Download 7/06 Atomic Spectra ATOMIC SPECTRA About this labAfter the

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Atomic Spectra
ATOMIC SPECTRA
About this lab After the discoveries that matter was atomic, that atoms contained
charged constituents, and that there was a massive, charged nucleus (Rutherford), there
was a major mystery. A classical planetary model of light, negatively charged electrons
orbiting a heavy, positively charged nucleus under the influence of an attractive 1/ r 2
force law (just the form of point gravitational attraction) was easy to construct. But this
suffered from major stability conflict with observation: the electron should orbit into the
nucleus in a death spiral, emitting a continuous spectrum as it did so. In fact, atoms are
stable, and the light they emit is not continuous, but involves very characteristic
wavelengths and corresponding frequencies.
Bohr provided an ad hoc particle solution by postulating unmotivated rules which
explained the observed spectrum of hydrogen, de Broglie gave a rationale involving
wave character of the orbiting electron, and Schrodinger extended the wave picture into
three dimensions, with probabilistic interpretation of the meaning of the wave
amplitude.
Apparatus: spectrometer, spectral tubes, power supply, incandescent lamp.
Introduction
Figure 1
Bohr's schematic planetary model of a multi-electron atom. The
number of negative electrons equals the positive charge on the nucleus, so the atom in
neutral.
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Figure 2
Bohr's planetary model of neutral hydrogen atom, with orbit allowed
by successful, but ad hoc, rules.
1
2 Coulomb force law, it was known that a negative electron would orbit a
r
positive, heavy nucleus in planetary ellipses, just as do satellites under the influence of the
1
gravitational force. But, classically, any orbit should be possible, and the
2
r
accelerating, charged electron should emit a continuum of light wavelengths, very quickly
losing its energy and spiraling in to the nucleus. So the stability of the atom posed a
conundrum for classical physics.
From the
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Figure 3
Energy levels of the hydrogen atom, with allowed electron
“transitions” between more energetic (“higher, nupper ”) states and less energetic
(“lower, nlower “) states. The state energies are given (in electron volts) by
13.6
En= - 2
, where the integer n is the orbit quantum number. A single photon is
n
emitted, with frequency given by energy conservation:
hc
E photon = ( Eupper - E lower ) = hf =
(h = Planck's constant).

Note that the total electron energies shown are negative (the electron is “bound” to the
proton (nucleus)) and ( E upper - E lower ) is positive ( E lower is more negative than
E upper (more tightly bound)).
http://www.physics.northwestern.edu/vpl/atomic/hydrogen.html
The theory of the discrete spectral lines and structure of the atom was first developed by
Niels Bohr (1913). He postulated that the negative electron moves with discrete integer
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multiples of angular momentum. In consequence, the electron also has quantized orbital
level energies and radii, and this explained the discrete spectral lines.
It was later realized from the work of de Broglie (1924) that the electron moves in an orbit
around the positive nucleus as a wave, with wavelength inverse to linear momentum p:
 de Broglie =
h
.
p
The electron wave can “fit” around the nucleus only as a whole multiple of a wavelength the electron wave must constructively interfere with itself over the orbital path, and only
certain wavelengths qualify. Any other wavelengths result in destructive interference. This
constructive interference means that the angular momentum, and correspondingly the
energy and radius of the orbiting electron, are quantized, just as Bohr postulated. These
discoveries were foundation stones of quantum mechanics.
(There is a different, fixed, wavelength associated with any material particle, the Compton
h
wavelength  Compton = m
where m 0 is the rest mass. The Compton wavelength relates
0c
to the Heisenberg uncertainty in position arising due to the finite rest mass.)
Figure 4
A stable electron orbit de Broglie wave that reinforces itself
http://mutuslab.cs.uwindsor.ca/schurko/molspec/animations/bird_concordia/HydrogenSpect
rum_2.htm
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Using a grating spectroscope to separate the colors of light emitted from hot, glowing
hydrogen gas, you see bright emission lines and not a continuous spectrum (rainbow) of
colors. Observed (inverse) wavelengths of the lines are given by:
1
1 1
= 0.01097{ 2 - 2 } nanometers-1

n l nu
Equation 1
n
I
4
3
2
1
Figure 5
The Balmer series, containing photon energies in the visible range for
the human eye. Balmer transitions end on nl = 2.
