Download The Atomic Emission Spectra of Hydrogen, Deuterium

Chemistry 2302 Atomic Emission Winter 2012 The Atomic Emission Spectra of Hydrogen, Deuterium and Sodium Recommended Preparatory Reading •
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Experiment 30 in Sime (2) entitled “Visible Spectrum of the Hydrogen Atom” Experiment 40 in Shoemaker (1) entitled “Spectrum of the Hydrogen Atom” Introduction If you have completed the Vibrational-­‐Rotational Spectrum of HCl/DCl experiment you might have noticed that the spacing of rotational and vibrational energy levels is quite small, consequently, the electron transitions are observed in the infrared region of the electromagnetic spectrum. In comparison, the spacing of electronic energy levels is quite large. To produce electronic transitions between energy levels in gaseous atoms, the gas is placed in a Geissler discharge tube in which it is subjected to a very high voltage. The light produced falls within the UV-­‐visible region of the spectrum and can separated into its spectral components using a diffraction grating or a prism. The hydrogen atom, having only one electron, has a very simple spectrum. This spectrum was first studied by Balmer in 1885. Spectra for other atoms are more complex since they have more electrons. In this experiment, the electron emission spectra of hydrogen, deuterium and sodium will be observed using two handheld spectroscopes and a UV-­‐visible spectrophotometer. For the hydrogen atom and one-­‐electron ions, the Schrödinger equation can be solved to give the energies, 𝐸 , of the quantized electronic states having principal quantum number, 𝑛: 𝜇𝑒 !
𝐸! = ! ! ! with 𝑛 = 1, 2, 3, … 8ℎ 𝜀! 𝑛
Equation 1 Here 𝑒 is the charge on an electron, h is Planck’s constant, and ε0 is the permittivity of vacuum. 𝜇 , the reduced mass, in this case is given by: 𝑚! 𝑚!
𝜇 = 𝑚! + 𝑚!
Equation 2 where 𝑚! is the mass of an electron and 𝑚! is the mass of a proton. In your report, simply give the relationship, carefully defining all terms and presenting any assumptions that allow application of this particular relationship to your systems. When an electron in an atom changes from a higher energy state, E1, to one of lower energy, E2, a photon is emitted. The change in energy is: 𝐸! − 𝐸! = ℎ𝑐𝜈 Equation 3 Chemistry 2302 Atomic Emission Winter 2012 where 𝑐 is the speed of light and 𝜈 is the energy of the photon in wavenumbers (cm-­‐1). When equations 1 and 3 are combined, the following equation is obtained allowing the calculation of the energy of the emitted photon: 1
1
𝜈 = 𝑅 ! − ! 𝑛! 𝑛!
Equation 4 where 𝑅 is the Rydberg constant given by 𝑅 =
!!! !! !
. It equals 109677.8 cm-­‐1 for !.!!!"#×!"!!" !! !!! !! ! !! !
the hydrogen atom. 𝑛! is the principal quantum number of the lower energy state and 𝑛! that of the higher energy state. The theoretical wavelength of the photon may be easily obtained by calculating the reciprocal of 𝜈 . Sime’s (2) figure 30-­‐1 shows some of the electron transitions that can occur for the hydrogen atom. This experiment will concentrate on the ones that terminate at the 𝑛! = 2 energy level, called the Balmer series. The energy of four lines in the Balmer series, the isotopic separation of hydrogen/deuterium emission lines, and the spacing of sodium doublets will be determined. Explain how attributing an intrinsic (spin) angular momentum, S, to the electron in addition to the orbital component, L, produces a total angular momentum, J, which can account for the fine structure (doublets) present in the sodium atomic emission spectrum. Section 13.2 of your textbook (Laidler) will help you with this explanation. A Russell-­‐Saunders term symbol can be written for each electronic energy level of an atom. It has the form n(2S +1)LJ where n is the principle quantum number. Define the other elements (S, 2S+1, L and J) of the term symbol and explain how values for each are assigned. Again Section 13.2 of your textbook will be of assistance to you. Also, section 13.9 of Physical Chemistry by Atkins & de Paula is quite good and available in C-­‐3041. Experimental Preliminary Observations: Observe, using the handheld spectroscope, the emission from a hydrogen discharge tube. Sketch the emission spectra, indicating the color and approximate wavelengths of the 4 strongest lines. Now observe using a Bleeker prism spectroscope and again note the wavelengths of the same four lines. Note the precision of each spectroscope. Also available for observation are neon, argon, and chlorine discharge tubes, and, of course, overhead lights, sunlight, etc. for the curious. Follow instructions provided in the lab carefully. The power supply operates at a high voltage...use care! Measurement: Measure the spectra in the visible region of hydrogen, deuterium and sodium using the Ocean Optics S2000 fibre optic spectrometer. Note its precision. This small grating spectrometer comprises miniaturized optical components, a CCD detector, and accesses light via a fibre optic cable! To perform a measurement, open the OOIBase32 software used to control the spectrophotometer. Point the fibre optic cable toward the middle of the discharge tube. The spectrum is constantly updated Chemistry 2302 Atomic Emission Winter 2012 on the screen in real time. You may need to move the fibre optic cable around slightly until the intensities of the peaks are reasonable (i.e. you should be able to see the 4 peaks but the highest one must not go off scale). Once the intensities are to your liking, hold the cable very still and click the camera button. This will freeze the spectrum. If your hand is unsteady you may choose to mount the fibre optic cable in a clamp attached to a ring stand. Save each spectrum by clicking on File à Save As à Sample. Repeat for the deuterium discharge tube and the large (bright!) sodium source lamp. Before