Chapter 3
Atoms
– tiny wonders worth studying
Dalton's original atomic theory had faults, but the basic idea that materials consist of tiny natural units
is fundamentally correct and sound. To his credit, these natural units are widely accepted as atoms,
whose shape is not known. However, we generally assume them spherical. Evidences show their radii
being in the order of 10-10 m. For convenience, such a length is called an Angstrom, (symbol Å). The
unit nanometer (10–9 m, symbol nm) is used more often in modern literature. The atomic radii are in
the order of tenth of nanometers. For example, the atomic radii of potassium, iron and copper are
0.235, 0.116 and 0.117 nm respectively. Look at them another way. Some hundred millions of atoms
line up to give a length of just one cm. Atoms are very tiny indeed, but they are wonders to study.
As a comparison, the wavelength of visible light ranges
from 350 (red) to 700 (violet) nm, thousand times larger
than the atomic radii of atoms. Using visible light to see
atoms is impossible.
Three quarks for muster Mark, sure he
hasn't got much of a bark
J. Joyce
in Finnegan's Mark
Studying the invisible tiny atoms is a challenge.
Fortunately, driven by energy, these tiny wonders undergo
changes. The study of energy absorbed and emitted in the
form of electromagnetic radiation is called spectroscopy. Spectroscopic results revealed information
about the tiny wonders.
Since Newtonian physics cannot explain phenomena of individual atoms a new theory called quantum
mechanics is required for their explanation. The formulation of this new theory generated new
concepts. Thus, the study of these tiny wonders is rewarding because we acquire new tools to
understand and interpret atomic phenomena.
As we study the tiny wonders, new phenomena such as X-rays and radioactivity were discovered.
These discoveries in turn are tools for the study of atoms as well as for other applications. Using one of
these tools, Rutherford revealed the structure of atoms. The atoms consist of electrons and a very small
heavy core called atomic nucleus. Almost all the atomic mass is concentrated on the nucleus. The
space occupied by an atom is mostly due to electrons.
65
Atomic Spectroscopy
In general, the study of electromagnetic radiation is called spectroscopy. It is one of the oldest
branches of science, yet it is continually evolving as new techniques are developed. Results from
spectroscopic studies reveal not only secret of nature, its techniques have many applications.
Electromagnetic radiation is emitted from atoms, and atoms also absorb this form of energy. The study
of radiation emitted or absorbed from tiny atoms is called atomic spectroscopy, which involves light
in the regions of infrared, visible, ultraviolet, and X-ray.
Visible Light
A narrow band of electromagnetic radiation that stimulates the sensory centers of our eyes is called
visible light. Our eyes are excellent
detectors for them. Therefore,
White light from a solid
ancient people knew something
about visible light. They saw a beam
of white light dispersed into colored
beams through a prism. Newton also
Line spectrum from a gas
studied visible light. He combined
the colored light beams from one
prism into a white beam by using a
second prism.
Continuous or white
The color of a light beam dispersed
from the prism depends on its
wavelength or the associated
frequency. The wavelength increases
whereas the frequency decreases
from violet to red light.
spectrum
Emission or line
spectrum
Dark line or absorption
spectrum
You have learned that a light beam consists of photons. The intensity of a beam is proportional to the
number of photons. The distribution of intensity versus frequency (or wavelength) is a spectrum.
A white light consists of photons with all frequencies in the visible region, and it has a continuous
spectrum, with intensities varying continuously as a function of the frequency. An object with various
amounts of energies for light emission, such as a hot solid, emits a white light beam.
A combination of red, green and blue light beams also gives us a sense of a whit light, but such a light
consists of only three lines when dispersed by a prism. Such as spectrum, when plotted, consists of
three peaks. Such a spectrum is an example of a line spectrum, which in general consists of some
lines when dispersed by a prism. A hot gas, such as the flame of a fire emits a light beam with a lime
spectrum. A real hot gas consists of individual atoms. These atoms have certain extra amounts of
energy and they release them in the form of radiation. Thus, if we want to study the atomic spectrum
66
of an element, we usually study the light from a hot gas of the element. For example, when a salt
solution is introduced into a hot flame, you will see the characteristic yellow sodium D line.
A gas absorbs light of certain frequencies. Thus only some of the photons of a white light beam will be
absorbed when it passes through a gas. The spectrum will have some dark lines due to the absorption.
Such a distribution of intensity is called an absorption spectrum, or dark-line spectrum.
Spectroscopy studies radiation in the entire electromagnetic spectrum. Continuous, line and absorption
spectra are not limited to those appear in the visible region. They also apply to microwave, infrared,
ultraviolet, X-ray and gamma ray regions.
Skill Building Questions:
1. What is light? (see Electromagnetic Radiation in the Chapter on Energy)
2. What is a spectrum? What are continuous, line and absorption spectra?
3. What is white light? How can it be separated into its components according to frequencies or wavelengths?
Line Spectra of Atoms
Set Up for a Spectroscope
As mentioned earlier, light emitted by a hot gas has
a line spectrum. When a white light beam passes
through a gas, a dark-line spectrum is observed.

What is the significance of line spectra?
What applications can be made of the atomic
spectra?
Telescope
Bunsen
burner
In order to study the emission spectra, R.W.
Bunsen (1811-1899) and G.R. Kirchhoff (18241887) dispersed the light from a Bunsen burner. They observed the spectrum using a telescope
mounted on a rotating table. They recognized that each element, when burned in a Bunsen burner,
emit a unique spectrum. For example, all compounds containing sodium, Na, burned in a burner give a
bright yellow color. Compounds containing copper give a blue or green color depending on the
temperature.
Mercury lamps were used for road illuminations because they were bright. However, they cause a glare
to the eyes. Especially on highways, the glare causes temporary blindness to drivers, creating dangerous
situations. The yellow light from sodium lamps is soothing to the eyes and causes no glare. Thus, more
sodium lamps are used to illuminate the highways now. Sodium light bulbs contain sodium vapor.
W.H. Wollaston (1766-1828) first observed some black lines appearing in the continuous spectrum of
sunlight. For example, when a bean of white light passes through a gas containing sodium atoms, the
yellow light is absorbed. A dark line appears in the yellow region.
67
Gas of an element not only emits a unique line spectrum, it also gives rise to a unique absorption
spectrum. This was known during the early stages of science development. Thus, spectra serve as
fingerprints of elements, and they have been used to confirm the presence or absence of a certain
element in a sample. Thus, atomic emission spectroscopy and atomic absorption spectroscopy
have been used for chemical analysis.
During the search for chemical elements in the 18th century, there was no method for the confirmation
of a substance as an element. When a substance was first thought to be a chemical element, there was
no guarantee that it would not someday be decomposed into simpler substances. Spectroscopy was
intensely studied and the results are used for elemental confirmation.
Skill Building Questions:
1. How can spectroscopy help to confirm a substance as a chemical element?
2. What is the color of the flame when sodium ion is introduced to it? Why are sodium lamps used for highway
illumination? What advantages do they have over other lamps? (Get information from other source).
Line Spectra of Hydrogen
The visible spectra can easily be studied using the
spectrometer invented by Bunsen and Kirchhoff.
The hydrogen spectrum has been intensely studied,
and it consists of these lines: red, (wavelength 656.3
nm), green (486.1 nm), blue (443.0 nm), indigo (410.1
nm), and violet (396.9 nm). Early spectroscopists
asked these questions.

