Experiment 19: Diffraction Grating Spectroscope
Purpose
(1) To observe spectra.
(2) To measure wavelengths in line spectra.
Apparatus
(a) a diffraction grating spectroscope; a mercury lamp; a desk lamp
(b) on the side: 4-5 helium gas tubes with bases
(c) tungsten filament (with a spare spectroscope), 2-3 sodium lamps with bases
Theory
(I) The Diffraction Grating Spectroscope.
Light passing through a narrow slit is collimated by a lens, resulting in coherent
plane waves falling upon a diffraction grating (Fig. 1). If the light is monochromatic,
of wavelength λ, the image of the slit can be observed only at particular angles θm
given by formula (1) where d is the distance between adjacent grooves in the grating
and m is an integer, called the order of the image.
BASIC
FORMULA
(1)
d·sin θm= m· λ
(II) Spectra.
If the light source emits light of several specific wavelengths, then the angles θm will
be different for different wavelengths, and the images of the slit will appear as a set of
lines of different colors, called a line spectrum.
For each order m (except for m = 0) there will be two identical spectra, to the right and
to the left from the central image, which corresponds to m = 0 and contains the
mixture of all wavelengths present in the source.
Glowing gases (at low density) produce such line spectra, each gas with its own
specific wavelengths. Glowing solids and liquids produce continuous spectra,
containing all wavelengths.
Preliminary Procedure: Optical Adjustments
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Experiment 19
The Central Image:
1) Your spectroscope is shown in Fig. 2. Familiarize yourself with it.
2) Turn on the mercury lamp.
Align the collimator and
telescope tubes and look
straight into the lamp. You
should see a white, vertical,
central image (zero order
image) of the slit.
Note: If the slit image is not
vertical, call your instructor.
3) Move the whole spectroscope as closely as possible to the cardboard slit on the lamp.
Move the whole spectroscope slightly to the left or to the right until the image is
as brilliant as possible. It should be so brilliant as to be uncomfortable to the eye!
AT THIS POINT, CALL YOUR INSTRUCTOR TO CHECK THAT YOU HAVE A
GOOD SPECTRUM. HE OR SHE CAN HELP YOU ADJUST THE COLLIMATOR.
Note: If you wear reading glasses, take them off; if you wear driving glasses, keep
them on.
The Focusing:
4) Relax your eye. Move the image focusing knob (Fig. 2) back and forth until the slit
image is sharp.
5) Move the telescope tube (only!) slightly sideways to get the slit image out of the field
of view. You should see the cross-hairs. Relax your eye completely. Then,
hand until you see the cross-hairs very sharply. Rotate the eyepiece until you see
the cross-hairs at 45º to the horizontal (that is, like X, rather than like +).
6) Move the telescope back to make the cross-hairs coincide with the slit image. Quite
possibly, the image will not be now sharp (out of focus). Repeat (4) to re-focus the
slit image; then repeat (5) to re-focus the cross-hairs and so on, until both the slit
image and the cross-hairs are sharp.
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Experiment 19
To check if you have it correctly: Move your eye sideways: if the slit image and the
cross-hairs appear to move together, without any mutual displacement, your adjustment
is correct. Otherwise, repeat (4), (5) and (6). Call your instructor if in doubt.
7) With the cross-hairs sharply centered on central image, the angle indicator should read
0º or within 0.5º from it (if not, call your instructor to adjust it). This is your zero
reading. Record it, estimating down to one tenth of a degree, to the best of your
ability; also record whether it is “to the right” or “to the left” (if it is exactly zero,
record it as 0.0º ).
8) Swing the telescope by some 15º to 20º to the right. You should see a line spectrum,
that is a set of colored images of your slit. Warning: during this motion the collimator
tube must remain motionless. If not, alert your instructor immediately.
If the lines are too high or too low, (or if they are missing altogether) call your
instructor; do not try any adjustments of your own.
AT THIS STAGE, CHECK AGAIN WITH YOUR INSTRUCTOR. DO NOT
PROCEED WITHOUT HIS OR HER APPROVAL.
Procedure Part I: The Mercury Spectrum
9) Record the grating constant of your telescope:
K = 6,000cm-1 (K is the number of grooves per centimeter)
d = 1/K = 1.67  10-4 cm = 1.67  104 Angstroms
10) Locate your first order spectrum as in (B), which should start at about 14º. You
should be able to see at least nine lines, usually more, sketched in Fig. 3.
Line (Describe
and relate to
your sketch)

The symbol for Angstroms is
: 1  = 10-8 cm
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Order
m
Angle Readings
Right
Left
Experiment 19
11) Set up your data sheet as shown in Figure 3. Sketch the lines that you see and can
measure. Label them by color and brightness in the proper sequence.
Measure and record the angles of all lines that you can identify, estimating the
readings to one tenth of a degree. Do this in first order both to the right and to the
left of the central image. You may be able to observe the two violet lines
in second order. If so, measure and record their angles (but do not go beyond the
scale).
Procedure Part II: Other Spectra
12) Your instructor will provide you with a Helium gas tube (to be shared with other
students). Sketch the helium spectrum, as in (10).
13) Measure and record the four brightest lines in first order both right and left.
Identify them in your sketch and recording them as for the mercury spectrum.
14) Observe the spectrum of the tungsten filament which will be set aside on a spare
spectroscope.
Lab Report
Part I
a) Set up the table below:
Line (Describe it with
Reference to your own sketch)
Order
m
Measured Angles
To the
To the
Average
Right
Left
λ (Angstroms)
Sin θ
Measured
Known
%
Errors
Carry out calculations of λ accurate to four significant digits (NOT more). Display the
calculation for the mercury green-yellow line (See Fig. 3).
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Experiment 19
The correct values of λ for the five strongest lines in mercury spectrum are:
Strong violet line
Strong blue line
(Strongest) green-yellow line
Orange/yellow doublet lower
higher
4,047
4,358
5,461
5,770
5,790
Angstroms
Angstroms
Angstroms
Angstroms
Angstroms
Enter these values in your table and calculate the % errors for these lines only. For other
lines, just calculate λ, leaving the last 2 columns blank. As a rule, your % errors should
not exceed 2%.
b) On the basis of your experience in the lab, and your calculations, pinpoint the two
most important sources of error. State them clearly.
c) Answer Question #1:
If your angle indicator could measure angles beyond 30º, calculate at what angle the
yellow-green 5461 A line of mercury would appear in third order? Also, comment on
this line in the fourth order.
Part II
d) Set up a table for helium as above. Calculate the measured values of the helium
wavelengths in the same fashion as for mercury but leave the last two columns blank.
e) Answer the questions:
Question #2: In what fundamental aspect the observed spectra of mercury and helium
different from the spectrum of tungsten filament? Why is this so?
Question #3: What is the major cause of discrepancies between the measured and the
correct wavelengths (excluding your own possible negligence)?
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