UTModPhy: Experiments: Atomic Spectra

Atomic Spectroscopy Experiment		AS
If you bombard a pure sample of an element with electrons, the atoms of the sample will reradiate the energy they absorb. You will find that the light emitted consists of discrete wavelengths of light, and that the wavelengths are unique for each element or chemical compound. The figure on the right, for instance, gives some of the spectral lines of Hydrogen and Helium. The light does not come in bands or preferred ranges of emission: as you can see, they are sharp peaks to at least one part in 10⁶ or 10⁷. How does the atom decide what wavelengths to radiate? What could make one energy preferable to another? It is not a feature of light itself, for it is easy to generate continuous spectra (e.g. by blackbody radiation), and because the spectra are unique to each atom. Furthermore, the lines may be determined with great accuracy, and are independent of the temperature, pressure, and physical state of the element. Thus, the source of this "fingerprint" must be intrinsic to the atom. There are patterns in each element’s series of emission lines. Balmer and Rydberg found an ad-hoc formula that matched many (but not all) of the observed lines of Hydrogen, and even predicted others. However, this only highlighted a pattern – it did nothing to explain the origin of this mystery. The Bohr model of the atom, on the other hand, not only gave a physical explanation for this pattern, but also made predictions and suggested further investigations. "This is the famous Bohr formula – by any measure the most important result in all of Quantum Mechanics. Bohr obtained it in 1913 by a serendipitous mixture of inapplicable classical physics and premature quantum theory." (Griffiths, Introduction to Quantum Mechanics, p 136) The Bohr model was historically indispensable: it led directly to the DeBroglie wave hypothesis and the development of the Schrödinger equation. However, it does not correctly predict the spectra of elements beyond hydrogen, and cannot be easily modified to do so. Even for hydrogen, it cannot predict the relative amplitudes of the spectrum peaks. It certainly cannot account for allowed/forbidden transitions, or the spectra of molecules.	Figure AS-1: Selected Spectral Lines Visible in Air. Source: CRC 63, pp. E241-E243
All these shortcomings notwithstanding, the Bohr model gives the best mental picture of what "happens" inside an atom. Its quantitative details are absolutely true: electrons are only found at definite, discrete energies and momenta; a transition between energy levels corresponds to absorption or emission of a photon; the energy of that photon is found with the Planck-Einstein formula E= h f / lambda

	Pre-Lab questions
	Identify the hydrogen lines that are predicted by the Rydberg equation, and give the transition (n ® m) that causes it. Give a diagram and short explanation of how the monochromator works. Mellisinos, Moore, and Preston and Dietz all describe the design and use of monochromators. Give a diagram and short explanation of how a PMT works. Moore, Preston and Dietz, and the Burle handbook are good references on photomultiplier tubes. Briefly summarize the procedure you will follow, including the ranges and variable you will record.

Procedure notes

You will take the spectrum of hydrogen and helium, and use the accepted values for their spectral lines to calibrate the monochromator. You will then be able to identify an unknown gas just by observing its spectrum.

A gas-discharge tube is used to generate the spectrum. The tube applies a large electric field to the low-pressure gas within the tube. This ionizes the gas: a significant fraction of the atoms will separate into an ion and a free electron. Recombination and collisions can leave an atom in an excited state; those atoms will subsequently return to a lower state and radiate a photon of characteristic wavelength.

The lab has a homemade and intentionally crude monochromator (built to the plans in Parkinson 1976) to read this spectrum. As you turn the micrometer handle, you rotate the grating to move the spectrum across the exit slit. A photomultiplier tube, mounted on the exit slit, measures the intensity.

Before you start, you can pull the cover off the monochromator (with the high voltage off!) and find the spectral lines by holding a card if front of the exit slit. While you’re in there, check out the construction of the monochromator. While performing this lab, you have to be very careful about alignment: if the lens or spectrum tube moves, you get to start over. So tape everything down. Also, if you reverse direction while scanning, the first micrometer ticks will just be to take up any slop in the linkage – this is called backlash – and so all your data should be taken in one direction only.

Help us out by observing these guidelines:

	You should run the PMT supply at 1.0 kV. PMT supply voltage is a tradeoff between intensity (higher voltage lets the PMT detect smaller signals…), noise (… but it magnifies the background noise…) and operating life (… and continued operation at high voltage ablates the cathode, which kills the PMT). One kV is the best compromise.
	As far as possible, try not to run the bulb for extended times – try to turn it off and let it cool periodically. The gas is at low pressure and gets slowly contaminated during warm operation. Also, avoid looking directly at the bulb, and cover everything with blackcloth. The bulb puts out potentially harmful UV radiation
	Do not take the cover off, or otherwise expose the PMT to large light levels, while the high voltage is on. You will saturate the PMT, which can destroy it (bad for us) and will make the measurements very noisy for up to a half-hour (bad for you).

	Points to consider during your analysis
	Remember the cardinal rule of data analysis: details improve credibility. Take full, careful data sets. Highlight anomalies in your data. Explain the features that you can and point out the features you cannot. This leads to a convincing, interesting report in a way that glossing over inconsistencies cannot. How well does the Bohr model predict the spectrum of each element? Be specific about which features of the Bohr model hold for all elements; and explain why the others fail. How is the reading on the ammeter related to the light intensity?
	References
	Parkinson, P.D. S. Am. J. Phys. 35 (1967), 1032. Details the construction of the monochromator. Moore, J.H., C.C. Davis, S. C. Greer, and M. A. Coplan. Building Scientific Apparatus, 2nd Edition (Addison Wesley 1989). A lot of great information on everything from glassblowing to photomultiplier tubes. Preston, D.W. and Dietz, E.R., Art of Experimental Physics (Wiley 1991) , p 127, 329, 379. Advanced for this class but often contains useful information. Photomultiplier Handbook (Burle Industries). You can get this free from Burle Industries (although it lists a 14.95 "optional price"); we have a copy available in the lab. It has everything you want to know about PMT’s. Mellisinos, A. Experiments in Modern Physics (Academic Press 1966). Born, Max. Atomic Physics (Blackie and Sons 1957). Modern physics from one of its pioneers.