Is there any regularity among these lines?
What is the rule governing the regularity?
The Visible Spectrum of Hydrogen
wavelength in nm
656
152
68
486 434 410 397
206 230 243 252
wave number (/104 in m)
In 1885, a Swiss schoolmaster Johann J. Balmer (1825-1898) published a paper giving an empirical
relationship for the wavelength  of the prominent lines of the hydrogen spectrum as:
 = 364.56
n2
nm
n2 - 22
(Balmer series)
where n is a whole number, (n = 3 for the red, 4 for the green, 5 for the blue, 6 for the indigo, and 7
for the violet lines). Johannes R. Rydberg (1854-1919) of the University of Lund revised the Balmer
formula by taking the reciprocals of both sides. The reciprocal of wavelength (1/) is the number of
waves per unit length, and it is referred to as the wave number (). The revised formula is now
commonly expressed as:
1
1
)
(Revised Balmer series)
2 
2
n2
where R is the Rydberg constant (= 10973731.534 m-1), and n the same whole number given by
Balmer. In words, a plot of  against 1/n2 is a straight line.
=
1
= R(
At that time, other spectroscopists tempted to speculate that a series of lines represented by the next
formula existed,
= R(
1
1
)
2 1
n2
(Lyman series)
Indeed, such a series of lines had been detected and confirmed by Lyman, and these lines are known as
the Lyman series, whereas the series discovered by Balmer is called the Balmer series. The wave
numbers of the lines in the Lyman series are higher, their average photon energy 4 times higher than
that of the Balmer series. The Layman series was found in the ultraviolet region of the electromagnetic
spectrum. Paschen found a low frequency series in the infrared region that satisfy this formula:
= R(
1
2
3
-
1
n
2
)
(Paschen series)
Recall Max Planck’s assumption that photon energy is proportional to the frequency or the wave
number (see the Chapter on Energy),
E = h  =hc
where h is the Planck constant and c the velocity of light.
69
Planck's theory of light emission led to the
Energy Diagram of the Hydrogen Atom
development of a theory called quantum
mechanics, which suggests that the electron in an
5
n= 4
hydrogen atom can be at some definite energy
3
levels. The energy of a level, En, can be represented
Balmer series
1
n =2
by En,= – R ( 2 ) , where n is a whole number.
n
Note that a negative sign is given here so that it
agrees with the original formula. An electron with
Paschen series
En,= 0 corresponds to the energy of a free electron
(not associated with any atom). A free electron can
acquire any kinetic energy, and the energy states (or
levels) above En,= 0 form a continuous band. Once
the electron is trapped by a hydrogen nucleus, the
Lyman series
electron can only be at an allowable energy state, En,
n =1
with n being an integer. When n = 1, E1 has the
lowest possible value, and this state is called the
ground state. An energy diagram is shown here for
such a system. Energy levels for n = 1, 2, 3, … are represented by long horizontal lines.
For a hydrogen atom, the energy made available for emitting a photon from energy level n to ni are
thus given by
1
1
En - Eni = – R ( 2  2 ) .
n
ni
The arrows in the diagram indicate these transitions from one energy-level to a lower energy-level. The
transitions corresponding to ni = 1, 2, and 3 are the Lyman, Balmer and Paschen series respectively.
Since n can be any integer greater than ni,
many more series are expected if nature
1
1
   R( 2  2 ) ;
really follows this regular pattern. However,
n
ni
other series than the three mentioned above
have very long wavelengths and they are
unlikely observable. The three series
mentioned here is sufficient to make the point.
ni = 1 for Lyman series,
2 for Balmer series,
3 for Paschen series
Review Questions:
1. Express the Rydberg constant R in terms of the value (364.56) given by Balmer.
2. Calculate the four highest wave numbers for the four lines in each of the Layman series, the Balmer series, and the
Paschen series. Give the energies of the lines in eV units.
3. What is the mass equivalence in amu of the most energetic photon of the hydrogen spectrum?
70
4. Use the energy-level diagram to explain the absorption spectrum of hydrogen.
The Discovery of X-rays
During the period when J.J. Thomson experimented with cathode rays, so did many other scholars,
including W.C. Röntgen*. In one late afternoon, he walked between the cathode-ray tube and a
fluorescence screen. Unexpectedly, he saw a shadow of his skeleton on the screen. He became so
excited that he forgot to go home (upstairs in the same building) for dinner. His wife eventually came
to see what was the matter with him. When she arrived, he showed her the mysterious rays he just
discovered. He asked her to put her hand on top of a wrapped photographic plate, which was placed
near the cathode ray tube. After the cathode-ray tube was turned on for a while, his plate recorded an
image of her hand bones plus the ring on her finger. He sent a letter and the photograph to the
magazine Nature. His letter published in Nature (Jan. 23, 1896) proclaimed his discovery of X- rays. He
did not know what X-rays were.


What are the X-rays and how to study them?
What are their properties and applications?
Why and how are X-rays generated?
Can they be generated by other methods?
The X-ray photograph published by Röntgen
(Nature, Jan. 23, 1896) showing a ring on the 3rd
finger.
Despite his ignorance of the nature of X-rays,
Röntgen observed that X-rays penetrate paper,
wood, aluminum and flesh. He is the first Nobel
Prize winner (1901) in physics for this discovery.
Over the years, many argued that if Röntgen did
not proclaim his discovery someone else would
have, because X-rays are generated whenever
cathode rays are in operation. During the
operation, when high-energy electrons (cathode
rays) striking a metallic or fluorescence plate, Xrays are generated.
In today’s technologies, X-rays are generated on
TV tubes and computer monitors tubes.
Electrons are accelerated to some thousand volts before they strike the fluorescence screens. Stopping
the electrons by the screen produces fluorescence and generates X-rays. Bright and dark spots due to
Whilhelm Conrad Röntgen (1845-1923), Professor of physics at Würtzburg, was one of the scientists who
studied cathode rays. He was particularly interested in the fluorescence emitted from various target materials.
During his research, his wrapped photographic plates were spoiled after being left in his laboratory for several
days. Instead of avoiding or ignoring the problem, he intended to find out exactly what caused the spoilage by
repeating his practice. After reproduced observations, he suspected that the glass tube gave out a mysterious
kind of radiation that penetrated the black wrapping paper and spoiled his plates wrapped in it.
*
71
intensity of fluorescence form the images for us to see, but the X-rays generated are hazardous.
However, these tubes are engineered to reduce the X-ray emission to save levels.
Eventually, we have learned that X-rays are
electromagnetic radiation as light is. They form part
of the electromagnetic radiation spectrum, with
wavelengths in the order of 1 to 0.01 nm, compared
to 350 to 700 nm in the visible region. Energies of
these photons are in the range of 120–12000 eV
compared to1-3 eV for photons in the visible region.
Due to their very short wavelengths or high-energies,
properties of X-rays are very different from those of
visible light.
X-ray Generation by Cathode Rays
Filament and thermal electron emitter
Electron beam
1000 V
X-rays
The spectrum of X-rays generated depends on the
target material and on the energy of the electrons.
For example, when the accelerating voltage is low, the X-rays have a continuous spectrum with a range
of wavelengths, as we shall see shortly in the next paragraph.
A spectrum of X-rays, is usually a plot the number X-ray Spectra of Low and High Voltages
of photons (or intensity) against their energies.
Sketches of two such spectra are shown here, one
Number of
corresponding to low voltage electrons and one to
photons
High
high-energy electrons. There is a shift of energy as
voltage
well as intensity when the voltage varies. The
intensities increase and the peak with the highest
Low
intensity shifts to higher energy. The emission of Xvoltage
Photon energy
rays is similar to the emission of white radiation by a
hot solid. Both produce continuous spectra. X-rays
are high-energy ionizing photons. X-ray intensities
are measured by the same technologies as those used
to measure radioactivity or ionizing radiation, and their discussion will be given later in a chapter after
you have learned more about radioactivity.
Review Questions:
1. How are X-rays generated? What are white X-rays and characteristic X-rays?
2. Calculate the wave number and the frequency of the characteristic X-rays of copper. (1.17x1011 m–1 and
1.95x1018 Hz)

The energies, wavelengths, or frequencies of the X-ray photons are determined by their diffraction off
crystals. X-ray diffraction will be discussed in the next section.
72
Properties of X-rays and Crystals
Although many properties of X-rays such as their ability to penetrate flesh, wood, black paper etc. have
been measured, the real nature of X-ray was not clear. Here are some fundamental questions to start
with.

What are X-rays, particles or waves?
What experiment will show X-rays as particles and what experiment will show X-rays as waves?

