UTModPhy: Experiments: H2D2

Hydrogen-Deuterium Line Splitting

H2D2

In 1937, Harold C. Urey postulated the existence of a hydrogen isotope: one neutron and one proton. He calculated the spectral shift predicted by the Bohr model, found the shifted spectrum next to the hydrogen spectrum – and thus discovered deuterium! In this lab, you will demonstrate the H-D line splitting and explain it using the Bohr model of the atom.

We usually assume infinite nuclear mass when we model the atom. As shown in P1, this approximation is quite good. However, an interesting feature appears if we extend the model to account for finite nuclear mass. We will apply some more "inapplicable classical physics:" a two-body problem, in its center-of-mass frame, may be turned into an infinitely massive body at the CM, acting on a "reduced mass" body. (You can find this trick in any mechanics text. You should reproduce – and explain – the derivation in your lab reports). The reduced mass of deuterium is slightly larger than that of hydrogen, and so the deuterium spectrum is shifted (slightly) from the hydrogen spectrum.

Prelab questions

How good is the infinite mass approximation… For instance, what is the percent difference between the reduced mass (for hydrogen and for deuterium) and the full electron mass? What is the change in energy?
Which atom has a smaller radius? Which has a greater electron velocity? (Hint: you can get this by just thinking about the two atoms… you don’t have to use the reduced mass equations).
Give a diagram and short explanation of how the monochromator works. (Mellisinos, Moore, and Preston and Dietz each describe the design and use of spectrometers in general. Make sure the device your reference describes is similar to the one you’ll use: it is a Czerny-Turner diffraction grating monochromator).
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

The procedure for this lab is straightforward. You will run the light from a gas discharge tube (filled with either water vapor or a mixture of water and heavy water vapor) through a monochromator to separate out each wavelength. The monochromator is old, and sometimes crotchety, but quite precise and well made. If it starts acting up, wait respectfully until it feels better, but do not engage the spectrum drive until the wheels are done spinning down. Hint: if you hear an awful gear-crunching noise, you are not being respectful. The intensity at each wavelength is measured with a PMT and recorded by an X-Y plotter.

You should first take some calibration runs using hydrogen, and then take data runs with the deuterium tube. You will have to adjust the slit width for the best tradeoff of intensity and resolution. Your plotter graphs should allow the best relative uncertainty you can manage… This means, at the very least, that the region of interest should fill the page.

Procedural Notes

Here are some useful initial settings:

87206 (H2 only) Bulb.

200 mV plotter offset.

1000 V to the PMT.

400 mV range.

Range 0.1V on the meter.

45s. total time.

You should get ~ 0.02V background.

A strong peak is at 6562 �; find a two-tick-mark deflection near there.

If you like, ask the TA to pull the cover off the monochromator (with the high voltage off!) so you can check out its construction. You have to be very careful about alignment: if the lens or spectrum tube moves, you get to start over. So tape everything down.

Please 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. These bulbs, believe it or not, cost about $800...
	Avoid looking directly at the bulb, and cover everything with blackcloth. The bulb puts out potentially harmful UV radiation.
	Insert the bulb with the base (black part) down. This is necessary to cool the bulb, and so that the "getters" in the bulb can remove contaminants.
	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).