SPECTRAL ANALYSIS
Introduction
An incandescent source such as a hot solid metal
filament produces a continuous spectrum of
wavelengths of light. However, light produced by
an electric discharge in a rarefied gas of a single
element contains a limited number of wavelengths,
an emission or "bright line" spectrum. The pattern
of colors in an emission spectrum is characteristic
of the element. The individual colors appear as
bright lines because the light passes through a
grating illuminated by the light source.
A grating is a piece of transparent material on
which has been ruled a large number of equally
spaced parallel lines. The distance between the
lines is called the grating line spacing, d.
Light striking the transparent material is diffracted
by the parallel lines. The diffracted light passes
through the grating at all angles relative to the
original light path. Most of the light rays diffracted
from adjacent lines will interfere destructively and
cancel one another out. However, if adjacent
diffracted light waves are in phase, constructive
interference occurs and an image of the light source
is formed. Light rays from adjacent lines will be in
phase if the rays differ in path length by an integral
number of wavelengths of the light. As shown in
Figure 1, the difference in path length between
adjacent rays is dsin, where d is the grating line
spacing and  is the angle of diffraction.
The condition for constructive interference of
adjacent rays is given by the Bragg equation,
Equation 1.
m = d sin,
1
where m = 1, 2, 3, . ., integer
In Figure 1, m = 1, i.e., the "first order" diffraction
line.
In this experiment, a spectrophotometer will be used
to determine the diffraction angles for the emission
lines in several spectra, Equation 1 will be used to
determine the associated wavelengths of light.
Equipment Setup
The equipment setup is shown in Figure 2.
Figure 2. Experimental setup
Turn on the light source. Once it is warmed up,
adjust the light source, Collimating Slits, Collimating Lens, and Focusing Lens so clear images of
the central ray and the first order spectral lines
appear on the Aperture Disk and Aperture Screen in
front of the High Sensitivity Light Sensor. Check to
see that the smallest slit on the disk is in line with
the central ray.
Figure 2. Equipment Setup
Turn on the Science Workshop interface. Click on
the Science Workshop icon and open the file
Spectra.sws.
Figure 1. Ray diagram for first order diffraction pattern
SPECTRAL ANALYSIS
1
Data Collection
Darken the room. Examine the spectrum closely.
List the first-order colors you see in order starting
with the color that appears farthest from the central
ray.
Use the Light Sensor Arm on the
Spectrophotometer to turn the Degree Plate until the
light sensor is beyond the last line in the first order
spectral pattern. Set the GAIN select switch on top
of the High Sensitivity Light sensor to the
appropriate setting, (1, 10, or 100).
Click on the Record (REC) button to start recording
data. Push on the threaded post under the light
sensor to slowly and continuously scan the
spectrum in one direction. Scan through the first
order spectral lines on one side of the central line,
through the central line, and through the first order
spectral lines on the other side of the central ray.
See Figure 3.
In order to measure the angle and intensity of a
given spectral line precisely; click on the button
with cross hairs (next to the button with  in the
lower left side of the graphical display). This will
change the cursor to a set of cross hairs, which you
should line up very carefully with the peak of the
spectral line of interest. The angle and intensity
values will appear near the labels for the horizontal
and vertical axes. It may also be helpful to expand
or contract the axes in order to analyze the data
more easily. This can be done by clicking on the +
(scale expansion) and  (scale contraction) buttons
in the lower right corner (one set for each axis).
Figure 3. Scanning the spectrum.
When the scan is complete, stop recording data by
clicking on the STOP button.
Data Analysis
Expand the Graph icon. Observe that the vertical
axis is Light Intensity (% max) and the horizontal
axis is Actual Angular Position (rad).
The spectrum shown on the graph should be similar
Figure
3. spectrum
Scanning the
Spectrum
in appearance
to the
shown
in Figure 4.
2
Figure 4. A first order spectrum pattern (Hg)
Record the angle of corresponding peaks on the
right and left side of the central maximum. The
diffraction angle  of a particular line in the spectral
pattern is one-half of the difference in angle
between the line on one side of the central ray and
the corresponding line on the other side of the
central ray. Record the intensity on one side only,
preferably the side that is producing larger
intensities, but use the same side consistently.
