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Vibrational and Rotational Spectra of Diatomic Molecules

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Vibrational and Rotational Spectra of Diatomic Molecules Vibrational and Rotational Spectra of Diatomic Molecules: Two Experiments in an Advanced Laboratory Course of Atomic and Molecular Spectroscopy Mario Freamat Morrisville State College, Physics Department, Morrisville, NY 13408 S. Burcin Bayram Miami University, Physics Department, Oxford, OH 45056 TOPIC AND COURSE THE DIATOMIC MOLECULE EXPERIMENTS B. Observations • In our lab, the students observe emission spectra originating from A. Subject and Target Audience A. Mechanical Model for the vibrational A. Experimental Setup the relaxation of nitrogen molecules after excitation via two different mechanisms: and rotational degrees of freedom of the N2 • We present a sequence of two instructional N2 Discharge Tube molecule 1. By resonance of N with argon residues ionized by electron Handheld spectrometer. 2 experiments scrutinizing the energy structure collisions into metastable states. The ensuing vibrational emission of molecular nitrogen – an epitomic Needs a resolution of 0.01 nm to observe spectrum is the Second Positive System: homonuclear diatomic molecule. N rotational features 33 • Easily adaptable for lower- and upper-level C v 0 B v 0,1,2... r ug courses; for instance: N N is excited in the 2. By ionization and then excitation mainly by electron impact, 2 + 1. Currently implemented in the Department of vicinity of electrodes followed by the decay of N2 to the ground. The ensuing Physics at Miami University, in an advanced where the spectrum rotational emission spectrum is the First Negative System: laboratory course of Atomic and Molecular can be read via an B. Quantum Mechanical Model optical fiber 22 Spectroscopy (PHY 4/542) – 9-15 upper-level Bug v 0, J X v 0, J undergraduate and graduate physics students • Molecular orbitals result from superposed 2. Downscaled version to be offered at atomic orbitals spawning electronic states Vibrational Structure: Rotational Structure: Morrisville State College in a course of Optics • Each electronic state comprises a structure of C. Potential Curves and Transition Diagrams and Modern Physics (PHYS 258) – 6-10 Branches vibrational levels indexed v, each split into a 13 25 ퟑ 2 engineering science sophomores 푪 횷 fine structure of rotational levels indexed J 12 퐮 1 P R v′= 2 23 0, 4 1 v′ = 0 ퟐ 0, 3 11 0 푩 횺퐮 v′, J′ 0, 2 02 0, 1 B. Goals • The strength and length of the inter-atomic 0, 0 10 De 6 21 01 5 v ′ 3 bonds depend on the particular electron 9 ω 4 2 ퟑ el 19 1 00 3 0 • Enable the students to establish an = 푩 횷퐠 8 v ″ 4 v″, J″ configuration, so the vibrational and rotational 3 2 ퟐ 0, 4 2 v″ 푿 횺 0, 3 understanding of the fundamental connections 1 1 17 퐠 7 0 3 0, 2 = 0 2 0, 1 properties of the molecule will depend on the v" 1 0, 0 Potential Energy [eV] Energy Potential between molecular spectra and the underlying [eV] Energy Potential 0 electron configuration 6 15 energy structures as an example of applied 0.9 1.1 1.3 1.5 1.7 1.9 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Internuclear Distance, r [Å] quantum mechanics. C. Electronic State Notation Internuclear Distance, r [Å] • Enhance the laboratory and analytical skills of State Symmetry under D. Spectra and Assignments the students. 180 16000 multiplicity, reflection about a 0-0 21S 160 14000 S = 1, 2... plane containing r • Develop the student’s ability to express and ) X 140 푵∗ (B →X) ug, 0-1 ퟐ 12000 communicate coherently their scientific 120 0-0 10000 R-branch Jʺ : JR = 20 15 10 5 0 findings Symmetry under 100 0-2 P-branch Jʺ : J = State label X Projection of orbital 8000 P 47 42 37 32 27 inversion about 80 ∗ 푁2 (B →X) 6000 (ground), A, momentum along r, 60 1-3 center of mass 1-2 0-1 C. Outcomes B… Λ = Σ, Π … 1-4 4000 40 0-3 1-0 (countsIntensity Intensity (counts)Intensity 1-5 20 2-4 2-5 0-4 2000 2-1 1-1 2-3 2-6 After completing the experiment, the students are D. Rotovibrational Energies based 0 0 expected to on Morse Potential 300 320 340 360 380 400 420 440 460 480 387 388 389 390 391 392 Wavelength, λ (nm) Wavelength, λ (nm) • Describe the principles of a simple E. Analysis 25740 ) 2 GGFF 1 spectroscopic setup designed to probe the v v J J el v v v v - 25720 rr0 for (v' = 0) → (vʺ = 0,1,2) 25700 GG (cm energy structure of a molecule V r D1 e v v el v v BJJBJJ 11 e vv J" 25680 ν BBB2 x 00 01 • Be able to collect and assign vibrational and 00 v x v 1 v 25660 -1 • Energy of vibrational level v (in cm ) The P-branch fit yields B' and Bʺ 25640 rotational spectra based on selection rules, 26BBB x 00 02 v x v 1 v 25620 2 25600 Franck-Condon Principle, and Fortrat 2 Solve for ωB and ωB xB P 00 BBJBBJ 11 Wavenumber, 25580 diagrams G v x v 2 4 6 8 10 12 14 16 18 20 22 v 0 22 0 0 • Know how to organize the data and use them F. Results Lower quantum number, J" in combination with simple quantum harmonic term anharmonic term -1 -1 -1 -1 -1 Constants ωB (cm ) ωBxB (cm ) De (eV) Constants ν00 (cm ) B' (cm ) Bʺ (cm ) mechanical models of molecular vibrators and • Energy of rotational level J (in cm-1) rotors to characterize diatomic molecules Experiment 1703 12.1 7.45 Experiment 25570 2.014 2.083 2 2 Literature 1730 14.1 7.37 Literature 25580 1.857 1.933 • Be able to discuss and report the results of the FBJJDJJ 11 model-based analysis to emphasize the limits v, J v v S.B. Bayram and M. Freamat, "Vibrational spectra of N2: An advanced under graduate laboratory in atomic and of the idealized models G. References molecular spectroscopy", Am. J. Phys. 80, 664-669 (2012). rigid rotor centrifugal distortion S.B. Bayram and M. Freamat, and P. Arndt “Rotational spectra of N2: An advanced under graduate laboratory in atomic and molecular spectroscopy", accepted for publication in Am. J. Phys. .
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