If X-rays are particles, what are their masses?
If X-rays are waves, what are their wavelengths, and how to measure them?
In many aspects, X-rays behave like particles. They penetrate wood, paper, aluminum, and soft tissues,
propagating in a straight line when unhindered. X-rays are invisible to the naked eyes, but X-rays cause
fluorescence on materials such as zinc sulfide. The material absorbs the energy of the X-rays and gives
out fluorescence, which is visible.
As mentioned in Chapter 1, Newton rings
observed on soap bubbles or thin oil films
have been explained as due to interference of
light as waves. Interference of waves is a
phenomenon due to their diffraction, which
is used to test wave properties.
D iffraction of X-ray W aves by Crystal Planes
X-ray
waves
A diffraction grating consists of a regular
two- or three-dimensional array of objects or
openings that scatter light according to its
wavelength. The distance must be
comparable with the wavelength of the light.
In 1912, von Laue* reasoned that distances
between atoms in crystals would be similar to
the wavelength of X-rays. Consequently, his
students Friedrich and Knipping subjected a
crystal of zinc sulfide, ZnS, to a beam of Xrays and took a photograph of the beam. The image consisted of several poorly resolved spots,
indicating that diffraction had occurred. The experiment showed that X-rays are indeed waves. Laue's
reasoning was excellent, and he was awarded the Nobel Prize for physics in 1914.
Max von Laue (1879-1950) of Zurich was awarded the Nobel Prize in 1914. William Henry Bragg (1862-1942)
and his son William Lawrence Bragg (1890-1971) shared the Nobel prize in 1915.
*
73
All leading scholars investigated X-ray diffraction
after its discovery. They used various crystals. The
nicely formed sodium chloride (table salt) crystals
were used in many experiments. W. H. Bragg (18621942) and his son W. L. Bragg (1890-1971) studied
X-ray diffraction patterns from sodium chloride,
and they deducted the crystal structure of sodium
chloride. A crystal structure refers to the
arrangement of atoms or ions in the crystal. One
layer of the arrangement of chloride (large) and
sodium (small) ions is shown here. In this structure,
every positive ion is surrounded by six negative ions,
and vice versa.
The Crystal Structure of Table Salt, NaCl
Only one layer is shown. The crystals consists
of many layers stacked on top of each other.
They further gave the equation of diffraction
2 d sin  = ,
where d is the distance between crystal planes,  is the angle of diffraction and  is the wavelength. Xray diffraction experiments not only established the wave properties of X-rays, they allowed the
measurements of wavelengths, since the distance from crystal planes can be calculated from density
measurements with the help of Avogadro’s number. The discovery of X-ray diffraction gave a
powerful technique for the study of crystal and molecular structures at the atomic scale.
Using X-ray diffraction, we now know that
Tetrahedral Bonding in Diamond, Silicon,
semiconductor materials such as germanium, silicon,
Zinc sulfide, Gallium Arsenide etc.
diamond, and the binary compounds cadmium
sulfide, gallium arsenide, zinc sulfide etc. all have
tetrahedral bonds around each atom in their crystal
structures. These are essential materials not only for
the computer industry, they also play important parts
in nuclear technology. For example, as we shall see in
later chapters, they are used as detectors for
radioactivity, cosmic rays, and gamma rays. X-ray
diffraction is an important technique not only to
determine semiconductor structures, but also their
orientation and crystal morphology.
X-ray diffraction has played an important role in the pharmacological development of "drugs" that
have so greatly influenced the modern practice of medicine. However the greatest triumph of
crystallography for modern medicine was the (1962) determination of the structure of DNA by Francis
Harry Compton Crick (1916-) and James Dewey Watson (1928-). This, followed by the determination
of the structures of proteins, has lead to the unraveling of the genetic code and the possible recognition
of the causes of bodily malfunction that result from defects therein. These results lead us to understand
the genetic effects of radiation.
74
Skill Building Questions:
1. Table salt has a density of 2.165 g/cm3. If a cubic unit contains 4 Na and 4 Cl atoms, what is the edge length of
this cubic unit? (Atomic weights of Na 22.99, Cl 35.45, Arvogadro’s number 6.0221 x 1023. If the
cubic unit has edge length of a, then density = 4 x (22.99 + 35.45) / (6.0221x1023 a3). Solving this
equation gives a = 0.564 nm. This problem illustrates that if the density is measured accurately, the
distances between planes can be evaluated.
2. The distance between the planes of NaCl crystals is 0.282 nm. The Bragg equation for X-ray diffraction is
2 d sin  = ,
where d = 0.282 nm, and  = 0.1542 nm if the characteristic X-ray of copper is used. Evaluate the angle of
diffraction, . ( = 15.87 degrees) This question illustrates the relationship between the angle of
diffraction and the wavelength of X-ray.
3. What is the angle if the X-ray of the copper K line ( = 0.139 nm) is used for the same plane of the previous
question? ( = 14.27 degrees, slightly less than 15.87 degrees)
4. Why is diffraction a test for the wave properties of X-rays? Further reading is expected to answer this
question, but you may have learned this in a general physics course.
The Moseley’s Law
When the accelerating voltages reach 20,000 V
or more in the cathode ray tube, some very
intense lines with photon energies very specific
of the target material appear. Investigation of
the characteristic X-rays became interesting.

Why are the photon energies or wavelengths
specific of the target material?

Is there any relationship between the
wavelength and the atomic weight?
Why if so?
What else has a relationship with the
wavelength of characteristic X-rays if not
atomic weight?
Target Material Dependent Lines of
X–rays.
Intensity
Energy h v
For example, when the target material is copper, the most intense line has a wavelength of 0.154 nm,
and the second most intense line has a wavelength of 0.139 nm. X-rays in these intense lines are called
characteristic X-rays, and their intensities are much higher than those of white (continuous) X-rays.
The characteristic X-rays and the white X-rays apparently are generated by different mechanisms, the
former specific to the target atoms, whereas the latter due to some randomness of the incoming fastmoving electrons.
75
Henry Gwyn-Jeffreys Moseley (1887-1915) used various metals as the target in his X-ray tubes, and
measured the wavelengths of the most intense (characteristic) lines. He noticed that frequencies of
characteristic lines increase with the increase of the atomic weights of the target metals. He plotted the
square root of the frequencies against the order of the elements in the periodic table, and got a straight
line. This is known as Moseley’s law.
Plot of Moseley’s Law
 /109
3.0
2.0
Atomic No.
1.0
25
The wavelengths and frequencies of
some familiar elements are given
here for your reference, and you may
plot the square root of the
frequencies against the atomic
number yourself as an exercise.
Moseley’s law not only provided
evidence for the confirmation of
substances as chemical elements; it
predicted missing elements between
Mo and Ru, Nd and Sm, and W and
Os due to gaps in his plot. X-ray
frequencies of elements also
provided information on the
ordering of the elements in the
periodic table. This was particularly
important in those days. Moseley’s
law was able to correct the positions
of Ni and Co in the periodic table.
Cobalt (atomic weight 58.9) should
be placed before nickel (58.7),
contrary to the arrangement
according to their atomic weights.
Moseley's plot showed that atomic
30
35
40
45
50
55
Wavelengths and Frequencies of Charactristic
Lines of Some Elements
Element
Wavelength
 in nm
Frequency,  (c/)
/(1018 s)
23
V
0.2503
1.199
24
Cr
0.2289
1.310
25
Mn
0.2102
1.427
26
Fe
0.1936
1.550
27
Co
0.1789
1.677
28
Ni
0.1657
1.810
29
Cu
0.1541
1.947
30
Zn
0.1435
2.090
42
Mo
0.0746
4.021
47
Ag
0.0559
5.363
79
Au
0.0180
16.650
Atomic
No.
76
weights are not reliable for ordering elements, and there is a need for an atomic number to place
elements on periodic tables. Atomic numbers were thought to be the numbers of electrons in the
elements. It also implied that there were equal numbers of positive charges. This concept was
key to the interpretation of the alpha-scattering experiment by Rutherford to be discussed later.
X-ray discovery impacts science development and X-rays are applied in medicine in many ways.
Review Questions:
3. Plot the square roots of the frequencies (or wave numbers) of the characteristic X-rays against the atomic number for
elements given in the table above to check Moseley’s law. What kind of curve will you get if you plot the frequencies
against the square of atomic number Z?
4. How did the Moseley's law predicted the existence of chemical elements unknown at his time?
How did Mendeleyev arrange the elements on the periodic table? Why was there a need for the atomic numbers?
Energy Levels of electrons in atoms
The emission spectra of hot hydrogen gas have been studied in detail and you have seen an energy
level diagram to explain the Lyman and Balmer series. Each spectral line corresponds to a transition
between energy levels represented by quantum numbers nf to nI .

Can the energy-level diagram of hydrogen atoms be generalized to all elements?
How are energy-level diagrams of elements different from each other?

Is the emission of characteristic X-rays due to transition of energy levels in a way similar to the
emission of spectral lines of hydrogen atoms?