The numerical constant, 0.01097 , is called the Rydberg constant and the n's are
“principal” quantum numbers. nl (lower level) is smaller than nu (upper level); both
n’s are integers equal to 1,2, 3... By trying various values for nu and nl , we find that
the only transitions we see with our eyes have nl = 2 and nu = 3,4,5,---. This set of
visible transitions with nl = 2 is known as the Balmer series. These are shown in the
figure above. Each transition down to a lower energy level (orbit) emits a photon of energy
equal to the difference between those of the upper and lower levels. Note that some Balmer
lines lie in the near-ultraviolet beyond the eye's sensitivity limit at 380 nm.
(Equation 1 is given by energy conservation, with Planck's expression for the quantization
of photon energy in terms of frequency f: E photon = hf
| E final |= | E initial | + hf = | E initial |+
hc

(E's are negative)
so
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−19
1 1
13.6 x 1.6 x 10
= ( E f - Ei ) =
 hc
hc
and E f are negative.)
(
1 1
- 2 ) meters-1 in mks units. (Recall that
2
n l nu
Ei
(The series of spectral lines involving electron transitions ending on nl = 1 are called the
Lyman series. These are too far in the ultraviolet for our sight, but are prominent
instrumentally and are seen strongly in stellar spectra.)
Procedure
Using a diffraction grating spectrometer, measure some of the wavelengths of the visible
members of the hydrogen spectrum Balmer series nl = 2) and compare the results with
the predictions of the Bohr model of the hydrogen atom. The diffraction grating equation
gives the wavelength  in terms of the measured deviation angle and the spacing d
1
between adjacent grating lines: d =
, in meters (mks unit).
# of grating lines per meter
Figure 6
grating.
Interference maxima of various “orders” produced by a diffraction
Diffracting grating maxima are given by the grating equation
m  = dsin(  ) where m is integral.
Equation 2
This implies that you may see more than one angle for a given wavelength or color
(multiple orders of m), as long as sin(θ ) < 1. (In this experiment, m is used in the grating
equation to avoid confusion with the orbital momentum integer, n).
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Figure 7 Hydrogen discharge light source with grating spectrometer
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Figure 8
A grating spectrometer. A lens at the entrance makes parallel the rays
diverging from a source slit. After diffraction by the grating , another lens refocuses
parallel rays diffracted at various angles onto corresponding portions of a focal plane.
The eyepiece is for adapting to the individual eye.
Since the light entering from the source is limited by a vertical slit, the image is linear:
a “line” spectrum, with various colors at different parts of the focal plane. You will
see the lines in first order (m = 1), and some, maybe, in second order (m = 2). Second
order of a given wavelength has the same color as first order. The grating equation,
with knowledge of the number of grating lines per meter and assumption as to order
number, permits conversion of the observed angle to the corresponding wavelength.
The essential elements of the spectrometer are:
* The slit entrance, aimed at the spectral lamp. The slit can be turned vertical
(parallel to the grating lines), and its width is adjustable, in general, (but leave yours
alone!). This shapes and limits the light beam entering the collimating lens.
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* A fixed diffraction grating. Most diffraction gratings for this experiment have 6000
lines per centimeter ==> 6 x 105 per meter. This implies that the slit separation
1
−6
meter = 1.667 x 10 meter = 1667 nanometers
distance is d =
5
6 x 10
*
A telescope tube with an eyepiece fitted with a cross hair for pointing. This
assembly rotates about the grating center. The angle with respect to the slit barrel
can be read to 0.1o with a vernier scale. (The Sargent-Welch spectrometers are
calibrated in wavelength-but for a different grating spacing than usually used.
Therefore, the spectrometer wavelength scale is not valid. You must use the
measured angle  (see below) and the integer order number m to calculate
wavelength λ from the grating equation (Eq.2)).
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Figure 9
Spectrometer table graduated in angle and wavelength.
wavelengths are valid only for a particular grating line spacing.
The
1. Hydrogen spectrum
a. First, pull out the telescope from the viewing end. Look through and adjust the eyepiece
to focus on the cross-hairs. The eyepiece slides in and out of its draw tube. Put the
telescope assembly back into the spectrometer. Be sure the eyepiece is focused on the
cross hairs. (If cross hairs are missing, you can later focus on a line image.)
b. Turn on the power supply that applies a high voltage to the tube containing hydrogen
gas.
