ATOMIC SPECTROSCOPY
I.
Introduction:
In this experiment you will study the line spectrum of hydrogen using a diffraction
grating. You will measure the wavelengths of some lines in the spectrum and
compare these wavelengths to those predicted according to the Bohr theory of the
atom. Then, you will measure the line spectra of hydrogen and some other gases or
vapors using a monochromator. Finally, the spectrum of a heated solid (light bulb
filament) is observed and the wavelength limits of your eye are deduced.
II.
Required Equipment:
Optical bench, diffraction grating, hydrogen discharge tube light source,
measuring tape, and meter scale. Other light sources: helium, mercury vapor, and
sodium vapor discharge tubes, and incandescent lamp filament, small grating
monochromator, magnifying viewer, various supports.
1
III.
Procedure:
CAUTION: DO NOT TOUCH the face of the grating; handle it only by the edges
or the handle. It is fragile and easily damaged.
CAUTION: The hydrogen, helium, and mercury vapor light sources should be off
unless actually in use! The sodium vapor (yellow) light source should be left on
during the entire laboratory.
CAUTION: Some lamps may become hot.
A. Wavelengths of lines in the hydrogen spectrum using a diffraction
grating.
1) Record the number of lines per millimeter listed on the diffraction grating on your
lab report form. Mount the slit and scale near one end of the optical bench and the
grating near the other end. The scale should be at right angles to the optical
bench. The separation should be about 50 cm or greater. Adjust the position of
the hydrogen light source behind the slit to provide maximum intensity through
the slit. Press the switch to turn on the light source (Do not keep the source on
for long periods of time [see above caution].) Look through the grating to see the
hydrogen spectrum. The spectrum can be seen by looking through the grating
toward, but off to one side of, the slit. Your eye must be fairly close to the grating
so you can see a wide range of angles. Adjust the separation between the slit and
grating, if needed, so that all of the spectral lines you see can be seen against the
scale.
2) Record the color of a bright line in the first order spectrum (n = 1) and its distance
(position on the scale) to the right and left of the slit. Estimate the errors in the
distances you measure. An average, x, of these distances should be used in the
analysis. (Why?) Repeat this procedure for two additional bright lines in the first
order spectrum.
3) Repeat the procedure for one line in the second order spectrum (n = 2).
4) Measure the distance D from the grating to the scale and estimate the error to use
later in the analysis.
B. Spectra of various light sources using a monochromator.
Experimental Hints:

Always align lamp and magnifier carefully with respect to monochromator slit for best
intensity.

Remove the exit slit occasionally to obtain a broader view of the spectrum.
2

Read micrometer scale (directly in nanometers) carefully and estimate to ±0.1 nm when
possible.

Sometimes reducing the intensity for bright lines, by moving the lamp farther away or
by covering the entrance slit with thin paper, may improve the image quality.
Symmetrical masking of the slit height may also improve resolution and precision.

Rotate observation duties with your lab partner, with one observing the spectrum
while another reads the wavelength scale.

Do not exceed the upper mechanical limit of the wavelength micrometer: 0-1200 nm;
(otherwise you will lose your calibration). The micrometer should always turn very
easily; do not force it.