What do Moseley’s law and the Rydberg’s formula suggest about the energy levels of electrons in
various elements?
The study of the hydrogen spectrum has established the energy of hydrogen atom being
En, = – R (
1
),
n2
where R is the Rydberg constant. Each n corresponding to an energy level. A generalization from the
hydrogen atom suggests that all elements have energy levels, but their energies are different. Rydberg
formula and Moseley’s law suggest that the values of R for other elements should be proportional to
the square of the atomic number, i.e. Z2. Electron transitions similar to those of the Lyman and Balmer
series in hydrogen lead to the emission of the characteristic X-rays. Usually, one of them is very
intense. Thus, energies for elements with atomic number Z should be proportional to Z2.
Actually, quantum mechanical results give the energy levels of an element as
77
2 2 Z eff m e 4
2
En = - (
h
2
1
)(
n
2
) ,
where Zeff is the effective atomic number; m is the
mass of the electron; e is the charge of the electron,
c is the velocity of light, and h is the Planck
constant. The effective atomic number Zeff is slightly
different from the atomic number Z, but we shall
not be critical about the precision at this time. The
transition between energy levels results in the
emission of the characteristic X-rays. A transition
from energy level with quantum number n = 2 to n
= 1 has an energy
3 2 Z eff m e 4
L (n=2)
electron
Characteristic X-ray
K (n=1)
2
E = (
2 h2
) .
Since E = h c , the wave number  of the X-rays for the transitions from quantum number nf to ni
can be represented by
2 2 Z eff m e 4
2
=– (
ch
3
)(
1
nf
2
-
1
ni
2
).
Quantum mechanics expressed the Rydberg constant in all known physical constants. It also
legitimized Moseley's law. From quantum mechanical point of view, fast moving electrons knock
atomic electrons with quantum number
n = 1 out, and when a higher-energy electron fills this position, it sheds the energy by releasing a
photon.
Skill Building Questions:
1. What is the frequency, wavelength, and wave number of the characteristic “X-ray” of hydrogen if Moseley’s law
applies to hydrogen? Is the wavelength really in the X-ray region?
2. How do atoms of metals provide energy to produce the characteristic X-ray photons?
78
Structures of Atoms
Discoveries of electrons, X-rays, and radioactivity around 1896 started the atomic age. For several
decades, scholars studied the tiny wonders of atoms for their structures, compositions, energy states,
sizes, and properties. The intense studies resulted in more discoveries, which had a great impact on
science, technology, and our lives. Furthermore, the discovery of radioactivity gave scholars more tools
to investigate not only atoms but also the much smaller atomic nuclei.
The Discovery of
Radioactivity
Becquerel’s Experiments Leading to the Discovery
of Radioactivity
After having learned Röntgen’s discovery
of X-rays, H. Becquerel* tried to see if
X-rays were emitted among the
fluorescence from uranium salts. He
further subjected his sample of uranyl
sulfate, K2UO2(SO4)2•2H2O, to sun light
hoping that his sample will collect the
solar energy for the release of
fluorescence. To his surprise, he found the
fluorescence persisted after the sample
was removed from the sun light. In his
first article reporting the phenomenon
(February 24, 1896), he stated that he
wrapped the silver bromide photographic
plate in two sheets of very heavy black
paper so that the plate did not fog on a
day's exposure to sunlight. A lamella of
uranium-potassium double salt was placed
above the paper on the outside and the
Uranium
salt
Ag Br Photographic plate
wrapped in black paper.
Image of uranium salt on plate
Henri Becquerel (1852-1908) inherited an interest in fluorescence material from his grandfather and his father
(Romer, 1964). His father Edmund Becquerel (1820-1891), a physicist who suggested the use of solid spectra
for temperature measurements, studied uranium salts for fluorescence properties. Henri Becquerel prepared
potassium uranyl sulfate, K2UO2(SO4)2•2H2O for the same purpose, and its use led him to the discovery of
radioactivity. In a recent publication, Ferradini and Bensasson revealed a different story about Henri Becquerel's
discovery. After having learned the discovery of X-rays, H. Becquerel planned an off-beat experiment; using
photographic emulsions, he tried to see if exposing the uranium salt to sunlight could produce X-rays. The
February sky of 1896 was stubbornly gray after he got the salt ready. He stored the emulsion in a drawer on top
of the wrapped photographic plates to wait for the sunny day. Four days later in the dark drawer, the
photographic plate had been sensitized and showed an imprint of the uranium salt emulsion. The uranium
emitted a mysterious radiation. Scientific publications often hide the non-technical facts, and it is conceivable
that the story was true.
*
79
whole was exposed to the sun for several hours. When the photographic plate was later developed, the
black silhouette of the double salt lamella appeared on the negative photographic plate. These
experiments have been repeated by placing a coin or a sheet of metal pierced with an open work design
between the salt disks and the paper. The images of these objects can be seen appearing on the
negative photographic plates. Thus, Becquerel concluded that the salt disk of fluorescence material
emitted radiation that penetrated black paper and reduced the silver bromide.
Becquerel found fluorescence also penetrated wood, glass and other material, i.e., it had the penetrating
power of the X-rays. Furthermore, his fluorescence persisted for days even when kept in the dark. A week
later, he published another paper reporting that other uranyl salts also emitted the same kind of
radiation. Becquerel prepared some uranyl compounds in the dark, and protected them from ever
exposed to light, but he found them emitting the same kind of radiation. He found the intensity
proportional to uranium content. Although he continued this study for several years, he only
concluded that these radiations, whose effects possess a strong analogy with the effects
produced by the X-rays studied by Lenard and Rontgen, might be invisible radiations emitted
by fluorescence, whose duration of persistence might be infinite. He further found that this
radiation discharged charged electroscope.
Pierre Curie and Marie Sklodowska Curie*, studying along a similar path, revealed that uranium rays
were an atomic phenomenon characteristic of the element, and not related to its physical and chemical
state. They introduced the term radioactivity for the phenomenon. Radioactivity is different from Xrays; the two kinds of radiation are generated by different methods.
At about the same time, but independently, Marie Curie and Gerhard Carl Schmidt, found that
compounds of thorium also emit similar rays. As she began to study minerals, she found the rays
emitted by pitchblende very strong and intense. Some ores of uranium were found to be more
radioactive than pure uranium or the chemically “synthetic ores” from uranium. These discoveries
were difficult to explain at that time, and the difficulty was a challenge that kept her research interest
on radioactivity. Marie Curie received the Nobel Prize for chemistry in 1911 for having discovered,
isolated, and identified the element radium isolated from pitchblende.
The Curie's daughter Irene also continued work on radioactivity and X-rays. She later married Marie's
assistant Frederic Juliot, and their joint effort has made X-rays an important tool for diagnoses. The
couple received the Nobel Prize for chemistry in 1935 for their success in the synthesis of new
radioactive elements.
Skill building Questions:
1. What is radioactivity?
2. What are the rays from uranium and thorium slats? Are they particles or waves? How many types are there?
The answer to question 2 requires much more research. It is posted for you to focus a strategy to get the
answer. A brief note is provided here to describe a modern view on radioactivity.
Pierre Curie (1859-1906), Marie Sklodowska Curie* (1867-1934), and H. Becquerel shared the Nobel Prize for
physics in 1903 for their discoveries of these new types of "rays".
*
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We now know that uranium is radioactive and it emits alpha particles. The products after alpha emission are
still radioactive, emitting beta and gamma rays. Thus, uranium salts consist of a range of atoms or elements
that are unstable, and they give out gamma rays that are similar to X-rays in nature, but have still shorter
wavelengths. X-rays and gamma rays penetrate materials made up of light elements such as hydrogen (H),
carbon (C), oxygen (O) and nitrogen (N). Light metals such as beryllium (Be), magnesium (Mg) and
aluminum (Al) have low stopping power for X-rays and gamma rays. The slightly more heavy elements
such as calcium (Ca) and phosphorus (P) present in the bones curbs the penetration of these rays better
than the flesh, which consists of light elements of H, C, N, and O.
Alpha, Beta, and Gamma Rays
After their discovery, radioactive rays were
intensely studied.

Bending of   and  rays by an Electric Field.
What are the radioactive rays, i.e. what are their
properties?
Are they particles or waves?
What are the compositions of radioactive rays?



Pierre Curie concentrated his study on the physical
properties of radioactivity from uranium and
thorium. He subjected radioactive rays to the
influence of electric and magnetic fields and found
them consisting of varying amount of three types.
Rutherford, working in Thomson’s lab, also
studied radioactive rays. Using metal foils as
absorbers, Rutherford also found three
components in the radioactive rays with different penetrating power. Curie and Rutherford called the
least penetrating and positively charged rays alpha (), the medium penetrating and negatively charged
rays beta (), and the most penetrating and neutral rays gamma (). They published these findings
before they have identified what   and  rays were. Concepts had yet to be developed, and
experiments had yet to be designed and performed in order to identify these three types of rays.
It took much more study to learn that alpha, , rays consists of heavy particles identical to the nuclei of
helium (He) atoms. Rutherford and his student Royds* allowed alpha particles to be defused through a
thin glass wall to an evacuated glass tube, in which they later detected the presence of helium from its
emission (line) spectrum. They concluded that alpha, , particles were indeed helium ions, in 1907.
Studies also showed that beta, , particles, are high-speed electrons emitted from atomic nuclei
whereas gamma, , rays are high-energy photons with wavelengths shorter than those of

J.J. Thomson and others found that X-rays causes the air to ionize and the ions produced discharged the
electroscope. This technique was soon applied to study radioactivity. Using the electroscope to measure the
intensity of radiation is more sensitive than using the photoelectric plates. Curie's and Rutherford employed this
technique and developed a more accurate electrometer for measuring the ionization.
* Rutherford and Thomas D. Royds received the Nobel Prize for chemistry in 1908.
81
X-rays. Alpha particles can be stopped by a thick aluminum foil, but beta rays require 100 times the
thickness to stop. The intensity of gamma rays falls off exponentially, and zero intensity can only be
achieved with very thick absorber. The ability to absorb these rays increases with the atomic weights of
material in the stopping medium.
Skill Developing Questions:
1. What is present in radioactive rays? What evidence showed that the alpha particles were helium ions?
2. How can you show that the beta particles are high-speed electrons? (A video clip showing the identification of
the three radioactive rays will be shown during the lecture.)
3. What are gamma rays? Do they have wave or particle properties?
Probing the Structures of Atoms – Rutherford's alpha scattering
experiment
Having identified the radioactive rays, the big puzzle to solve was the structure of the atom.
Experimental evidence from radioactivity studies showed that all atoms had positive charges to counter
balance the negative charges of electrons.

