Figure 5
Don't touch the sample tube with the power on or you may be electrocuted.
Purpose
To identify several unknown elements by comparing their optical emission spectrum with the known spectra of the elements.
Equipment
Preparation and lab work
To measure the emission wavelengths of the samples provided in the lab the angles of the corresponding diffraction maxima produced by the grating must be measured. One possible method for measuring line spectra is to pass the light through the grating and project it onto a circular screen as illustrated in Fig. 5.
Figure 5
The angles 
1, 2 etc. of the maxima from the line N - N' normal to
the grating correspond to each of the component wavelengths making up the light
from the source. By measuring these angles and using the grating equation,
these wavelengths can be determined. This set of wavelengths is then compared
with tables of known spectra to identify the elements present in the source.
For precise measurements of very weak sources, a problem commonly faced by
astronomers working with starlight, photographic paper is placed on the screen
and long time exposures are made.
With the relatively bright discharge tube sources used in the lab, the observer's eye can be used directly in place of the screen, but this method restricts our measurements to the visible portion of the spectrum. The setup to be used in the lab is drawn in Fig. 6.
Figure 6
When you look through the grating illuminated by one of the discharge tube
sources, you will notice a set of colored images of the discharge tube. Each
colored image corresponds to one of the components of the emission spectrum for
the gas in the tube. The "first-order" set of spectral line images,
corresponding to n - 1 in the grating equation, will be seen at the smallest
angles 
(closest to the source itself). Further on down the angle scale
you will probably see another set of lines similar to the first; this is the
"second-order" spectrum corresponding to n - 2. The image of the source
corresponding to one of the discrete wavelengths (colors) in the emitted light
is located by means of a moveable marker whose position can be read on an angle
scale. Notice that the angle read on the scale is not the same as the
angle we used in deriving the grating equation. Do you know how to
determine 
from the angles 
and shown in Fig. 6?
There are three angles in the apparatus: the grating angle , the
diffraction angle and the effective image angle (= +
). The grating equation indicates that many combinations of and
are possible, but a particularly useful combination is one in which the
image angle does not change much when is changed. Such a
circumstance is desirable because of the difficulty in finding = o
which is the normal to the actual grating surface. It is possible to show that
the grating equation leads to
when 
(or = )
This is exactly what we were seeking because it says that small errors in
setting will have no effect on .
You may also show, using calculus, that the setting where
occurs also corresponds to being a minimum angle. An empirical
approach to setting is then possible. Simply rotate the grating while
watching a particular color of the spectrum and when that color has moved
closest to the discharge tube ( at a minimum), then you have found the
place where = /2 for that color. Once is set this way,
merely move the marker to the color and measure . This whole procedure is
a good example of what is loosely called "experiment design," i.e., finding
ways to optimize accuracy or sensitivity when there are many combinations
possible for measuring some parameter ( in this case).
We should also examine how slight inaccuracies in reading the diffraction angle
will affect our determination of the spectral wavelengths. Taking
,
the grating equation for the first order spectrum is
From the differential calculus we have for the errors 
in caused by an error 
in the result
(for in radians) Now, it is clear that for a given ,
the size of will depend on itself through the cos
/2 factor. Consider, as an example, the midpoint of the visible spectrum
( = 5,500
),
and a grating with exactly 104 lines/cm (d = 10-4 cm =
10
).
Then for /2 we have
and
,
so
/radians
= 
/radians
= 146 
/radians
Thus a 0.5 degree error in will produce a 73
measurement error in a wavelength of 5,500 
.
You will notice in a lab that if you move your head while looking through the grating at an image, the line will appear to shift position slightly. This can introduce a significant error into your measurements. The grating has a mask with an arrow or line drawn on it parallel to the grating rulings. If the grating is mounted so this line is on the axis of rotation of the marker arm, then you can eliminate the above uncertainty in image position by simultaneously lining up the image, the marker, and the line on the grating mask. The sample tubes have a small glass protection sticking out perpendicularly near one end. When changing sample tubes, be sure that this projection is at the top end of the tube, for otherwise you will not be able to put the tube into the high voltage socket of the power supply box without breaking it off.
IMPORTANT NOTE:
Before mounting or changing one of the discharge tubes be sure that the power supply switch is off and that the power line cord is unplugged. Ask the laboratory assistant to show you how to change the tubes before attempting it by yourself. This extreme caution is necessary because the 5,000 volt output from the power supply could be lethal. To avoid accidents it is best to turn the supply off when not actually in use. This also preserves the tubes which have a rather limited lifetime.
Basic laboratory measurements
Several of the discharge tubes are labeled as to their contents. These known
spectra might be useful for calibrating the apparatus used in determining the
unknowns. A first step is to see if a constant must be subtracted from your
measured to obtain agreement with known spectra. Note in particular
the spectrum for the tube labeled nitrogen. This is the only example provided
of a diatomic molecule discharge spectrum. As a result of the formation by the
nitrogen atoms of N2 molecules, the sharp atomic nitrogen lines are
spread out into broad bands.
Measure the positions of the 1st order spectral lines for the three unknown elements. Calculate the corresponding wavelengths, including the experimental uncertainty of each, and identify the elements by comparison with the wavelength tables given at the end of these notes.
Observe the 2nd order spectrum from one of the discharge tubes (either labeled or unknown) and verify that the grating equation is satisfied for n = 2. Because the 2nd order spectrum is not so intense as the 1st, you may have to take special care to darken the room in order to see it.
(Wavelength given in 
)
H He Ne A I Hg 3970 3889 4538 3948 3940 3650 4102 4471 4704 4044 4862 3663 4340 4686 4715 4159 5119 4047 4861 4922 4827 4164 5465 4358 6563 5016 4957 4191 6082 5461 5876 5038 4345 6294 5770 6678 5145 4510 6566 5791 7065 5341 4596 6959 5400 4702 5764 5188 5852 5496 5882 5651 6030 5912 6074 6032 6143 6043 6163 6059 6217 6416 6267 6753 6402 6965 6506 6599 6929 7032