THEORY
When a high-voltage discharge takes place in H2 gas at low pressures, many molecules are dissociated into atoms by electron impact. These atoms are often produced in excited electronic states. Such H atoms in excited electronic states spontaneously undergo transitions to lower energy electronic states with the emission of readiation. Quantum mechanics (to a high detgree of approximation) gives an expression [1,2] for the allowed electronic energy levels of an H atom in terms of a single (principle) quantum number, n
where e is the charge on the electron, h is Planck's constant, and epsilon_0 is the permittitivity of vacuum. The reduced mass mu is given in terms of the mass of the electron m and the mass of the proton M by
There is no selection rule for changes in n; that is, transitions may occur between any of the levels given by Eq. (1). An energy-level diagram for the H atom is given in Fig. 1. Transitions from upper energy levels to lower levels are shown by the vertical lines.
FIGURE 1 Electronic energy-level diagram for the hydrogen atom.
These transitions form several series of lines depending on the quantum number of the lower state. Note that the energy levels converge toward a limit as n -> infinity. The shaded area above n = infinity indicates a continuum of energy states corresponding to complete separation of the proton and the electron (i.e. ionization).
We shall be concerned with the Balmer series, the lines of which fall in the visible region of the spectrum. From Eq. (1), it is possible to predict the frequency of a transition from any upper state with quantum number n, to any lower state with quantum number n2, since
where c is the speed of light in cm.s-1 units and (v_bar) is the frequency in wavenumber units of cm-1 (equal to the reciprocal of the wavelength (lambda) in centimeters). Thus,
The quantity R is called the Rydberg constant and has the calculated value 109 677.5805 cm-1 for the reduced mass of the H atom. For the Balmer series, n2 = 2 and n1 = (3, 4, 5, ...) .
The above equation predicts a series of lines in the Balmer series that converge to a
high-frequency limit at R/n22 wavenumbers.
You should probably scan this region in your
experiment to see if you can directly detect the Ionization Potential of H in the n=2 state.
METHOD
The frequency (or wavelength) of the Balmer lines can be determined experimentally by comparing the hydrogen spectrum with a reference spectrum for which the wavelengths are known. The iron , neon, or mercury spectra are common choices for reference spectra. (Such reference spectral lines must, of course, have been measured absolutely, as by an interferometric wavelenght measurement or by direct frequency counting.) In this experiment, a Ne lamp will be used because the lines of the Ne spectrum can be identified quite easily, and Neon displays are common and available. In other work, the Fe spectrum is preferable, since there are many more lines. Sometimes, lamps are constructed with several emitters present, so that even more calibration points can be obtained.
A wide variety of spectrometers and spectrographs (instruments that record the spectra on a photographic plate) can be used to study spectra in the visible and near ultraviolet region. A description of such instruments is given in most modern Instrumental textbooks, and this material should be read as background for the present experiment.
Figure 2 shows a schematic diagram for a typical grating spectrometer, which consists of a monochromator, light source and detector. In this experiment, we will be studying the line output of the source, so no absorption sample is present. The source should be mounted in such a way that the hydrogen discharge tube will illuminate the slit at the same time as the Neon reference lamp.
FIGURE 2 Spectrometer, viewed from above.
For wavelengths shorter than about 300 to 350 nm, most glasses absorb light strongly but quartz optics may be used. Even Quartz begins to absorb light below about 190 nm. Other factors, such as detector response, also limit the accessible waveltght range of a given experimental setup.
Since the Balmer lines studied here are more and more closely spaced and have decreasing
intensity as the short-wavelength limit is approached, both high resolution and high sensitivity are
needed to observe lines with high n1 values. For this reason, one may want to increase the gain
and decrease the slit width to obtain the part of the Balmer spectrum at short wavelength. The
determination of the Rydberg convergence limits and the assignment of the states involved in the
atomic energies is always easier with at high resolution.
Sources.
The best Ne light source is a simple low-pressure neon lamp that operates from a small ballast transformer. Neon bulbs which operate at 110 VAC are common panel display lights.
Many designs of hydrogen discharge tubes are available. A convenient commercial hydrogen source is a Geissler tube, since the pressure has been adjusted (0.1 to 0.5 Torr) to give strong Balmer lines. In addition, there is always a weak band spectrum due to molecular hydrogen; hydrogen atoms, formed by the electrode discharge, may recombine on the walls to give H2 molecules in excited electronic states which will emit radiation. Such a band spectrum should be so weak that it will not interfere with determining the Balmer lines. The Geissler discharge tube operates from a neon-sign transformer at about 5000 V and 15 mA; it should glow steadily with a bright red color. The hydrogen discharge tube operates on high voltage which is possibly lethal; be very careful, especially when adjusting the position of the reference lamp.