leaving, transfer the saved data files to a flash drive (or e-­‐mail them to yourself) as you will need them to complete the lab report. The files contain two columns of data – a column of wavelengths (nm) and a column of intensity values. Results The spectra that you saved during the experiment will have the extension .wav. Open these files in Notepad (or other simple text editing software). Copy the columns of data (wavelengths and intensities) and paste them into a spreadsheet. For all species, recreate the spectrum you observed during the experiment by plotting a graph of intensity versus wavelength. Choose a graph type that will draw a smooth line through the data points without displaying the actual points. Enlarge (zoom in on) the four strongest emission lines in only the hydrogen spectrum and submit these as individual plots. Identify the upper and lower states of each strong spectral line measured by its atomic term symbol n(2S + 1)LJ . You will need to consult the literature for these assignments. An energy level diagram for hydrogen can be found in Sime. The diagram for sodium (taken from Noggle) is given later in this outline. On your printed spectra, next to each intense peak, identify the electronic transition responsible for its presence with the term symbols. The notation representing an electron transition is written follows: Upper state term symbol à Lower state term symbol For hydrogen and deuterium, only consider the 4 strongest emission peaks. For sodium you need only consider the first line in the principle series (see the diagrams on the next two pages, from Noggle). Hydrogen Correct the wavelengths observed in air, of the hydrogen emission lines, to vacuum then convert the wavelengths to wavenumbers (cm-­‐1). The correction involves the refractive index of air and can be found in Shoemaker. Now use equation 4 to calculate the four theoretical energies of the emitted photons for the first four lines in the Balmer series. Deuterium As for hydrogen, correct the observed wavelengths of the four emission lines to vacuum then convert to wavenumbers. Calculate the Rydberg constant for deuterium (Hint: what is added to a hydrogen atom to make deuterium?) and use equation 4 to calculate the theoretical energies of the emitted photons for the four lines. Chemistry 2302 Atomic Emission Winter 2012 As you have probably noticed, the spectrum for hydrogen and deuterium are almost the same, except that each line is shifted to a slightly higher energy in the deuterium spectrum. Using your calculated theoretical wavenumbers, calculate the isotopic shift (difference in energy) for each corresponding pair of lines. Organize the data for hydrogen and deuterium into a table with the following four headings: Isotope, Transition (term symbol notation), 𝜈!"# , 𝜈!!!"#$ Sodium Write term symbols denoting electron transitions for the first four lines in the principal series (see the term diagram below). Note that each line in this series is a doublet (called the “fine structure”), although the fibre optic spectrometer that we used does not have a high enough resolution to see them. Print your spectrum and try to find peaks corresponding the principal series transitions (see the diagram below for wavelengths of the first five lines in the principle series). If you can find the peaks, label them with the term symbols you have written. Measure the separation of the doublet for the first lines in the principal and sharp series. Since you cannot see the doublets on your experimental spectrum you must use the spectra provided on the page after next, which were measured on the Coderg Raman spectrometer with a precision of ~ 1 cm-­‐1. The spectrum on the top is for the first line in the sharp series and on the bottom is for the first line in the principal series. Chemistry 2302 Atomic Emission Winter 2012 Chemistry 2302 Atomic Emission Winter 2012 Chemistry 2302 Atomic Emission Winter 2012 Discussion Contrast the construction, optics, range, resolution, sensitivity, method of detection, and applicability of the two relatively simple spectroscopes and fibre optic spectrometer. A cracked-­‐open spectroscope is on display. Compare your experimental energies of the strong emission lines of hydrogen, deuterium and sodium with the literature values. Remember, you have already calculated the “literature” values for hydrogen and deuterium in the results section. The literature values for the sodium principal series lines are given in the diagram on page 3. Hydrogen and Deuterium Compare the experimental isotopic shift with the theoretical isotopic shift. Address the applicability to your systems, any assumptions made in the development of the theory. If the hydrogen and deuterium emission spectra had been measured simultaneously, instead of individually, would the isotopic separation have been observed? What resolution would be required to see the isotopic shift of a hydrogen / deuterium mixture? Sodium Compare the experimental splitting observed in each doublet with the splitting reported in the literature (see the term diagram on page 3 for literature values for the first line in the principle series) References Available in the lab: 1. Shoemaker et al., "Experiments in Physical Chemistry", 5th ed., McGraw Hill, Toronto (1962). 2. Rodney J. Sime, "Physical Chemistry", Holt, Rinehart, and Winston. Orlando, 1990. 3. Frank L. Pilar. Elementary Quantum Chemistry. McGraw-­‐Hill Publishing Company, Toronto. 1990. 4. Ira N. Levine, Quantum Mechanics, 5th Edition, Prentice Hall, New Jersey, 2000. Available on reserve in library: 5. G. Herzberg, "Atomic Spectra and Atomic Structure", Dover Publications, New York (1944). 6. H.G. Kuhn, "Atomic Spectra". Available in lab and in periodicals section of library: 7. Fred Stafford and James H. Wortman, J.Chem. Ed. 39 (1962), 630.