SPECTRA
White light is a mixture of all wavelengths. When white light is sent through a prism or a
diffraction grating it is broken up into a continuous distribution of colors called a spectrum. The
relation between wavelength and color is given in the following table.
color
wavelength (nm)
violet
400 - 450
blue
450 - 480
blue-green
480 - 510
green
510 - 550
yellow-green
550 - 570
yellow
570 - 590
orange
590 - 630
red
above 630
A rainbow is a spectrum produced when sunlight is refracted through raindrops. Any thin slice of
color in a continuous spectrum is called a spectrally pure color and is characterized by its
wavelength . Spectrally pure colors are rare in most of our natural environment but they are
easily produced in the laboratory.
When an electric current is sent through a diffuse transparent gas the gas is heated and glows. If
the light from such a gas is passed through a prism or diffraction grating, a discrete set of bright
colors will typically be seen. When a diffraction grating is used the colors appear to be narrow
lines parallel to the slits of the grating and are called spectral lines. A collection of these lines
(usually in the form of a table or graph) for a gas composed of a given chemical element is called
the line spectrum of the element.
A very different sort of spectrum is produced by a hot opaque object like a lightbulb filament.
Instead of discrete spectral lines this incandescent light source produces a broad distribution of
colors. Every color in the visible range is represented in such a spectrum and the relative
intensities of various colors depends on the temperature of the hot object.
3.1
Experiment 1: Grating Spectroscope
Apparatus: CENCO grating spectroscope, variac-controlled light bulb, sodium and
mercury vapor lamps.
Procedure: Hold the device so that its right angle is on your left. View through the
grating fixed to the aperture at the short end. Illuminate the vertical slit on the left with
the light to be studied. The nominal wavelength is read on the scale to the right of the
slit.
A. The spectroscope is not accurately calibrated; the nominal wavelength appearing on
the scale is not the true wavelength. Use the fluorescent lights in the room to make a
table of true vs. nominal wavelength
The actual wavelengths, in nm, are:
violet
blue
green
orange
red
436
489
545
585
612
Compare to the observed lines. Make a table of corrections to be used for subsequent
measurements.
B. Use the spectroscope to find the wavelengths of light from sodium and mercury
vapor lamps.
C. Examine the light from the filament of an unfrosted light bulb. Begin by turning the
current up to a significant value but not so high that its light is painful. Use the
spectroscope to compare the intensity of the violet light to that of the red light. As the
current is turned down, all intensities decrease. Can you see a relative difference in the
intensity of the violet light compared to the red light? Which color’s intensity decreases
fastest as the current is turned down? Repeat a few times to make sure of your result.
D. Take the instrument home for a day or two. Look at and report your findings for light
from: a gas flame, a candle flame, automobile headlights, a room lamp, commercial
neon lights and the sun at midday and at sunrise or sunset (of course you should not
use light directly from the disk of the sun).
3.2
Experiment 2 : Prism Spectrometer
Apparatus: Prism spectrometer, mercury and sodium vapor lamps, hydrogen discharge
tube, helium-neon laser
The prism spectrometer consists of an equilateral flint prism fixed to a stand containing
an adjustable slit, an objective lens that focuses the light from the slit onto the prism,
and a telescope consisting of an objective lens and an adjustable ocular with built-in
cross-hair. The telescope sits on a platform that is free to rotate about a vertical axis
through the prism. Gross rotation angle of the telescope is changed by moving the
telescope support with the hand while fine adjustments are made with a screw on the
right side of the support. Angle of the telescope is measured on a principal scale and on
a vernier scale equipped with a viewing lens to read minutes of arc.
Procedure:
A. Calibration of Angles
Light enters the device through the slit. A typical experiment consists of measuring the
angular positions of spectral lines produced when light has gone through the prism.
This light emerges as colored images of the slit. The slit should first be opened
relatively wide and placed so as to view the light from a mercury vapor lamp. The line
spectra can be located by gross rotation of the telescope housing. Then close down the
slit until only narrow spectral lines remain. These will often be slightly curved, forming a
bow rather than a straight line. Use the fine adjust to line up the vertical cross-hair with
the center of the bow of each spectral line. There will be a dim line far in the violet
(404.7nm), a bright violet line (435.8nm), green (546.1nm), and a yellow doublet
(577.0nm and 579.1nm). Make a table of the angular position of the telescope for each
of these lines. The yellow doublet lines are so close together that, unless you feel
confident that you have resolved them into two separate lines, it is better to regard them
as a single line at the average wavelength. The work should be done by at least two
students and the results averaged. Then do the same with a hydrogen discharge tube,
recording the position of the bright red line (656.3nm) and the blue line (486.1nm).
B. Mathematical Description of the Calibation
You now have six spectral lines that span most of the visible spectrum. Use the
pointplot function in MAPLE to graph this data and re-measure any points that look like
they do not lie on a smooth curve.
To use the prism spectrometer to measure the wavelength of unknown lines it is
necessary to fit the data to a formula. Use the least squares fit command in MAPLE to
fit the wavelengths to a polynomial in the angles. It is first necessary to convert to
decimal angles. It is suggested that instead of demanding a fit directly to the angle,
which is often a large number of degrees that varies only slightly over the visible range,
you first subtract from all angles the angular position of the green line. Then your
angular positions will be small positive and negative numbers. The fit will benefit greatly
in accuracy from this procedure. When using your formula you will have to remember to
3.3
always make this change to any measured angles.
