Laser Induced Fluorescence of Iodine

Transcription

1 Laser Induced Fluorescence of Iodine (Last revised: FMH 29 Sep 2009) 1. Introduction In this experiment we are going to study the laser induced fluorescence of iodine in the gas phase. The aim of the study is to determine the following molecular parameters of iodine in the ground state: the dissociation energy (D e and D 0 ), vibrational wavenumber (ν e ), anharmonicity constants (x e ) the exponential factor in the Morse potential (a) and the force constant (k). 2. Theory The experiment is performed at room temperature and most of the iodine molecules will be in their lowest vibrational level, v = 0, but there are some molecules in the vibrational level v = 1. This could complicate the analysis since the vibrational population in the electronically excited state will be broadened. However, emission from these extra vibrational states is weak and we will not be concerned with it here. The rotational distribution of iodine at room temperature has a maximum around J = 50, but the distribution is very broad and both J around 11 and 104 are sufficiently populated. A green He-Ne laser at nm is used to excite iodine to its B state. At this wavelength two nearly degenerate rovibrational levels in the B state will be populated, see Fig.1. Fig.1 The rovibrational levels in iodine excited with a laser at nm.

2 The excited molecules will relax to different vibrational levels in the ground state by 2 emitting fluorescence with intensities depending on the Franck-Condon factors, S ν,ν (Fig. 2). Sν,ν = ψ ν *(R)ψ ν (R) Fig 2: Franck-Condon factors as illustrated by the wavefunction overlap for vertical transitions between vibrational levels of the ground and excited electronic states. The absorption and fluorescence intensities are affected accordingly. The two different excited vibrational levels will give rise to their own Franck-Condon progression (see Appendix 1), and each level can undergo transitions to two different rotational levels in the ground state (the selection rule for rotational transitions is ΔJ ±1). Therefore, there will in general be two doublets associated with each vibrational level of the ground state. The possible transitions are schematically shown in Fig. 3(a) below. The separation between the ΔJ±1 transitions is about 15 cm -1 for the J = 104 state, but only 1.5 cm -1 for the J = 11 state. Since the resolution of the monochromator we use is ~10 cm -1, only the former doublet will be resolved. Thus, these lines will appear in the spectrum as a triplet consisting of a doublet separated by 15 cm -1 and a third, slightly broadened line (Fig. 3(b)). The separation between the doublet and the broadened line will shift relative to each other for transitions to different vibrational levels in the electronic ground state. This is due to the coupling of vibrational and rotational motion.

3 For some of the transitions one of the lines in the doublet will overlap with the broadened line, resulting only a doublet in the spectrum. In addition, as the Franck-Condon factors vary rather erratically, for some values of ν, the transitions from both ν =26 and ν =28 will be visible. For other values some ν, by contrast, either one or both of them are missing. (a) ~15 cm -1 ~1.5 cm -1 (b) Fig 3: (a) Transitions associated with the fluorescence emission lines from I 2 excited at nm. (b) Schematic of the doublet and single broadened peak arising from radiative transitions from ν = 28 and ν = 26, respectively.

4 The Morse potential In order to take into account the anharmonicity of vibrations, we use the Morse potential (Eq.1) to describe the potential curve (D e in cm -1 ): where V a( R R ) { 1 } 2 e = hcd e e (in joules) a { ( R Re 1 ) 2 } = D e e (in cm -1 ) Eq.1 a = k 2hcD e Eq.2 and k is the force constant: k = (2πνec) 2 μ Eq.3 1 k where ν e = (in cm -1 ) Eq.4 2πc μ If we put the expression for the Morse potential into the Schrödinger equation, we obtain the expression for the energy levels of an anharmonic oscillator: E υ = ν e (υ+½) - x e ν e (υ+½) 2 (in cm -1 ) Eq.5 where x e is the anharmonicity constant. The difference in energy between adjacent vibrational levels are then given by: ΔE υ = E (υ+1) - E υ (in cm -1 ) Eq.6 = ν e [1-2x e (υ+1)] υ = 0, 1, 2, 3... If ΔE υ is plotted versus (ν+1), a straight line will be obtained. This is the so called Birge-Sponer plot illustrated in Fig.6 below. The area under this line (extrapolated to ΔE υ = 0) is the dissociation energy, D 0 : D 0 = D e - ½ ν e (in cm -1 ) Eq.7

5 3. Experimental Initial setup: Check the instrumental setup by first recording a spectrum of the light from the lamps in the room (fluorescent tubes Hg spectrum). Arrange the experiment according to the scheme in Fig.4. Put the iodine cell as close as possible to the entrance slit of the monochromator. Turn off the light or cover the monochromator with a black blanket in order to reduce background light. Fig.4 Experimental setup Iodine cell Optimization: Record a spectrum between 545 and 570 nm where the first vibronic transitions should appear. For instructions on how to handle the spectrometer, see separate manual. Optimize the resolution of the monochromator so that the spectral lines are resolved (see Fig. 5). This is done by decreasing the slit widths and increasing the integration time. Fig. 5: An optimized fluorescence spectrum of I 2, where the spectral lines arising from transitions from the excited electronic state B, ν = 26 and ν =28 are resolved.

6 Measurement: When the resolution is optimized, record a full spectrum between 545 and 750 nm. This will take around min. 4. Calculations Identify and tabulate the transitions associated with the various lines in the spectrum with the help of the enclosed calculated Franck-Condon factors. Note that some of the lines may be missing or very weak due to the very small or vanishing Franck-Condon factors. Calculate and tabulate the energy differences between the vibrational levels in the electronic ground state for I 2 (NB: units!!) and make a Birge-Sponer plot (see Fig 6). Use only either the ν = 26 or the ν = 28 spectral lines (and the corresponding ΔJ values) in your calculations and not a mixture of these values. Remember also to account for the missing transitions, as identified above. Calculate D 0 and D e (in cm -1, J, and kj/mol), as well as x e, ν e, a and k (give appropriate units!) using the Birge-Sponer plot. (Hint: what do the slope and intercept of the Birge-Sponer plot represent?) Compare your results with literature data and discuss what you observe. ΔE υ +1 υ Fig. 6: A schematic representation of a Birge-Sponer plot υ +1

7 Appendix 1: Franck-Condon factors for I 2 laser induced fluorescence, from ν = 28 and ν = 26