5000 VOLTS: BE CAREFUL ABOUT
ELECTRIC SHOCKS.
c. Align the entire spectrometer in a straight line. Look through the eyepiece and put the
slit in the center of the field. Set θ = 0o on the base plate. This is the m = 0 maximum
which occurs at θ = 0° for all wavelengths; thus, you see a mix of all original colors.
You may need to rotate the entrance slit to get it upright and parallel with the grating
lines.
d. Increase θ by swinging the telescope part to the left, and locate the angular position of
the first (m = 1) three or four lines (red, green-blue, and two (?) violet) in the visible
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spectrum of hydrogen. Ignore the fainter lines, which are from contamination (water
and air).
e. If the cross-hairs cannot be observed, center the slit image in the telescope eyepiece and
average a few readings. Record the wavelengths of any other observed lines.
f. Compute the wavelength of each of the three (four?) lines from the grating equation and
give the differences from the wavelengths predicted from quantum theory (Eq.1) for
n l = 2 and nu = 3,4, --- . If there is sufficient intensity, measure the second order
angle (m = 2) to double check your measured λ's.
2. Atomic spectra of other elements
The spectrum of atomic hydrogen, an atom with just one electron, is simple and the energy
levels are given by the simple relation of Eq. 1. Other elements with many orbiting
electrons have more complicated atomic spectra; their electrons interact with each other ,as
well as with the dominant nuclear charge. Nevertheless, the spectral line pattern is unique
for each element.
You will be given spectral tubes of "unknown" elements, helium (He), neon (Ne), or
mercury (Hg), which you must identify. Measure the wavelengths of the lines in the
emission spectrum of each. Identify each element by referring to the list of wavelengths of
prominent spectral lines in the table below. Use your wavelength measurements, not chart
colors. Note that some lines will be brighter than others.
Observe also, qualitatively, the sodium (Na) yellow “doublet” line, in first and second
order.
Be careful when changing spectral tubes: they become hot. It
is best to hold them at the larger ends, which are cooler.
3. Absorption spectrum
An emission spectrum is caused by electrons “dropping” to lower atomic energy states;
electromagnetic energy in the form of photons of light is given off in each transition
“downwards”. The electrons got into the higher energy states by collisional excitation,
namely atomic collisions with other energetic free electrons.
Now, we are going to investigate the opposite effect. Imagine an electron in a low orbital
energy state, and along comes a photon of energy that the electron absorbs. The energy is
the correct amount to boost the electron into a higher energy state. The excited atom will
give up this energy very quickly in any number of ways: re-emit the same energy photon
but in a direction different than the original photon; emit two or more lower energy photons
as the electron "cascades" down through two or more energy levels or, before the atom can
emit a photon, interact with another electron or atom with de-excitation of the atom back to
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its original state. The net result is that photons of a particular energy are removed from a
beam of light. If we are observing a continuous spectrum (think of a rainbow) with a
spectroscope, we will see a zone of relative darkness, an absorption line, superposed on the
continuous bright wavelength spectrum. Remember that energy is not destroyed, just
converted to other wavelengths or even thermal energy.
The procedure is first to observe a continuous spectrum emitted by a tungsten filament
lamp. Then attach to the front end of the spectroscope a didymium filter that produces the
absorption spectrum. Determine the central wavelength of a few of the dark absorption
"lines" by measuring the angles corresponding to the left and right fringes of the dark
absorption band and averaging to estimate the center of the band.
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SPECTRAL LINE WAVELENGTHS
Wavelengths are in nanometers. The colors are approximate;
they should not be used to identify the elements.