Your formula should reproduce all of the wavelengths to an accuracy of 4nm or better.
Modify the fitting procedure or return to the angle calibration if this has not been
achieved.
C. Making Measurements
Now use the sodium vapor lamp and determine the wavelength of the bright yellow
lines. Then prepare the red beam from helium-neon laser for viewing by sending the
beam through a pair of crossed polarizers. These do not block all of the light since they
are not 100% efficient but the little light that goes through them both will usually be
dimmed sufficiently that it cannot cause damage to the eye. When using an especially
strong laser it may be necessary to use three polarizers. The way to check that no
damage can be done to the eye is to be sure that the beam emerging from the
polarizers does not cast a visible spot on the hand or on a screen. If it is too dim to be
seen in diffuse reflection it is too dim to damage the eye. Adjust the laser and/or
spectrometer until the dim red beam falls on the slit. Compare your results with the
known values: sodium 589.5nm, He-Ne laser 632.8nm.
3.4
Experiment 3 : PC Spectrometer
This device, manufactured by Ocean Optics, sends light through a fiber optic cable to
illuminate 600 lines of a diffraction grating. The resulting dispersed light passes through
a semiconductor photodetector which produces an electrical signal that is, within limits,
proportional to the light intensity. The grating and detector are mounted on a card
connected directly to the pc bus inside the computer housing.
A. The software is activated by clicking the OOI icon. The end of the fiber cable used as
a light detector is kept screwed into the black end of a rigid container when not in use. A
blue colored cylindrical screw driver is provided and it is a good idea to use this as a
housing to protect the end of the cable in all applications. The container has a number
of functions, including protecting the sensitive cable and providing a dust cover. Please
remember to store the cable in this container when it is not in use.
Fiber optic cables are glass structures that are easily damaged and cannot withstand
much mechanical loading. Never clamp such a cable tightly. Unscrew the cable from
the black end of the container and, keeping it inside the blue screwdriver, sample the
light from the overhead fixtures. You may lightly clamp the screwdriver to a lab stand for
support.
Take some time to familiarize yourself with the features of this spectrometer. In
particular, you should note the freeze-frame feature (camera icon), pixel width feature
for averaging (summation icon), integration time (integral icon), graph scale adjust (icon
with vertical and horizontal arrows) and peak locator (icon looks like a graph of a bellshaped curve with a colored vertical line running through the graph). The arrow icons
move the peak indicator display over the spectrum.
B. Take a spectrum of the mercury and sodium vapor lamps and the hydrogen
discharge tube. Compare your results to the published values of these wavelengths as
a check on the calibration of the instrument and note any discrepancies.
C. Next find the wavelength of a He-Ne laser using a polarization-damped beam. Do
not put an unfiltered laser beam directly into the cable.
D. Take at least five spectra of the variac-controlled light bulb at different intensities.
For each spectrum, note the variac setting and find the intensity at which the spectrum
is most luminous and also the intensities at 450nm, 550nm, and 650nm. Find the ratios
of blue/green, blue/red, and red/green. Plot the wavelength of maximum brightness vs
variac setting (use the pointsplot feature in MAPLE) and comment on regularities. Do
the same for the intensity ratios.
3.5
Spectral Lines
Niels Bohr explained spectral lines as due to the relaxation of excited atoms. There are only a
discrete number of stable orbits in which
bound atomic electrons can move about the
nucleus. When an atom absorbs energy from
its environment the internal state of motion of
the atom changes from its most relaxed state
(called the “ground state”) to one of its
excited states. These states are different for
different chemical elements but the same for
every atom of a given element1. It is common
to diagram the states of an atom using a
vertical energy scale with a horizontal line
segment drawn for each state. The figure
illustrates the energy level diagram for
hydrogen, the simplest atom.
An atom in an excited state will eventually relax into a state of lesser energy and release some of
its excess energy, often in the form of electromagnetic radiation. The energy radiated depends on
the difference between the energies of the initial and final atomic states. That is
(3.1)
energy radiated = energy of initial state - energy of final state Ei - Ef
The radiated energy appears as a pulse of electromagnetic radiation called a photon. The energy
of the photon is directly proportional to its frequency f
(3.2)
energy radiated = photon energy = h f
where h is a constant of nature called Planck’s constant, with the approximate value h = 6.626 ×
10-34 Js. Therefore, higher energy photons have larger frequencies (shorter wavelengths). The
energies of atomic states are very well defined, usually to within a part in 105 or less, so that the
frequencies (and therefore the wavelengths) of atomic radiations are correspondingly well
defined. The resulting sharp spectral lines are as close as unaided nature comes to providing
spectrally pure light.
Problem: The first excited state of neutral sodium occurs at an energy of 2.10eV. When electrons
in this state emit radiation and decay into the ground state, what wavelength radiation is formed?
1
Actually, there are slight differences in the spectra of atoms of the same element that
have different numbers of neutrons in the nucleus, i.e. different isotopes of the same element.
3.6
What color is the resulting illumination?
3.7