How are the positive and negative charges distributed in an atom?

How are the masses of atoms distributed?
The structures of atoms had yet to be explored prior to 1911. No one knows how the negative
electrons and positive charges were distributed in an atom. Some people believed that electrons were
distributed in an atom similar to seeds in a watermelon, with positive and negative charges almost
evenly distributed throughout the entire body.
In 1904, a Japanese physicist proposed an atomic model with electrons revolving about a central
nucleus. The proposal was not taken seriously, because classical theory about electrons would indicate
that such a model would not be stable. Since Rutherford understood alpha particles well, he and his
students began their study of the interactions of alpha particles with thin plates and foils hoping to get
some answers to the above questions.
82
A beam of fast moving alpha particles usually
Interpretation of Rutherford's alpha
produces a sharp image on a photographic plate.
scattering experiment
In 1911, Rutherford and his student Hans Geiger
(1881-1945) observed a diffuse image when a beam
of alpha particles was blocked by a thin layer of
mica plate. They concluded that the alpha particles
must be deflected through small angles as they pass
close to the atoms of the mica. Rutherford's
calculation showed that the ability to deflect fast
moving alpha particles must come from very
concentrated positive charges in the atoms. In view
that mica consists of light elements, this was an
Most alpha particles are unaffected,
amazing conclusion. He further suggested to
few deviated by large angles.
Geiger and another student, Ernest Marsden, to try
the experiment using a thin gold foil. Gold (at. wt.
197) is a heavy element, and he anticipated alpha
particles to be scattered backward, i.e., bending more than 90o from their paths. To their astonishment,
a few alpha particles in every 10,000 did scatter backward. They concluded that all positive charges of
a gold atom are concentrated in very small heavy nucleus with radius 100,000 smaller than that
of an atom. They further concluded that all the mass of an atom is concentrated in the
nucleus, which is very dense, and that the electrons around the nucleus occupy most of the
atomic volume. This is known as the Rutherford atom. A graphic interpretation of the alpha
scattering experiment is shown here. Only when an alpha particle passes the vicinity of a nucleus will it
be scattered by a large angle from its path.
The film “Rutherford Alpha Scattering Experiment” will be shown during the lecture, and you should
watch it.
Skill Building Questions:
1. Describe the Rutherford alpha scattering experiment. What did he and his students observe, and what conclusions did
they give?
2. What is the impact of Rutherford’s conclusions on the structures of atoms? How did Rutherford’s conclusions changed
your view of the structure of atoms?
The Bohr Atom – a tiny solar system
Rutherford, Geiger and Marsden's alpha scattering experiments concluded that all positive charges and
most of the mass are concentrated in very small heavy nucleus, and the electrons around the nucleus
occupy most of the atomic volume. They redefined the atom. However, classical electrodynamics
suggested that electrons orbiting around the nucleus would not be stable. Problems regarding the
atomic structure remain.
83

How can Rutherford atom be stable?
Do the electrons revolve around the atom? How can such a system be stable?
Niels Bohr considered the electrons revolving around the atom, and proposed a condition to achieve
the stability. He borrowed an idea from Max Planck, and assumed that the hydrogen atom would be
h
stable if the angular momentum of the electrons around the nucleus is a multiple of ( /2).
The angular momentum is the product of mass, m, velocity, v, and the radius of the orbit, r (m v r).
Thus,
h
m v r = /2.
He further assumed that the Coulombic force and the centrifugal force are equal for the electron,
Z e2
mv2
,

r
4o r 2
Energy States of an Electron in the H Atom
where Z (=1) is the atomic number, e
(=1.60217733x10-19 C/e) is the electric charge of
the electron, and o (8.85419x10–12 C2 N–1 m–2) is
the permittivity constant. From these two
equations, the following results can be derived.
However, we avoid mathematical manipulations in
this course and the derivation is left for those who
are interested in it.
-0.85 eV
-1.5 eV
-3.4 eV
Free electron
-Hau/2n2
The radius of the atom r is
n 2 o h 2
r=
m Z  e2
-13.6 eV
For Z = 1, and n = 1, the smallest radius is called
the Bohr radius, ao = 0.0530 nm.
 h2
ao = o 2
me
The sum of kinetic energy and potential energy is the total energy of the electron,
Z2
e2
Z e2
1
2
En = m v 
= 2
.
2
4 o r
2n 4o ao

Niels Bohr (1885-1962), Danish physicist, received the Nobel Prize for physics in 1922 For his work on the
electron energy levels of hydrogen. The value (h/2) is known as the unit of angular momentum, where h is the
Planck constant.
84
The quantity
e2
(= 4.3598x10–18 J = 27.199o eV) is a natural atomic energy unit called hartree
4 o a o
Hau. Thus, in terms of Hau,
En = 
Z2
Hau
2n 2
The energy states of the electron in a hydrogen atom are - 13.6, - 3.4, - 1.5, - 0.85, …eV, and an energy
level diagram for the hydrogen is shown here. With his assumption, Bohr has given a theoretical base
for the energy level diagram that explains the Lyman, Balmer, and Paschen Series.
Using the Planck's formula, (E = h v = h  c), it can be shown that R = Hau/2hc (= 10973862 m–1) is
the Rydberg constant in the equation given earlier for the transition from state ni to nf:
1
1
 = – Z2 R ( 2  2 )
ni
nf
The Rydberg constant R (so calculated is in excellent agreement with the observed value, and the
hydrogen atomic radius of ao (= 0.0530 nm) agrees with modern quantum mechanical results.
However, atomic radii calculated for n > 1 are too large and unrealistic. Quantum mechanical results
obtained after Bohr are more realistic and useful.
The Bohr results suggest that the energy states are proportional to the square of the atomic number,
(Z2), in agreement with the Moseley's law. Thus, transitions between states in metals may be
responsible for characteristic X-ray emissions. The wave-numbers (or frequencies) of the characteristic
X-rays are proportional to Z2. The plot of wave-number versus Z2 is a straight line. In the exercise, you
had plotted the square-root of the wave number
versus Z.
Need a New Perception of the Atom
The solar-system Bohr atom is the most common
perception of atoms. Many pictures depict atoms this
way. However, this perception hinders further
discussion of particles and energy. Nevertheless, the
Bohr atom is an important step in the development
of quantum mechanics.
Skill Building Questions:
1. Describe the Bohr atom? What did Bohr assume in order
to explain the line spectra of the hydrogen atom and what
results did he get?
2. Confirm the Bohr radius, the atomic energy unit hartree, and the Rydberg constant by calculation using the formulas
given in this section.
85
A Quantum Mechanical View of Atoms
Before John Dalton and Max Plank introduced atoms
and photons as the natural units for material and light
respectively, everyone thought material and energy as
continuous entities. Now, you know natural units do
exist for material and energy. These are discrete rather
than continuous entities. Furthermore, Einstein's theory
of relativity suggests that energy and material are one,
because they inter-convert.

