 spectra on films for a higher resolution image. Resolving Overlapping Peaks Because of low resolution in our spectrum, many of our peaks overlap. A common strategy for dealing with overlapping peaks in spectra, chromatographs, or other data sets is to deconvolute 1 the summed peak to resolve the multiple peaks that contribute to it. Appendix 1 provides an example using Mathematica to resolve 4 peaks in the v = 1 overlapping bands at 315 nm using 4 Gaussian functions and baseline shift. Although the peaks are not truly Gaussian in shape, this approximation allow us to resolve 4 unique peaks and provide estimated peak positions as the mean value in the 4 Gaussians. Copy your spectrum to a text editing software and crop it as is done in the example in Appendix 1. Use this method to resolve your peaks in the v = 0 group (5 total peaks) and the v = +1 group (4 total peaks). Table 2. A Delandres table of PN bands 7.Band-head frequencies are in cm 1 and difference between the entries in rows 0 and 1, 1 and 2, and 2 and 3 are in parentheses. 1 It is usually called deconvoluting peaks, but this term is not mathematically correct.

4 3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy 4 ṿ. v Avg. diff (1087.4) (1090.7) (1086.8) (1088) (1072.9) (1069.0) (1071.6) (1071) (1061.2) (1061.2) Build a Deslandres Table Once you have a good start at peak assignments, construct a Deslandre table following the example for PN in Table 2. This table will summarize your peak assignments in an organized way such that you ll be able to determine the vibrational splitting for each electronic state as visualized in Figure 1, inset. Note that the entries in the Deslandre table are in wavenumbers. Key results to include in your report You will not submit a written report this week. Prepare the following figures with captions: A figure showing your calibration curve. Include in the caption a comment on how this calibration compares to the calibration method we used for the H-emission experiment. A figure showing the resolution of the peaks in the v = 0 or v = +1 band. Include both the total fit as well as the individual Gaussian functions as in the plot in Appendix 1. Your Deslandre table with your peak assignments and vibrational energy differences for both the C and B states. References 1. McQuarrie D. J. Quantum Chemistry, 2 nd ed; University Science Books: Mill City, CA, 2008; pp McQuarrie D. J. Quantum Chemistry; University Science Books: Mill City, CA, 1983; pp See course webpage for link. 3. Strong Lines of Mercury (accessed Feb 23, 2015). 4. Bayram, S. B.; Freamat, M. V. Am. J. Phys. 2012, 80 (8), Lofthus, A.; Krupenie, P. H. J. Phys. Chem. Ref. Data 1977, 6 (1), Camancho, J. J.; Poyato, J. M. L.; Díaz, L; Santos, M. J. Phys. B: At. Mol. Opt. Phys. 2007, 40, 4582.

5 3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy 5 7. Shoemaker, D. P.; Garland, C. W.; Steinfeld, J. I.; Nibler, J. W. Experiments in Physical Chemistry, 4 th ed; McGraw-Hill: New York, 1985; pp