Figure 3 Neon reference spectrum. The air wavelengths (in Angstrom) Ne lines are given.
EXPERIMENTAL (from K Zientek)
Instructions for the operation of the spectrometer to be used will be given in the laboratory. The adjustable parameters that need to be considered include: The slit widths, the PMT Voltage (gain), the stripchart gain and chart speed, the monchromator scan range and speed, and the position of the lamps. (BTW: always scan spectra in the same direction to avoid errors due to backlash in the screw drive on the grating).
In this particular experiment, a computer will be taking the place of a strip chart recorder. In traditional experiments, a strip chart recorder (which moves a strip of paper at constant speed) would be use to record the data coming from the PMT as the monochromator scans wavelenght at constant rate. The strip chart pen would move proportional to the signal coming from the PMT and the distance down the paper would be proportional to the wavelength. In this lab you will use a computer program and an Analog to Digital card to measure the signal, replacing the mechanical stripchart with digital data acquisition.
It is important to note that the computer is not synchronized with the monochromator at the beginnig of a scan except by your actions (just like the stripchart recorder). The computer will record data at regular intervals when it is told to and will continue to record data until it is told to stop. It becomes important to use a method in which the signal versus time readings may be converted into a signal versus wavelength readings (a spectrum). Calibration of wavelengths is crucial. There are several methods by which you can do this. One method is to produce a 'marker' on the computer plot at know wavelength by briefly blocking the light coming into the monochromator, producing a spike in your data. It is also possible to turn on and off the 'signal simulator' ( a box in the signal cable with a switch and knob), which will also produce a spike in the spectrum. With this, you can at least transfer a reading from the monochromator scanbox to the compure plot. But that is just a beginning...
Procedure
First you must turn on all the instrumentation, including the various
power supplies and the monochromator. Allow the monochromator to
'warm up'. On the desktop of the computer, open the program called “A-D
Converter.” Go to “DAQ type” and select “DAS005” and exit. Go to
“Printerport” and select address. In the section labeled “Other Address”
type in “3bc.” Then click on “Find Port” until something appears. The
click “Intialize,” and click on 'okay' to ackowledge printer port intialization.
Go to File Load and load the file called “ Once you are ready to begin recording data, go to “'Setup”' then go
to “'Logging”' and then “'Parameters'.” Go to 'Input file name' and type in
the name of the file, making sure you save to correct drive. Every
individual scan must have a new file name. Return to “Setup” then go to
“Logging” and then choose the other option. This should bring up a
screen with a checkbox in the lower left hand corner that says “Start
Logging.” A soon as you click in this check box the computer will begin
to collect data at a rate of 5 samples/sec (how many nm / sample?). To stop logging data unclick
the check box. It is possible to watch the data, by returning to the “View-
Trends” window. Remember, the computer will continue to log data until
you unclick the “Start Logging” checkbox.
In order to obtain good data it is possible to vary several settings.
These include the slit width, the voltage setting on the High Voltage box,
the base signal on the signal simulator (do not increase this above 4050
mV), and the scan rate. (What effect would each of these have on your
signal?)
Measurement of spectral lines. From a convenient
reference point in the data file,
measure the position, x, of each spectral line center as a count of number of samples from the
reference. Continue this process for all lines, both Ne
and H atom (disregard the H2 molecular band spectrum) and
tabulate these positions. Make sure
to indicate which lines are Ne and which H. Compare your Ne spectrum with the literature
spectrum that and assign air wavelengths to all Ne lines. Using a least-squares routine and an
empirical polynomial,
l = a0, + a1x + a2x2 + . . . , fit
the variation of the wavelengths
l with the position x of the Ne lines in the file.
Once this calibration formula has
been established, used it to convert the positions of the H-atom lines into their air wavelengths.
Then convert the air wavelengths to vacuum wavenumbers. In all this work, wavelengths in air
have been measured; these are related to vacuum wavelengths by
where nair is the index of refraction of air,
which approximately equals 1.00027 at these
wavelengths. The wavenumber, as a unit of frequency, does not change with the medium the light
travels in, so the unit 'air wavenumbers' is nonsense.
CALCULATIONS
DISCUSSION
Note: The best experimental value of R for hydrogen using vacuum wavelengths is known with
even greater precision than the theoretical value, which is affected by uncertainties in e, h, and U.
The experimental value usually quoted is R_infinity (109 737.31534 cm-1), the extrapolated value
for a one-electron atom with a nucleus of single positive charge but infinite mass.
REFERENCES
[1] Atkins, "Physical Chemistry"
[2] Herzberg, Atomic Spectra and Atomic Structure, (Dover, New York, 1944) {a very cheap
investment for the budding spectroscopist}
Above are the spectra I took on 10/8/98.