How are waves related to particles?
Is there a theory to make waves equivalent to
particles as does Einstein's formula making matter
equivalent to energy?
Continuous versus Quantized States
A discrete
material world
A system (an electron, an atom, a molecule, a crystal or even a hunk of material) needs room to store
energy. The available rooms for energy storage are called energy states or simply states, because a room
is not a 3-dimensional space. At each state, there are certain characteristics. In a bulk material, the states
are very close, and they form a continuous band. In small systems, the energy states are well separated.
This condition is known as quantizition, and energy states in such systems are quantized. Whether a
system is continuous or discrete depends on how close you examine it. A large quantity of material
appears to be continuous in that we can take any quantity from it. However, when there are only a few
atoms, we begin to see the discrete nature of material, because we cannot remove less than a molecule
or atom from it.
De Broglie considered Planck’s photons as particles of waves because light was waves. He intuitively
thought that waves are equivalent to particles. Depending on how he examined a system, a particle
might appear as a wave and vice versa. At his time, no wave equivalence was ever suggested for
particles. This rich prince was determined to develop a theory to make particle and wave equivalent.
His research was purely theoretical nature, and he derived of a formula to show that a particle with
mass m moving with a velocity v has a wavelength  by the formula
 = h / m v.
This formula has made a particle equivalent to a wave. This formula is less popular compared to
Einstein's equation of E = m c 2, but both formulas bridges between two very different forms of matter
or energy. This formula unites the particle-wave duality of matter and energy.
De Broglie theorized the equivalence of waves and particles in motion just as Einstein theorized the
equivalence of matter and energy.
86
Positions of moving particles are not important,
according to Heisenberg’s uncertainty principle, which
suggests that positions cannot be measured exactly if
we also measure the velocity simultaneously.
Traveling Waves
A moving particle not confined by any field can be at
any speed and its kinetic energy forms a continuous
band, according to Newtonian physics. Its
wavelength can be of any value. Bohr suggested that
the angular momentum of electron in a hydrogen
atom is quantized (have certain values), its
wavelength is limited to some discrete values.
Standing Waves
Schrodinger treated particles as waves. A traveling
wave can have any wavelength, and this is equivalent
to a particle under no influence of any force. A
standing wave such as the vibration of a (violin)
string is a stationary wave because it is confined to a
certain space. Only waves with certain
wavelengths can exist in standing waves. Wave
motions on strings are easy to depict and visualize, but three dimensional wave motions are difficult to
illustrate. However, we all have some experience with sound waves confined in a cavity. The right
sound resonates in a cavity for a long time before it dies off, and sound waves occupy the whole
volume of the cavity.
Wave mechanics treated electrons in an atom as
standing waves. An electron in an atom is a standing
wave confined by the field of the nucleus. The state
of a wave refers to the energy, distribution of
amplitudes (activity), and characteristics of the wave.
Energy put into or extracted from a wave (by a
photon for example) causes the state of the electron
(wave) to change. Emission or absorption of a
photon changes the state. When enough energy is
acquired, an electron leaves the atom all together,
showing more particle property. Such a process is
called ionization.
Atomic Orbitals
4f– – – – – – –
4d– – – – –
4p– – –
4s–
3d– – – – –
3p– – –
3s–
2s– 2p– – –
1s–
In wave mechanics, states of an electron are
represented by three quantum numbers: n, l and m. A state is also called an atomic orbital, which is
characterized by a set of three quantum numbers. However, only n and l affect the energy and m is
important only when a magnetic field is present. Traditionally, symbols s, p, d, f, and g are used to
represent the states when l = 0, 1, 2, 3, and 4 respectively. The quantum number n is placed directly
before any one of these symbols. Some atomic orbitals are given in the textbox here.
87
An electron not belonging to an atom is a free electron. It moves as a whole like a particle when
driven by its kinetic energy. Thus, a free electron can move with any velocity, and its wavelength ( = h
/ m v) associated with the momentum can be any value. The energy states of free electrons are the
kinetic energy, and they form a continuous band. In contrast, electrons bounded to an atom lose their
free particle character, and they must be treated as standing waves confined by the atomic field.
There are several approaches to quantum mechanics, each using a different mathematical technique,
but the concepts are very similar. A wave mechanics view is also a quantum mechanical view.
Skill Building Questions:
1. What is an energy state of an electron? Why energy states of a free electron form a continuous band, but energy states
of electrons in an atom have discrete energy states?
2. How do we specify the energy states of electrons in an atom? (quantum numbers)
3. What is the wavelength of an electron whose kinetic energy is 100 eV? (1/2 m v2 = 100 eV; evaluate v. Apply
de Broglie's formula  = h / m v to evaluate the wavelength ).
4. Explain the Heisenburg's uncertainty principle?
5. Draw the energy level diagram of the electron in a hydrogen atom.
Quantum Mechanics and the Periodic Table of Elements
You have learned the periodic table of the chemical elements when you studied module on natural
units. At that time, I mentioned that the inventors of the periodic table of elements Mendeleyev and
Meyor might not recognized the modern periodic tables. However, their inventions have driving the
chemistry discipline into a theoretical study of finding reasons for the presence or existence of the
periodic table. The theoretical studies developed into a field called
Electronic configurations of
quantum mechanics.
some light elements
The quantum number mentioned above rationalized the organization of
Ne
1s2 2s22p6
the elements as shown on the periodic table. A hydrogen atom has one
F
1s2 2s22p5
and only one electron, and its energy state is 1s. Due to the intrinsic spin
O
1s2 2s22p4
of the electron, an energy state accommodates two electrons. Thus, the
N
1s2 2s22p3
energy state of both electrons in helium, He, is 1s. We usually represent
C
1s2 2s22p2
this electronic configuration by 1s2. Since this energy state is fully
B
1s2 2s22p1
occupied, a single helium atom is stable. Therefore, the helium gas
Be
1s2 2s2
consists of single atoms. Single hydrogen atoms are not stable, because
1s2 2s1
the energy state is not filled. Two hydrogen atoms bind together to form Li
He
1s2
a molecule and a hydrogen gas consists of H2 molecules. Thus, quantum
H
1s1
mechanical results explain the chemical properties of elements.
88
A lithium atom has 3 electrons, and its electronic configuration is 1s2 2s1. Due to the lone electron in
the 2s orbital out side a stable He core, properties of lithium resemble those of hydrogen.
As the energy states of the electrons are filled with electrons, the elements progress to Be, B, C, N, O,
F and Ne. Like He, the electronic configuration for Ne is stable because it forms a closed shell. It is
also an inert gas as is He. The electrons in the partial filled shell dictate the chemical properties of these
elements.
Elements having one electron outside a closed shell tend to lose this electron to form a cation. Thus,
Li, Na, K, Rb, and Cs form positive ions in their salts. These positive ions have electronic
configurations of the inert gas preceding each of them. The first two groups of elements on the
periodic table are called s-block element. The second group of elements form positive ions with twice
the atomic charge, because they lose two electrons to form these ions. The higher charge plays a role in
the properties of these compounds.
Elements with one electron less than an inert gas tend to acquire an electron forming an anion. Thus,
F, Cl, Br, and I form negative ions in their salt. These ions have electronic configurations of the inert
gas following them. Sodium and chlorine react violently, releasing lots of energy. However, after the
reaction, they are very stable. We use this compound daily in our diet. Elements in the groups starting
with B, C, N, O, F, and Ne are called the p-block elements. The O group elements form doubly charge
negative ions such as O2–, S2–, and Se2–. These ions are stabilized by picking up a hydrogen ion forming
OH–, SH–, and SeH–.
Elements in B, C, and N groups tend to have covalent bonds by sharing electrons.
Filling the d orbitals results in the transition elements. The ten elements Sc, Ti, V, Cr, Mn, Fe, Co, Ni,
Cu, and Zn have partial filled d orbitals. Their properties are less different than those of the s– and p–
block elements.
Filling the f orbitals results in the rare earth elements ranging from La, Ce, Praseodymium, to Lu, 14
elements in all. The same is true for the actinides Ac, Th, Protactinium, and U. The rest of the actinides
are man made elements, and we shall talk about them later in this course.
The quantum mechanics explain much more chemistry than what I have just described. If you can
think of an explanation, it will be great.
Skill Building Questions:
1. What is the electronic configuration of argon and krypton?
Why are argon and krypton inert elements?
2. What is the electronic configuration of iron, Fe?
Why is iron a ferromagnetic material?
89
The Atomic Nuclei
All positive charges of an atom and almost all its mass are located in the tiny nucleus, whose radius is
only 100,000th of that of the atom, according to atomic models of the Rutherford and Bohr. The
establishments of these facts extend the exploration frontier to atomic nuclei to satisfy human desire to
understand the material world. We now have many theories about atomic nuclei, and they explain
some phenomena related to the atomic nuclei.
The Proton – the positive charge carrier
During the time when the charge and mass of electrons were investigated, some positively charged
particles were detected moving in opposite direction of the cathode rays in the cathode ray tube.

What are these positively charged particles?
How are they related to the atoms?

What are other components are present in atoms
in addition to electrons?
Properties of the Proton
Rest mass
1.6726231x10–27 kg
1.00727647 amu
938.2723 MeV
Spin
1/2
Magnetic
2.7928474 N
moment
Electric charge +1 atomic charge
In 1886 Goldstein (1850-1930) discovered what he
termed Kanalstrahlen, or canal rays, also called positive
rays; in a perforated cathode in an evacuated tube. In
1898, Wilhem Wien (1864-1928) and J.J. Thomson
found the mass of these positive particles equal to that of hydrogen atoms. E. Rutherford (1919)
detected the same particles when he studied alpha particles. By 1920, Rutherford was convinced that
the nucleus of a hydrogen atom was a fundamental particle, and he called it proton (symbol p). The
fundamental properties of the proton (not the hydrogen atom) are listed in the Table.
Since the electron and proton carry the same amount but opposite charge, the hydrogen atom with one
proton and one electron remains neutral. Further work revealed that protons are present in all
elements, and the number of protons present in the nuclei is equal to the number of electrons. This
number is the same as the atomic number assigned in early periodic tables to satisfy Moseley’s law.
Skill Building Questions:
1. What are canal rays and how are they formed and discovered?
What are protons?
2. Evaluate the rest mass of a hydrogen atom from the fundamental constants. Are your values the same as those given
in the Constant Table? Depending on the source, these data may differ slightly.
90
Neutrons – companion particles of protons
The nucleus of a hydrogen atom consists of a
proton and an electron. The atomic weights of
most elements are more than twice their
atomic numbers.