When the angle  has been determined for a spectral
line, one can use Equation 1 with m=1 to determine
the associated wavelength of the line.
SPECTRAL ANALYSIS
Calibrating the Grating
The line spacing of the grating must be determined
in order to use Equation 1 to calculate wavelength.
A value of d can be determined using the hydrogen
spectrum to calibrate the grating.
Using the energy levels of a hydrogen atom:
En = -13.6eV/n2
and the fact that the red line in hydrogen arises from
a transition of an electron from the n=3 state to the
n=2 state, calculate the wavelength of the red line in
the hydrogen spectrum.
Use the hydrogen spectral lamp and obtain the first
order spectrum using the procedure described in the
Data Collection and Data Analysis sections below.
Determine the diffraction angle for the bright red
line in the spectrum. Then find d using equation 1.
Use this value of d in all subsequent calculations of
wavelength.
First Order Spectrum of Mercury
Replace the hydrogen spectral lamp with the
Mercury light source. (Note: It is best to allow the
mercury source to warm up before using it.
Consequently, it is good to turn it on well before it
is to be used.) Obtain the first order spectrum with
a GAIN setting of 1. Determine the wavelengths
and intensities of the lines in the spectrum which
have intensities greater than 4.5 when obtained at
this GAIN setting.
Repeat this procedure to get a second determination
of the wavelengths and intensities. This will give
you a feel for the accuracy of the measurements.
Use an average value for any calculations.
Now obtain a set of data for mercury using a GAIN
setting of 10. Measure the wavelengths and
intensities of any lines which had intensities less
than 4.5 (and may even have been unobserved) in
the first sets of data. Since the GAIN value is 10,
you must divide all your intensity values by 10.
You should be able to obtain data for a total of 5 or
6 spectral lines of mercury.
Find the percentage errors between your values for
the wavelengths in the mercury spectrum using the
accepted values given below.
Mercury Emission Spectrum
Yellow 2
Yellow 1
Green
Blue-green
Blue
Violet 2
Violet 1
579.1 nm
577.0 nm
546.1 nm
491.6 nm
435.8 nm
407.8 nm
404.7 nm
Transmission Spectra of Filters
Continue using the mercury source, being careful
that no element of the setup moves between the
previous part of the experiment and this part.
The green filter provided is the same filter that was
used in the photoelectric effect experiment. In that
experiment, we wanted to filter out all but the green
line of mercury, so we were sure to see the voltage
created by light of this one wavelength. In this
experiment we will determine how well the filter
achieves this.
Place the green filter on the holder with the grating.
Obtain the first order spectrum with a GAIN setting
of 1. Determine the intensities of the lines in the
spectrum which have intensities greater than 4.5
when obtained at this GAIN setting. There is no
need to recalculate the wavelengths, but you will
want to measure  to determine which line is which.
Now obtain a set of data using a GAIN setting of
10. Measure the intensities of any lines which had
intensities less than 4.5 in the first set of data, but
now are greater than 4.5. Again, with this setting
you must divide all your intensity values by 10.
Now obtain a set of data using a GAIN setting of
100. Measure the intensities of any lines which had
intensities less than 4.5 in the first sets of data.
Now you must divide all your intensity values by
100.
SPECTRAL ANALYSIS
3
Calculate the percent transmission of this filter for
each wavelength in the mercury spectrum, by
comparing the intensity with the filter to the
intensity without the filter. Graph the percent
transmission of this filter as a function of
wavelength.
Question:
Does this filter block all other
wavelengths effectively? Does this filter block all
shorter wavelengths effectively? Is blocking all
shorter wavelengths good enough for use in the
photoelectric effect experiment?
Repeat the above determination of percent
transmission using the neutral-density (gray) filter.
Graph the percent transmission of this filter as a
function of wavelength.
Question: In what sense is this filter “neutral”?
Repeat the above determination of percent
transmission using some other transparent material
as a filter. Plot its percent transmission as a
function of wavelength, and comment.
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SPECTRAL ANALYSIS