Neon
489, 496 (blue-green),
534 (green),
622, 633, 638, 640, (orange-red)
585 (yellow)
651, 660, 693 (red)
Helium
447 (blue)
471 (turquoise)
492 (blue-green)
501 (green)
587 (yellow)
667(red)
Mercury
404 (violet)
435 (blue)
491 (green)
546 (green)
576 (yellow)
579 (yellow)
Sodium
568, 569 (green), 589, 590 (yellow), 615, 616 (red)
Figure 10
Emission spectra of some multi-electron elements
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Appendix 1
The Bohr Model
The total energy of an negative electron (charge -e) held in circular orbit by the electrostatic
attraction of the oppositely charged heavy nucleus with charge +Ze is
E = KE + PE =
E =−
kZe
2r
2
1
2 kZe
.
mv r
2
2
F = ma or
2
2
kZe mv
kZe
1
=
 KE =
=− PE and
2
r
2r
2
r
2
(negative because the negative PE is twice as big as the positive KE).
So, for classical physics, any total energy E and any r is possible.
Bohr's orbital angular momentum rule limited the coupled r and E:
h
L = mvr = n ℏ where n is integral and ℏ =
is Planck's blackbody constant h over
2
2π. Substituting this restriction leads to
2
rn = (
2
ℏ
n
)
and
2
mke Z
2 4
2
1 mk e Z
En= - (
) 2 n = 1, 2, 3, 4, --- . Substituting numerically,
2
ℏ2
n
2
E n =−13.606 (
Z
) eV where 1electron volt = 1.6 x 10−19 Joules .
n2
Energy is conserved in transition between upper (less bound) and lower (more tightly
bound) states by emission of a single photon of energy hf (note h , not ℏ :
E final = E initial + hf = E initial +
hc
so

1 1
13.6 x 1.6 x 10
= ( E f - Ei )=
 hc
hc
E i and E f are negative.)
−19
Z
2
(
1 1
- 2 ) meters-1 in mks units. (Recall that
2
nl nu
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How to Read a Vernier Scale
A vernier scale, shown below in the dashed box, is used to interpolate an extra digit of
accuracy. The position of the zero is used to read the scale to the accuracy of the drawn or
"ruled" lines. The extra vernier's digit will line up with the scale's ruled lines to indicate the
next digit of accuracy. Below, the vernier zero lies between 23 and 24. Notice that the
vernier's "6" lines up with a ruled line on the scale. This means the answer is 23.6.
Figure 11
Venier scale
Split Personalities: Wave and Particle
Bohr's quantization of atomic electron orbits, and de Broglie's more profound matter
wave description established wave/particle duality for matter, just as Planck and
Einstein had done earlier for the photon messenger particles of the electromagnetic
interaction.
This completion established Planck's tiny quantum h as the organizing
principle of our universe.
Bohr lived and worked in his native Copenhagen, which became a center for research and
for discussion of the interpretation of the quantum mechanical wave function. During
World War II, Bohr and his family fled occupied Denmark to Sweden in a fishing boat. He
later made his way to America, where he was very influential in the development of the
first nuclear bomb. A recent play, Copenhagen, examines the political and moral issues
involved in nuclear weapons development, in terms of an historical wartime meeting
between Niels Bohr and Werner Heisenberg.
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In 1913 de Broglie was awarded his Licence ès Sciences from the Sorbonne, but before his
career had progressed much further World War I broke out. During the War de Broglie
served in the army. He was attached to the wireless telegraphy section for the whole of the
war and served in the station at the Eiffel Tower. During these war years all his spare time
was spent thinking about technical problems.
Niels Henrik David Bohr
Born: 7 Oct 1885 in Copenhagen, Denmark
Died: 18 Nov 1962 in Copenhagen, Denmark
1922 Nobel Laureate in Physics
for his services in the investigation of the structure of atoms and of the radiation
emanating from them.
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Louis Victor Pierre Raymond duc de Broglie
Born: 15 Aug 1892 in Dieppe, France
Died: 19 March 1987 in Paris, France
PRINCE LOUIS-VICTOR DE BROGLIE
1929 Nobel Laureate in Physics
for his discovery of the wave nature of electrons.
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The Nobel Prize in Physics 1929
Presentation Speech by Professor C.W. Oseen, Chairman of the Nobel Committee for
Physics of the Royal Swedish Academy of Sciences
Your Majesty, Your Royal Highnesses, Ladies and Gentlemen.