Why atomic weights of most elements are
more than twice their atomic numbers?
What else is present in the atomic nucleus?
Atomic Weights of Some Light Elements
Element
Hydrogen
Helium
Lithium
Beryllium
Boron
Carbon
Nitrogen
Oxygen
At. Number
1
2
3
4
5
6
7
8
In 1920, Rutherford speculated that atomic
nuclei consist of protons and neutrons. He
even ventured to suggest that protons and
neutrons had about the same mass, but neutrons carried no electric charge.
At. weight
1
4
6.9
9
10.8
12
14
16
Around 1930, many scholars used high-energy alpha particles to bombard various elements. Walther
W.G.F. Bothe (1891-1957) and H. Becker of Germany found a very penetrating radiation when they
bombard beryllium with alpha particles. The Joliot-Curie team in Paris also worked on the beryllium
experiment, and they observed the ejection of protons from the hydrogen-containing paraffin by the
penetrating radiation. James Chadwick, while working with Rutherford at the Cavendish Laboratory
(1932) in England found the same phenomenon, but he noticed that this neutral radiation transferred
kinetic energy to other light nuclei as well as hydrogen. In a paper published in 1932, he called it the
neutron, n, as suggested by Rutherford. Later that year, he showed that this particle was slightly
heavier than a proton. At that time, the Cavendish scholars considered both protons and neutrons
fundamental particles.
The production of neutrons, n, observed by Bothe, Becker, Joliot, Curie and Chadwick has been
interpreted this way: When a beryllium atom, Be, combines with an alpha particle, , Be is converted
into a carbon atom, C, and a neutron, n. This reaction is written as
Be +  = C + n + Energy.
Since boron nuclei absorb neutrons readily, a common neutron detector makes use of the reaction,
B + n -> Li + .

James Chadwick (1891-1974) began his article "Possible Existence of a Neutron" (published in Nature on Feb.
27, 1932) with: It has been shown by Bothe and others that beryllium when bombarded by -particles of polonium emits a
radiation of great penetrating power, .…and concluded with: It is to be expected that many of the effects of a neutron in passing
through matter should resemble those of a quantum of high-energy, and it is not easy to reach the final decision between the two
hypotheses. Up to the present, all the evidence is in favour of the neutron, while the quantum hypothesis can only be upheld if the
conservation of energy and momentum be relinquished at some point. He was referring to the quantum and neutron
hypotheses. The article summarized more than ten years of research. Chadwick received the Nobel Prize for
physics in 1935 for his discovery of neutrons.
91
A detection chamber is usually filled with gaseous boron trifluoride, BF3, with enriched 10B (see
Nuclides for notation). Neutrons entering the chamber react with 10B to give off  particles. The 
particles cause ionization of the gas. The ionization gives out signals that can be counted by electronic
techniques.
The discovery and confirmation of protons and neutrons have revealed the composition of nuclei as
predicted by Rutherford. Neutrons are emitted when atomic nuclei are bombarded with high-energy
particles such as alpha particles.
Skill Building Questions:
1. What is a neutron? Find and list all physical constants of neutron.
2. How do you account the fact that boron has an atomic weight of 10.8?
Deuterium, an isotope of hydrogen
Neutrons have been discovered to be companion particles of protons in the nuclei. The new
discoveries and revelation suggest more problems to solve. Some take a closer look at the atomic
weight while others are on a different track.

Why do Mg, Cl, and Cu have atomic weights 24.3, 35.5, and 63.5 respectively, while most other
atomic weights are close to integers, for example 1.0, 4.0, 12.0, 16.0, 31.0, and 101.1 for H, He, C,
O, P, and Ru respectively?
Do all atomic nuclei of an element have the same number of neutrons?

Is it possible that some hydrogen atoms contain neutrons?
After the discovery of neutrons, some scholars noticed that the atomic weight of hydrogen was slightly
more than the mass of proton plus that of electron. They speculated the existence of heavy hydrogen
atoms and named them deuterium, D whose nucleus assumed to be consisted of a proton and a
neutron. Harold C. Urey (1893-1981) predicted a difference in vapor pressure between hydrogen H2
and hydrogen-deuterium, HD. Urey and his students F.G. Brickwedde, and G.M. Murphy distilled
liquid hydrogen, and confirmed the presence of deuterium in the residue from its atomic spectra. This
demonstrated the presence of isotopes in the element hydrogen.
Since then, the term isotopes is used for atoms of the same element, but they have different numbers
of neutrons in the nuclei.
The abundance of deuterium in hydrogen has been measured to be 0.014%. Water is hydrogen oxide,
H2O, and deuterium oxide, D2O, is called heavy water. By chance, there should be more HDO

Harold C. Urey (1893 - 1981) was awarded the Nobel Prize for Chemistry in 1934 for his discovery of the
heavyform of hydrogen known as deuterium. In 1931 he and his associates announced their discovery of heavy
water, composed of an atom of oxygen and two atoms of deuterium. He also examined the chemical properties
and separation of radioactive isotopes of carbon, oxygen, nitrogen, and sulfur.
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molecules than D2O in water. When water is decomposed by electrolysis, the remaining water has a
higher concentration of HDO and D2O than ordinary water, because they are more difficult to
decompose. Reducing the volume of water to 1/100,000th of its original volume by electrolysis, G.N.
Lewis obtained rather pure D2O. This method has been used during World War II to produce heavy
water. Other methods of producing heavy water were developed later.
Electrolysis of heavy water produced a
H2
pure D2 gas, first by Lewis. Properties of
––––
H2, HD and D2 are compared in a table
Triple point (K)
13.96
form here. These properties are precious
vapor pressure at triple
information for nuclear technology. This
point (mm Hg)
128.6
table also illustrates the differences in
heat of fusion at triple
physical properties of isotopes. There
point (J mol–1)
117
should also be a difference in chemical
properties, and that difference is used for
Boiling point (K)
20.39
the separation of heavy water from
heat of vaporization at
ordinary water. It should be pointed out
boiling point (J mol–1)
903
that deuterium is a stable isotope, and its
abundance in nature remains relatively
constant. It is present everywhere, including our body, which contains 70% water.
HD
––––
16.60
D2
––––
18.73
92.8
54.0
159
197
22.13
23.67
1074
1225
A yet heavier isotope of hydrogen called tritium, T, can be produced by nuclear technology. We only
mention it here at this time. If you speculated that it has two neutrons and a proton in its nucleus,
you are absolutely right. Thus, it is possible for an element to have more than two isotopes.
Skill Building Questions:
1. How was deuterium isolated and its existence confirmed?
2. What are isotopes?
What are the isotopes of hydrogen?
3. Suppose 50% of deuterium is extracted from a heavy water production facility, how much water is required to produce
1.0 L of heavy water?
4. Under similar pressure, which one of the following should have the highest boiling point: T2, D2, H2, HT, HD, or
DT? (Can be answered by extrapolation)
5. Compare physical properties of heavy water with those of ordinary water. (Searching for properties in literature
is an interesting exercise).
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Nuclides
The term isotope was used to describe the relationship between hydrogen and deuterium, but the
existence of isotopes was inferred from the (1907) study of radioactive decay schemes by F. Soddy,
who found several radioactive species that had the same chemical properties as thorium. He called
them isotopes. Thomson suggested the existence of non-radioactive isotopes in 1912. Lead refined
from uranium ores had a significantly smaller atomic weight (206.05) than that (207.8) from the
thorium ores, found Honigschmid. Atomic weight for normal lead is 207.2. Using his mass
spectrograph, Aston showed that most elements have isotopes.