Estimate and record wavelength reading errors in all cases.
1) Set up the helium (He) lamp and insert the 25 micron slits. Set the monochromator to
588 nm and align the He lamp for maximum brightness. Record your value for the
observed wavelength to at least the nearest 0.1 nm. Find other lines near 447, 502,
and 668 nm and record your values. Include your estimated measurement error.
2) Set up the mercury (Hg) lamp, using 250 micron slits. Observe the approximate
wavelengths of several strong lines and compare with the known values ( 404.7,
435.8, 546.1, 577.0, 579.1 nm). Estimate the resolution of your spectrometer by
observing the 2.1 nm splitting of the yellow "doublet" lines near 580 nm, first with
250 micron slits, then with 25 micron slits. Include your estimated measurement
error.
3) Set up the sodium (Na) lamp, using 25 micron slits. Measure the fine-structure
splitting of the prominent yellow doublet ("D-lines") in first order near 590 nm, and
then as precisely as possible in second order near 1180 nm. Compare your measured
splitting and its error with the accepted value of 0.597 nm. Convert your measured
wavelength splitting (and its error) to the equivalent energy splitting (in eV).
4) Set up the hydrogen (H) lamp and the 25 micron slits. Record wavelength
measurements to the nearest 0.1 nm for the Balmer series lines at 656, 486, 434, and
410 nm, including your estimated measurement errors.
5) Insert the 250 micron entrance and exit slits into the monochromator, adjust the
magnifier to focus on the exit slit, and set up the white-light continuum lamp at the
entrance slit. First look for the zero order image ( = 0 nm). Each lab partner should
then view briefly the colors and extent of the continuous spectrum, with the exit slit
first removed, then inserted. Record the approximate red, yellow, green, and violet
wavelength regions, as they are centered at the exit slit. Record the value of the
3
smallest and largest wavelength limits of the visible spectrum for each observer.
These may vary slightly between observers.
IV. Analysis:
Part A
1) Compute the distance d between the slits of the grating from the given number
of lines per millimeter which was recorded on the grating.
2) (See Figure.) For each spectral line whose position you measured, compute
the average, x, of the distances of the line to the right and left of the slit and
the error in this average. Compute H = (x2 + D2)1/2. Compute the
wavelengths  in nm ( = 10-9 m) of the three spectral lines in first order (n =
1), and the one wavelength in second order (n = 2) for the hydrogen gas
discharge tube from the equation:
n = d sin  d (x / H)
where n = the order number (n = 0 at  = 0). Determine the errors in these
wavelengths. Compare the two values and errors for the wavelength of the
spectral line which was measured in both orders.
3) Compute the energies E in eV corresponding to the photons emitted for each
of three observed wavelengths. E = hc / where hc = 1240 eV nm.
Compute the errors in these wavelengths.
4) According to the Bohr theory of the atom, the energy level of a hydrogen atom
in the orbit with quantum number n is given by the expression:
.
En = - m e4 / (o2 8 n2 h2) = - 13.6 eV / n2
Using this expression, compute the energy levels En (in eV) for n = 2, 3, 4, 5,
and 6.
4
5) Now determine which specific transitions are responsible for the wavelengths
you have observed from the hydrogen lamp. (A transition occurs when an
electron "jumps" from an initial energy level i to another energy level f,
emitting a photon whose energy E = (Ei - Ef) is equal to the difference in
energy between the two levels involved in the transition.) Use the results of
A.4. to compute the energies predicted by the Bohr model for the photons of
the wavelengths you observed. Compare the predicted photon energies with
your determinations of these energies from A.3. Do they agree within errors?
If not, can you think of possible reasons?
Part B
1) Compare the values and measurement errors for the Helium spectrum that you
determined using the monochromator with the accepted wavelengths for He. These
can be found at the following website: [http://www.whfreeman.com/modphysics] in
Chp. 7 under the heading Multielectron Atoms.
Plot the difference between your
measurements and the accepted wavelengths versus wavelength, i.e.  vs ,
including error bars. This plot is the calibration curve for your instrument and is to be
used below to correct your hydrogen spectrum data. Sketch a partial energy level
diagram for He and indicate the transitions you have measured.
2) Correct your observed wavelengths for the hydrogen spectrum found using the
monochromator by the calibration curve for your instrument obtained in step [B1]
above. Correct your wavelength values, measured in air, to vacuum wavelengths and
then calculate the Rydberg constant, RH, using these vacuum wavelengths. Use vac
= nairair = 1.00027air (good to 1 part in 105 for  > 200 nm). Refer to Tipler and
Llewellyn, pg. 160 for a discussion of the Rydberg formula. Calculate your error in
RH and compare your measured value with the accepted value, 1.0973732x107 m-1.
(Note: use propagation of errors to find the average value of RH and its error from the
four Balmer-series lines you measured).
NOTE: Before you leave the lab, all measurements must be complete and each lab
partner must have a complete data sheet for parts A and B, initialed by your TA. If
possible, compute at least some values of  and the corresponding values of E for the
hydrogen spectral lines you observed.
5