The question as to the nature of light rays is one of the oldest problems in physics. In
the works of the ancient philosophers are to be found an indication and a rough
outline of two radically different concepts of this phenomenon. However, in a clear
and definite form they appear at the time when the foundations of physics were laid, a
time that bears the stamp of Newton's genius. One of these theories asserts that a light
ray is composed of small particles, which we may term corpuscles, which are
projected into space by light-emitting substances. The other states that light is a wave
motion of one type or another. The fact that these two theories, at this elementary
stage, are equally possible, is attributable to their explaining equally well the simplest
law governing a light ray, viz. conditions being undisturbed it propagates in a straight
line.
The 19th century sealed the victory of the wave theory. Those of us whose studies
coincide with that period have certainly all learned that light is a wave motion. This
conviction was based on the study of a series of phenomena which are readily
accounted for by the wave theory but which, on the other hand, cannot be explained
by the corpuscular theory. One of these phenomena is the diffraction undergone by a
light beam when it passes through a small hole in an opaque screen. Alongside the
diffracted ray there are alternate light and dark bands. This phenomenon has long
been considered a decisive proof of the wave theory. Furthermore, in the course of the
19th century a very large number of other, more complex, light phenomena had been
learnt of which all, without exception, were completely explainable by the wave
theory, while it appeared to be impossible to account for them on the basis of the
corpuscular theory. The correctness of the wave theory seemed definitely established.
The 19th century was also the period when atomic concepts have taken root into
physics. One of the greatest discoveries of the final decades of that century was the
discovery of the electron, the smallest negative charge of electricity occurring in the
free state.
Under the influence of these two currents of ideas the concept which 19th century
physics had of the universe was the following. The universe was divided into two
smaller worlds. One was the world of light, of waves; the other was the world of
matter, of atoms and electrons. The perceptible appearance of the universe was
conditioned by the interaction of these two worlds.
Our century taught us that besides the innumerable light phenomena which testify to
the truth of the wave theory, there are others which testify no less decisively to the
correctness of the corpuscular theory. A light ray has the property of liberating a
stream of electrons from a substance. The number of electrons liberated depends on
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the intensity of the ray. But the velocity with which the electrons leave the substance is
the same whether the light ray originates from the most powerful light source that can
be made, or whether it originates from the most distant fixed stars which are invisible
to the naked eye. In this case everything occurs as if the light ray were composed of
corpuscles which traversed the spaces of the universe unmodified. It thus seems that
light is at once a wave motion and a stream of corpuscles. Some of its properties are
explained by the former supposition, others by the second. Both must be true.
Louis de Broglie had the boldness to maintain that not all the properties of matter can
be explained by the theory that it consists of corpuscles. Apart from the numberless
phenomena which can be accounted for by this theory, there are others, according to
him, which can be explained only by assuming that matter is, by its nature, a wave
motion. At a time when no single known fact supported this theory, Louis de Broglie
asserted that a stream of electrons which passed through a very small hole in an
opaque screen must exhibit the same phenomena as a light ray under the same
conditions. It was not quite in this way that Louis de Broglie's experimental
investigation concerning his theory took place. Instead, the phenomena arising when
beams of electrons are reflected by crystalline surfaces, or when they penetrate thin
sheets, etc. were turned to account.
The experimental results obtained by these various methods have fully substantiated
Louis de Broglie's theory. It is thus a fact that matter has properties which can be
interpreted only by assuming that matter is of a wave nature. An aspect of the nature
of matter which is completely new and previously quite unsuspected has thus been
revealed to us.
Hence there are not two worlds, one of light and waves, one of matter and corpuscles.
There is only a single universe. Some of its properties can be accounted for by the
wave theory, others by the corpuscular theory.
In conclusion I would like to point out that what applies to matter applies also to
ourselves since, from a certain point of view, we are part of matter.
A well-known Swedish poem has as its opening words "My life is a wave". The poet
could also have expressed his thought by the words: "I am a wave". Had he done so,
his words would have contained a premonition of man's present deepest
understanding of the nature of matter.
Monsieur Louis de Broglie. When quite young you threw yourself into the
controversy raging round the most profound problem in physics. You had the
boldness to assert, without the support of any known fact, that matter had not only a
corpuscular nature, but also a wave nature. Experiment came later and established
the correctness of your view. You have covered in fresh glory a name already crowned
for centuries with honour. The Royal Academy of Sciences has sought to reward your
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discovery with the highest recompense of which it is capable. I would ask you to
receive from the hands of our King the Nobel Physics Prize for 1929.