Department of Physics, Middlebury College 1992-93
High Resolution Optical Spectroscopy


XI. High Resolution Optical Spectroscopy


Discussion

The goal of this experiment is to familiarize you with the operation of a modern, microprocessor-controlled, high resolution spectrometer. The SPEX Model 1704 spectrometer in our laboratory is a research-grade instrument capable of providing high-resolution spectra in the range from 1,750 to 15,000 Å. Fig. 1 shows the location of the various optical components inside the spectrometer housing. The positions of the grating and two mirrors in this spectrometer are characteristic of what is called a Czerny-Turner configuration. In this configuration, light enters through a narrow entrance slit that lies at the focus of a concave mirror of 1 m focal length. The concave mirror reflects the light to produce a cylindrical beam of parallel rays that illuminate the full surface of a rotatable diffraction grating. The grating diffracts the light, dispersing the various wavelengths of the light to different angles in the horizontal plane. The diffracted light is collected by a second concave mirror that focuses the light through a narrow exit slit to a photomultiplier tube. As the grating rotates, different wavelengths pass through to the photomultiplier. A spectrum is recorded by plotting the photomultiplier tube output current as a function of the grating angle.

Fig. 1 summarizes the manufacturer's specifications for the Model 1704 spectrometer; however, it should be noted that an 1800 groove/mm grating is installed in our spectrometer at the present time. The greater number of grooves per mm has the effect of decreasing the spectral coverage of the spectrometer while providing increased wavelength resolution in the visible. The wavelength resolution of the spectrometer is defined as the minimum wavelength separation between two infinitely narrow peaks, such that two peaks, rather than just one, can be readily discerned in an experimental spectrum. In Fig. 1 the resolution of the Model 1704 is stated to be better than 0.08 Å at a wavelength of 3131 Å. This particular wavelength is chosen because it corresponds to the location of a pair of intense, narrow lines in the ultraviolet emission spectrum of a simple mercury spectral lamp. Fig. 2 shows a typical spectrum of the these two emission lines taken with the SPEX 1704. Note that increasing wavelength is to the left in Fig. 2 and that the horizontal scale has a calibration of 0.95 Å/cm. The asymmetrical lineshapes of these two lines are due to the isotope shift and hyperfine interactions present in the Hg isotopes that make up the Hg lamp vapor. The full width at half maximum of the left peak at 3131.84 Å is found to be 0.045 Å, confirming the expected improvement in resolution with the 1800 groove/mm grating.

Another important specification of a spectrometer concerns the absolute accuracy of its wavelength readout mechanism. After learning that the wavelength resolution of the Model 1704 is 0.045 Å, it may surprise you to read in Fig. 1 that the digital readout in Å is only accurate to ▒1.0 Å. The inaccuracy of the digital readout can be seen in Fig. 2 where the 3131.84 Å line in Hg is observed at 3132.52 Å according to the CD2A Compudrive Controller. An absolute inaccuracy of nearly 0.68 Å is present. Fortunately, we rarely need absolute wavelengths in physics experiments; in most experiments we can use wavelength differences for making comparisons to theory. The wavelength difference between the two peaks in Fig. 2 is found to be 0.29 Å, as expected, even though both peaks are measured to have wavelengths that are 0.68 Å higher than accepted values.

Procedure

Take detailed notes on the operation of the SPEX Model 1704 spectrometer and the CD2A Compudrive controller. Make sure that you can operate this instrument from a "dead start" without assistance. Make a sketch of the data acquisition electronics and record the settings of all major components.

(1) Mercury (Hg) Lamp.

Place the Hg lamp near the entrance slit of the spectrometer.
(a) Obtain a high resolution spectrum of the 3131.55 Å and 3131.84 Å lines.2 Suggested spectrometer parameters are: (i) entrance and exit slits at 2 Ám (closed), (ii) collimator at the center dot, (iii) spectrometer scan rate of 0.00417 Å/s, and (iv) strip chart rate of 2.5 cm/min. Compare your spectrum to that shown in Fig. 2.

(b) Compare the peak centroids of your Hg data to the accepted values given above. Are the centroids of the two Hg peaks within the ▒1.0 Å wavelength accuracy specified by the manufacturer? Does the separation of the Hg peaks in your data agree with the accepted spacing?

(c) Determine the full width at half maximum (FWHM) in Å of the 3131.84 Å line. Does your FWHM value for this line indicate an acceptable value for the wavelength resolution of the Model 1704 spectrometer?

(2) Sodium (Na) Lamp.

Place the Na lamp near the entrance slit of the spectrometer.
(a) Obtain a high resolution spectrum of the 5889.950 Å and 5895.924 Å lines ("sodium D lines").2 Suggested spectrometer parameters are: (i) entrance and exit slits at 10 Ám, (ii) collimator set to 0.2 cm, (iii) spectrometer scan rate at 0.0417 Å/s, and (iv) strip chart rate at 2.5 cm/min.

(b) Compare the peak centroids of your Na data to the accepted values given above. Are your measured values for the two Na peak centroids within the ▒1.0 Å accuracy specified by the manufacturer? Does the separation of the two Na peaks in your data agree with the accepted spacing?

(c) Determine the FWHM of the two peaks in your Na spectrum. How do these widths compare to the widths of the two peaks in the Hg spectrum? (3) Hydrogen (H) Lamp.

(a) In the next lab experiment you will make measurements of the Balmer lines of atomic hydrogen and deuterium. As practice for that experiment, locate the hydrogen Balmer alpha line near 6563 Å. By now you should have enough experience to find this line on your own.

(b) Determine the FWHM of the hydrogen Balmer alpha line. How does its width compare to the measured widths of the Hg and Na lines?

References
1. SPEX 1704 Operations and Maintenance Instructions, manual (SPEX Industries, Metuchen, NJ, 1983).
2. American Institute of Physics Handbook, edited by D.E. Gray, 3rd ed. (McGraw-Hill, New York, 1972), p. 7-29.

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