OBJECTIVES
The objectives behind this laboratory are to calibrate a grating spectrometer with known gas
spectral lamps, and then to use the spectrometer to measure and identify an unknown source and
to measure and analyze sources to be chosen.
THEORY
Spectroscopy is simply the study of spectra. Each element, by virtue of the electronic transitions
occurring within the atoms of any given element, exhibits a characteristic spectrum. Through the
application of a digital spectrometer, light from a source can be converted in a binary signal
suitable to be processed by a computer.
For a perfect blackbody, that is an object that is both a perfect emitter and absorber, the energy
density of photons as a function of frequency and temperature is given by


8 2 d  h 
 ( , T )d 

c 3  hkT
 e 1
(1)
where  is frequency, T is temperature, h is Planck’s constant, k is Boltzmann’s constant and c is
the speed of light. If (1) is integrated over all frequencies from zero to infinity, then the total
energy density is obtained:

 (T )    ( , T )d 
0
8  5 k4 4
T  aT 4
3
3
15 c h
where the constant a has the numerical value of 5.67  10 8
(2)
W
.
m K4
2
In each atom of any given element, Bohr’s model of the atom can be used as an calculative
approximation to obtain the differences between energy levels in the atom. For a given stationary
state in an atom, the energy E is given by
E
Z 2 me 4 1
8 02 h 2 n 2
n  1,2,3,...
(3)
Here, Z is the atomic number of the element under consideration, m is the mass of the electron, e
is the electronic charge, 0 is the permittivity of free space, and n is an integer denoting energy
levels (for the ground state, n = 1). The energy emitted by the atom as electromagnetic radiation
when a transition occurs from one energy level to another one nearer the ground state is simply
the energy difference between the two levels.
Z 2 me 4
E 
8 02 h 2
1 1
  
 n1 n2 
(4)
Here, E is the energy of the photon that is emitted, n1 is the final level of the electron and n2 is
the initial level of the electron.
For any spectrometer, the optical resolution is defined as the Full Width Half Maximum (FWHM)
of a monochromatic light source. The optical resolution for the spectrometer can be obtained by
finding the product of the spectral range of the grating, number of detector elements and the pixel
resolution.
APPARATUS
The basic experimental set-up used in this experiment consisted of a light source, a S2000
spectrometer manufactured by Ocean Optics Inc., and an NEC laptop computer equipped with a
special spectrometry software analysis package. Along with the components already listed, a
fiber-optic cable was sometimes used throughout the experiment as well, one end of which was
attached to the spectrometer and the other end pointed at a light source. However, sometimes the
strength of the light source was such that the spectrometer optical input port to which the fiberoptic would have been attached could obtain a good sample without having the cable attached.
Another accessory used from time to time throughout the experiment was a set of neutral density
filters. When placed between the light source and the spectrometer optical input port, they served
to attenuate the light reaching the spectrometer, preventing strong light sources from saturating
the spectrometer. Various combinations of neutral density filters could be constructed to produce
varying degrees of attenuation.
The S2000 spectrometer will now be described in some detail. Light enters the spectrometer,
either directly into an optical input port from the light source, or via a fiber-optic cable connected
to that port. As shown in Figure 1, once inside the spectrometer, the light is collimated by a
spherical mirror M1, and diffracted by plane grating P1, focused by spherical mirror P2, and
finally reaches a linear one-dimensional charged couple detector (CCD) array. From the CCD
array, an A/D converter processes the signal before transferring it to the computer.
FIGURE 1: The workings of the S2000 spectrometer and its connections to other components of
this apparatus.
The principles behind the operation of the CCD array used in this experiment are as follows:
Light, pictorially represented by the rainbow at the top of Figure 2, is incident upon photodiodes
with CCD pixels. Each of these photodiodes discharges a capacitor at a rate proportional to the
illumination upon the given photodiode. After the integration period of the detector has finished,
a series of switches close, transferring the stored charge into a shift register. Upon the completion
of the transfer, the switches open, the capacitors begin recharging and a new integration period
commences. Simultaneously with the integration of the light energy, the stored data is shifted out
of the register through an A/D converter and transferred to the computer.
FIGURE 2: A pictoral representation of the operation of a CCD.
The CCD used in this experiment is the SONY ILX511 2048-pixel CCD linear image sensor
(B/W).