6 3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy 6 Appendix 1: Resolving overlapping peaks with Mathematica spec = , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , 99.00<, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <, , <<; gauss@x_, c_, m_, s_d := c * - Hx-mL2 2 s 2 g1@x_d := gauss@x, a1, m1, s1d g2@x_d := gauss@x, a2, m2, s2d g3@x_d := gauss@x, a3, m3, s3d g4@x_d := gauss@x, a3, m4, s4d nlm = NonlinearModelFit@spec, g1@xd + g2@xd + g3@xd + g4@xd + c, 88a1, 200<, 8m1, 310<, s1, 8a2, 200<, 8m2, 311<, s2, 8a3, 600<, 8m3, 313<, s3, 8a4, 1200<, 8m4, 315<, s4, 8c, 100<<, xd; Print@"Peak 1 is at ", m1 ê. nlm@"bestfitparameters"d, " nm"d Print@"Peak 2 is at ", m2 ê. nlm@"bestfitparameters"d, " nm"d Print@"Peak 3 is at ", m3 ê. nlm@"bestfitparameters"d, " nm"d Print@"Peak 4 is at ", m4 ê. nlm@"bestfitparameters"d, " nm"d nlm@"parametertable"d c = c ê. nlm@"bestfitparameters"d; a1 = a1 ê. nlm@"bestfitparameters"d; m1 = m1 ê. nlm@"bestfitparameters"d; s1 = s1 ê. nlm@"bestfitparameters"d; a2 = a2 ê. nlm@"bestfitparameters"d; m2 = m2 ê. nlm@"bestfitparameters"d; s2 = s2 ê. nlm@"bestfitparameters"d; a3 = a3 ê. nlm@"bestfitparameters"d; m3 = m3 ê. nlm@"bestfitparameters"d; s3 = s3 ê. nlm@"bestfitparameters"d; a4 = a4 ê. nlm@"bestfitparameters"d; m4 = m4 ê. nlm@"bestfitparameters"d; s4 = s4 ê. nlm@"bestfitparameters"d; Show@Plot@8nlm@xD, c + gauss@x, a1, m1, s1d, c + gauss@x, a2, m2, s2d, c + gauss@x, a3, m3, s3d, c + gauss@x, a4, m4, s4d <, 8x, 300, 320<, PlotRange Ø 88300, 320<, Full<D, ListPlot@specDD Peak 1 is at nm Peak 2 is at nm Peak 3 is at nm Peak 4 is at nm Printed by Mathematica for Students

7 2 Untitled-2 3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy 7 Out[38]= Estimate Standard Error t-statistic P-Value a m µ s a m µ s a µ m µ s µ a µ µ µ m µ s µ c µ Out[52]= Printed by Mathematica for Students

8 3.1: Molecular Emission Spectroscopy of N 2 CH342L: Spectroscopy 8 Appendix 2: Responsible Conduct of Research Knowledge of the professional code of conduct is a requirement to work in any field 2. For example, the prime directive in medicine is First, do no harm. Scientists have a clear code of conduct, but many aspects of this code are not specifically addressed in the classroom or teaching laboratory. Clearly, everyone knows that plagiarizing a reference or making up data is unethical, but you may encounter gray areas or unanticipated situations that pose ethical challenges. Scientists are often viewed as highly logical individuals with the highest ethical standards. However, there are numerous classical cases of research misconduct, and rogue scientists continue to operate. The U.S. Congress became interested in research misconduct in 1981 when the Oversight Subcommittee of the House Science and Technology Committee held the first hearing on the emerging problem. Eventually, the Office of Research Integrity was created within the Department of Health and Human Services (HHS). Currently, institutions receiving federal research grants are required to provide training in the responsible and ethical conduct of research to all research staff, including undergraduate students. Professional organizations such as the American Chemical Society and the American Society for Biochemistry and Molecular Biology also have the expectation that science graduates will have knowledge of research ethics. Colby meets its training requirement through a series of on-line ethics training modules. If you work in a research lab that has NSF or NIH funding, you should have already completed this training. (Please let your instructor know if this is the case.) Otherwise, you will complete these modules during your quantum lab time on Febuary or Here are the steps required for using the ethics modules at Colby College hosted by Ethics Core Digital Library: 1. Log in and set up an Ethics Core account with a user name and password: 2. Go to the new user registration page and affiliate with the group Colby College : 3. Once you have joined the Colby College group, you can complete the online ethics tutorials: 4. Complete each of the three modules: Module 1: Rights and Obligations Module 2: Collaboration, Communication, and Grants Management Module 3: Intellectual Property 5. When you have completed the modules, Seven Grenier in the Corporate, Foundation, and Government Relations Department will receive notification, which she will share with your instructor. 2 This material was prepared by Prof. Julie Millard for use in BC368.