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CHE 3200 ATOMIC SPECTRA 2015 OBJECTIVE : (a) To measure the angular positions of the 7 lines of the spectrum of helium gas with a spectrometer. (b) To construct a calibration curve for the spectrometer using the known wavelength of the 7 lines of the helium spectrum. (c) To determine the wavelength of the 3 lines of the spectrum of deuterium gas using the spectrometer and the calibration curve. (d) To determine the Rydberg constant RD for deuterium. (e) To determine the error of RD . (f) To find the wavelenths of the spectral lines of the atomic spectrum of an unknown gas . BACKGROUND : Read : Chapter 1 ofJames E. House, Fundamentals of Quantum Chemistry The following quantities will be used: Z = nuclear charge number me = mass of one electron mN = mass of the nucleus m= me mN = reduced mass me + mN e = elementary charge h= Planck’s constant = h/2 n = principal quantum number = 1, 2, 3, …… c = speed of light ~ = /c = wavenumber RH = Rydberg constant for hydrogen (1H) RD = Rydberg constant for deuterium (2H) The energies of hydrogen-like “atoms” are En = -Z 2 2p 2me 4 1 h2 n2 En = - R hc with R= (1) 1 n2 (2) Z 2 2p 2 m e 4 h 3c (3) using these formulas one arrives at 1 4 ~ R H 1 n2 1 for the wavenumbers ~ of the lines in the Balmer Series of hydrogen when n 2 Similarly for deuterium : æ1 1 ö ÷ è 4 n2 ø n = RD ç since = c (4) it follows that n 2 - 4) æ1 1 ö ( = RD ç - 2 ÷ = RD è4 n ø l 4n 2 1 and l= 4 n2 R D ( n 2 - 4) (5) (6) therefore a graph of versus n2/(n2 – 4) should give a straight line with the slope m = 4/RD PROCEDURE : 1. Use the prism spectrometer (with the prism replaced by a diffraction grating) to record the angular positions (in degrees) of the 7 lines in the atomic emission spectrum of helium. Note : If you want extra credit, you could try to use a compact disk instead of the diffraction grating. But you need to talk to me before you start. Extra credit is only available if you can make it work in such a way that next year’s students can use it. 2. Record the atomic spectra (using scale readings in degrees) of (a) deuterium (be sure to record all three lines). (b) an unknown gas ANALYSIS : 1. Assign the following wavelengths to the He lines: 447.1 nm, 471.3 nm, 492.2 nm, 501.6 nm, 587.6 nm, 667.8 nm, 706.5 nm 2. Construct a calibration curve for your spectrometer by graphing (He) in nm on the y-axis versus scale reading in degrees on the x-axis. Make sure to allow enough room on this graph for lines which may lie outside the wavelength range of your He lines. This should be done using an Excel spreadsheet. Include a trendline and the equation of the trendline. 3. Use your calibration curve to assign wavelengths to all the recorded lines of deuterium 4. Determine the Rydberg constant of deuterium the following way: Graph the wavelengths of deuterium (measured by you) versus n2/(n2 – 4) where n is the principal quantum number of the upper level for that particular transition (equation 6). Use Excel and LINEST to calculate m, b, e (m) , e (b) , e (y) 5. 6. 7. 8. Calculate RD the Rydberg constant for deuterium from the slope. Calculate the error in RD using the error in the slope. Use the calibration curve to assign wavelengths to all lines of the spectrum of the unknown gas. Try to determine the identity of the unknown gas. 2