PROCEDURE
1. The equipment was set up as shown in Figure 1. The whole apparatus was located in
a dark room so that background light did not affect the experimental data.
2. The software was set up to use Slave 3 to acquire the data.
3. When necessary, optical attenuators were used to decrease the intensity of the
incoming light so that a clear reading could be obtained. Attenuators with different
abilities to block light were used, depending upon the strength of the light source.
4. The software provided a graph of the spectrum, and was used to determine the
wavelengths of the peaks. Analysis of these peaks was used for determining the
identity of samples.
5. A neon laser and mercury and hydrogen gas lamps were used to calibrate the
equipment.
6. Data was collected from two gas lamps of unknown sources.
7. By analyzing the peaks on the spectra, the identities of the unknown samples could be
determined.
8. Data was collected for a desk lamp, a sun lamp, and sunlight from outside.
9. The curves were compared qualitatively, and the absorption lines were compared to
determine what elements were present in the earth’s atmosphere.
OBSERVATIONS
The graphs of the experimental data are shown in the Appendix.
Calibration:
Neon Laser (Graph 3): (Filters = 5.0)
Theoretical
Experimental
Error
632.8
632.6
.2
Theoretical
Experimental
Error
365.015
404.656
435.833
546.074
576.960
578.966
No good match
No good match
364.59
404.33
435.41
545.66
575.96
577.99
762.25
810.58
.425
.326
.423
.586
1.0
.976
-
Theoretical
Experimental
Error
486.12785
656.28672
486.51
656.37
.38215
.08328
Mercury Lamp (Graph 2):
Hydrogen Lamp (Graph 1):
Error Used: 1.0 nm
Unknown Sources:
Table 1 (Graph 4): Unknown I
Experimental
(+/- 1.0 nm)
Possible Elements
364.95
Lu I, Fe I, Tc I, Dy II,
Hg I
U I, La II, Fe I, Dy I,
Hg I,
Hg I, Tm I, Cs II,
Sr I, Cl II, Hg I, I II
Cu I, Gd III, Hg I
I II, I I, Pu I, Hg I
404.33
435.77
546.00
576.30
578.33
Consistent for all
Lines
Fe I, Hg I
Hg I
Hg I
Hg I
Hg I
Table 2 (Graph 5): Unknown II (Helium)
Experimental
(+/- 1.0 nm)
Possible Elements
388.49
Er II, TmI, Tm II,
Sm II, Zr I, Nb I, Fe I,
La II, Tm I, Cs III, Nd
II, Ce II, Zr I, U II,
He I
Sm II, Pu II, Rb II,
Cm I, V I, Bk I, He I
Ti I, Pb I, Ba II, He I
He I, Kr I, Gd III
He I, Cl II, Cm I
He I, Pu I, BaI
446.76
500.80
586.77
666.54
705.20
Consistent for all
Lines
Sm II, He I
He I
He I
He I
He I
Blackbody Sources:
Desk Lamp:
A blackbody curve was observed and the result can be seen in Graph 6 in the Appendix.
Sun Light:
A blackbody curve peaking at about 580nm and showing noticeable atmospheric
absorption at some wavelengths was produced. See Graph 7 in the Appendix.
ANALYSIS
The first part of this experiment involved calibrating the equipment so that we could
estimate the experimental error. Data was collected from a neon laser as well as a
mercury lamp and a hydrogen lamp so that the wavelengths of the peaks could be
compared to known values. The spectra collected are shown in Graphs 1, 2 and 3.
For the neon laser, the wavelength was provided in the manufacturer’s description. For
the gas lamps, the theoretical data values were found on the NIST Atomic Spectra
Database (http://physics.nist.gov/PhysRefData/contents.html). The element in question
was entered with a range of expected wavelengths. The database returned all of the
spectral lines within that range along with the relative intensities of the lines. The
relative intensity was used to choose the appropriate line because there were several more
lines than we were able to observe using our equipment. In most cases, the line with the
highest relative intensity was used.
To determine the experimental error, the difference between the theoretical value and the
experimental value was calculated. The largest difference found was used as the value
for the experimental error in the rest of the experiment.
The second part of the experiment involved determining the identity of two unknown gas
lamps. The spectra of the unknown elements are shown in Graphs 4 and 5.
The
wavelengths of the unknown peaks were entered into the NIST Atomic Spectra Database
and all of the elements with lines in the specified error range were returned. The relative
intensities were used as a guideline to determine all of the possible elements. A process
of elimination was used in determining which element was consistent for all of the
observed spectral lines. In both cases there was only one element that matched for every
absorption line observed. The first unknown was determined to be mercury and the
second unknown was determined to be helium. The graph of the first unknown, Graph 4,
was compared to the graph of the mercury lamp, Graph 2, and was found to be very
similar. This provided further evidence that Unknown 1 was mercury.
The third part of the experiment was concerned with observing some black body sources.
The data taken from the incandescent desk lamp was graphed to provide an example of a
blackbody curve shown in Graph 6. As expected, the sunlight yielded a classical
blackbody curve with noticeable atmospheric absorption at certain wavelengths. The
curve is shown in Graph 7 in the Appendix. Both curves supported the claim that the sun
lamp and sunlight were black body radiators.
DISCUSSION
In the tables presented in the Observations section, the close correspondence between the
experimental and the theoretical values of the spectral lines, in those cases where the type
of source was known, verifies the usefulness of spectroscopy as a means to distinguish
between the elements of nature. More specifically, in the first part of this lab, where the
spectral lines of known lamps were obtained, the experimentally determined peaks of all
spectral lines fell within the theoretical values with a difference in all cases less than the
experimental error of 1.0nm. This demonstrated accuracy yields a great deal of
confidence in the determinations of the unknown spectral lines and the solar spectrum as
found in the second and the third parts of this experiment.
A number of systematic errors were present in this experiment that could have adversely
affected the results. First, any aberrations in the construction of the planar and spherical
reflecting mirrors inside the spectrometer would have made the plots of intensity versus
wavelength less precise. Although any such deficiencies were not expected to be large,
the degree of accuracy with which measurements were taken was rather high, so even
small imperfections could have caused noticeable skewing in the results. Second, any
stray light present in the room when measurements were being taken would have
essentially appeared as noise superimposed upon the profile of the light emitted by the
source under investigation. Steps were taken to minimize the effect of this error by
attempting to eliminate the effects of all extraneous light sources (i.e. the door of the
room was closed and all room lights other than the one being studies were turned off).
Even so, light leaking out from under the door and that emitted by the laptop computer
undoubtedly did cause some effect on the results. However, the magnitude of this error
was rather small as the sources under study in all cases far outshone any extraneous light
sources, so no substantial effects resulting from this error are expected.
The most significant source of error in this experiment was probably the stray light
streaming in from under the door and from the laptop screen. This light could not be
completely eliminated, so that some extraneous signal was always present on the plots of
the intensities versus wavelengths for each of the sources.
In the first part of this experiment, the accuracy with which the spectrometer can discern
spectral lines and their corresponding wavelengths was clearly demonstrated. In the
second component of the experiment, the important application of using spectroscopy to
identify an unknown element was demonstrated, with the spectrometer providing
compelling evidence that the gas lamps containing unknown elements were in fact
mercury and helium lamps. Finally, in the third part of this experiment, the usefulness of
spectroscopy in solar physics was demonstrated by obtaining a profile of the sun. Many
more applications of spectroscopy exist which have aided in developing humankind’s
understanding of the world and the universe.
APPENDIX
Intensity
Graph 1: Hydrogen Lamp
1500
1000
500
0
0
200
400
600
800
1000
Wavelength (nm)
Intensity
Graph 2: Mercury Lamp
6000
4000
2000
0
0
200
400
600
800
1000
800
1000
Wavelength (nm)
Intensity
Graph 3: Neon Laser
6000
4000
2000
0
0
200
400
600
Wavelength (nm)
Intensity
Graph 4: Unknown 1
6000
4000
2000
0
0
200
400
600
800
1000
800
1000
800
1000
Wavelength (nm)
Intensity
Graph 5: Unknown 2
4000
3000
2000
1000
0
0
200
400
600
Wavelength (nm)
Intensity
Graph 6: Desk Lamp
600
400
200
0
0
200
400
600
Wavelength (nm)
Intensity
Graph 7: Sun Light
4000
3000
2000
1000
0
0
200
400
600
Wavelength (nm)
800
1000