How to differentiate isotopes from one another?
How can isotopes be represented?
Depicting a Nuclide or an Isotope
M
EZ
Since the confirmation of isotopes in hydrogen and other
chemical elements, there is a need to distinguish isotopes
from one another and each isotope must have a unique
representation.
M, mass number
Z, number of protons
N,(= M – Z) number of neutrons
Furthermore, we define a nuclide as one that has specific
numbers of protons and neutrons. Of course, nuclides with
the same atomic number are isotopes. In most literature,
however, the two terms are used interchangeably.
Note that Z is often omitted, because its value is
implied by the symbol E.
A nuclide has specific number of neutron, N, and number of proton, Z. Neutrons and protons are
called nucleons. The mass number, M, is the number of nucleons (M = N + Z). These numbers are
unique to a nuclide. Thus, superscript the mass
number M before the element symbol is adequate
Masses of Some Particles and Nuclides
to specify a nuclide. However, for clarity,
Particles
Mass /amu
Remarks
sometimes we super script both M and Z on both
M Z
sides of the element symbol E as E , (N = M 12C,
12.000000
the standard
Z). This notation distinguishes one isotope or
1/1823th amu
e, electron
0.00054858
nuclide from another
The three commonly known isotopes of hydrogen
are: 1H, 2H, 3H. They are called hydrogen,
deuterium (D = 2H), and tritium (T = 3H)
respectively. There are times for specific
representation of molecules by indicating the
isotopes. For example HD represents a hydrogen
molecule consisting of a hydrogen atom and a
deuterium atom; D2O is heavy water; and 14CO2
means carbon dioxide of isotope carbon with mass
number 14.

n, neutron
1.00866501
1.009 amu
1H,
hydrogen
1.00782505
1.008 amu
2H,
deuterium
2.014102
3H,
tritium
3.016049
4He,
hellium
4.002603
Frederick Soddy (1877-1956) received the Nobel Prize for Chemistry in 1921 for investigating radioactive
substances and for elaborating the theory of isotopes.
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Some of the terms are similar but they are specifically defined. Mass number (M) is the number of
nucleons in the nucleus, whereas atomic mass is the mass of an atom. The mass of a single 12C atom
is defined as exactly 12 atomic mass unit ( 12.00000 amu or u). This is the international standard. For
D, M = 2, atomic mass is 2.014102 amu or 3.3445 x 10-27 kg. The masses of some particles and
elements are given here. Atomic weight is a value used in chemical stoichiometry dealing with large
numbers of atoms. Thus, when viewed at an atomic scale, the atomic weight of an element is the
abundance-weighted average of all its stable isotopes.
An example of the atomic weight calculation is illustrated in the table here for hydrogen, which
essentially has only two isotopes, H and D. In the table, the abundance is the fraction of the isotope in
the element, 99.985% H, and 0.0148% 2H. Usually, the atomic weight for H is the sum of the products
(of atomic mass multiplied by the abundance). For hydrogen, the sum is 1.007972, but for chemical
stoichiometry calculation, 1.008 is adequate.
Calculation of Hydrogen Atomic Weight
Isotope
atomic mass
Abundance
atomic mass abundance
1H
1.00782503
0.99985
1.007674
2H
2.014102
0.000148
0.000298
3H
3.016049
Trace
Atomic weight for H = 1.007674 + 0.00298 = 1.007972
Skill Building Questions:
1. What is a nuclide? What are the atomic number, mass number, and number of neutrons for nuclides 59Co, 60Co
and 60Ni?
2. Give the chemical formula for hydrogen deuterium oxide? Give the notations for isotopes of uranium with mass
numbers 235 and 238.
3. Explain and distinguish these terms: mass number, atomic mass, and atomic weight.
4. According a Table of The Isotopes from a CRC Hand Book of Chemistry and Physics, the abundance of stable
isotopes of carbon are 98.89% 12C, and 1.11% 13C. There is only a trace of the radioactive 14C. The rest mass of
13
C is 13.003355. Estimate the atomic weight of ordinary carbon.

In 1960s, mass spectrometers were developed to measure masses of atoms very precisely, and as a result, a
new scale was required for atomic weight. The scale is based on the mass of 12C nuclide being defined as 12
exactly, and masses of other isotopes are measured against this standard.
95
The quarks
Humans' desire to know the fundamentals of the material world led us to explore the small frontier of
subatomic particles. The exploration has revealed the energy levels of electrons, developed a quantum
theory to explain the observed spectra, and identified subatomic particles: electrons, protons, and
neutrons. Regarding atomic nuclei, many questions remain.

Are electrons, protons and neutrons fundamental particles in the sense that they can not be further
divided? Are they particles (corpuscles), waves or both?

How are protons and neutrons arranged in the atomic nuclei?
Do atomic nuclei really consist of individual neutrons and protons?
In 1968, electron scattering experiments by proton at Stanford gave hints that point-like particles
existed inside a single proton. Other particle scattering experiments also indicated that the proton and
the neutron had three centers. These results indicated that they were composite particles, consisting of
two or more simpler particles.
There were theoretical considerations as well. Based on the properties and relationships of particles
known in 1962, Gell-Mann in the US and Y. Neémen of Israel predicted the existence and properties
of some unknown particles in considerable detail. Gell-Mann and Zweig from Caltech suggested that
some heavy particles such as protons and neutrons (called baryons) were made up from three
entities called quarks, so named by Murray Gell-Mann after a quote "three quarks for muster Mark, sure
he hasn't got much of a bark, etc..." from the novel Finnegan's Mark. J. Joyce, author of the novel, used
quarks to rhyme with Mark, bark, lark etc.... The three quarks they proposed were called up, down and
side ways (represented by u, d and s respectively). Among their properties is fractional charge of
electron (e) of +2/3e and -1/3e for the u and d quarks respectively. Thus, a combination of two u and
one d quarks gives a (2(2/3) - 1/3 =) +1 for the proton, whereas a combination of one u and two d
quarks gives a zero charge to neutron (2/3 - 2(1/3) = 0).
Although abundant evidence led to the quark model, free or unbound quarks have never been
observed. No quark has ever been emitted from atomic nuclei either. Their existence is based on
products produced in high-energy particle collisions.
Skill Building Questions:
1. What are the features of quarks?
2. How many up and down quarks are there in the atomic nuclei of H, D, 4He, 12C, 16O and 235U?

Gell-Mann, Murray (1929-) winner of the Nobel Prize for Physics for 1969 for his work pertaining to the
classification of subatomic particles and their interactions.
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The standard model and the material world
Human beings speculated that materials were derived from two opposite forces Yin and Yang or four
primal substances. Later exploration revealed chemical elements, atoms, sub-atomic particles (electrons,
radioactive rays, protons and the neutrons) and quarks.

Have we found the fundamental natural units of mater?
How are materials related to these fundamental natural units?
Is there a simple model to correlate materials to fundamental natural units?
Chemical elements were thought to be fundamental with atoms being their natural units. Period Tables
have organized them for an easy understanding and reference. A closer (10-15 m by alpha scattering
experiment) look at the atoms revealed the atomic nuclei (radius 10-15 m) and their electrons. At the
time of their discoveries, proton, neutron and electron were thought to be fundamental particles, and
we believed that all materials were made up of neutrons, protons, and electrons. This model is
adequate to explain all phenomena related to radioactivity to be discussed in the next Chapter.
As we shall see in the next two chapters, high-energy physicists have discovered many more particles in
the mean time. Furthermore, a closer (less than 10-15 m) examination of protons and neutrons showed
they too have some structural centers. It is desirable to consider all matter (material and some transient
particles) conglomerations of a few fundamental natural units, which are simple (not made of
anything) and no structural feature. In order to organize and classify these particles, existence of quarks
has been proposed together with a standard model for all particles.
In the standard model, all matter is made of quarks and leptons. Strong force binds the quarks
together to form hadrons. There are two types of leptons, a charged and an uncharged. Charged
particles exchange force by carrier particles called bosons. The forces between leptons and quarks are
called weak interactions.
For ordinary material the two quarks are up (u)
and down (d), and the two leptons are electron
(e–) and neutrino (e). These are first
generation fundamental particles. Protons and
neutrons are made up of three quarks, whereas
electrons occupy the space around the nuclei.
Neutrinos are very difficult to detect, they
accompany the electrons in beta decays.
The Standard Model
Generation:
First
Second
Third
Quarks
u, d
c, s
t, b
Leptons
e, e


Some particles produced in high-energy particle collisions and discovered in cosmic rays suggest the
existence of heavier quarks. The second-generation quarks are called charm ( c) and strange (s), and
the leptons are called muon () and muon-neutrino (). At yet higher energy collisions, particles
containing third generation quarks top (t) and bottom (b) have been observed, and the corresponding
leptons are tau (t) and tau-neutrino ().
97
Particles formed by the second and third generation quarks are unstable, as are these leptons. They
decay into first generation particles. In stars where the temperatures are high, high-energy particle
collisions generate particles of second and third generations. Some of them reach the Earth as cosmic
rays. Particles generated by even-higher energy particle collisions remain mysterious.
Theoretical and experimental evidences have shown that mass and energy are equivalent. A certain
amount of energy forms a particle and exhibits a mass and occupies a volume. The amount of energy
in a particle can be increased or decreased by certain definite jumps; it does not vary in a continuous
fashion. Protons are stable particles because they last for an indefinite period of time. Free neutrons
exist only for a short period of time, convert to protons and electrons in a few minutes, which will be
discuss further in the next Chapter. The combination of protons and neutrons results in many stable
and unstable nuclides. We do not know if nucleons retain their identities in atomic nuclei, but their
counting serves useful purposes.
Matter must interact to be observed; the observer and the observed are one. To separate particle from
energy and to separate wave from particle are fine, but they are ultimately (Tai-chi) indivisible. Particle is
also energy, and wave is also particle.
Skill Building Questions:
1. What are the fundamental natural units of material?
How do they conglomerate to make all the materials of the world?
2. Explain these terms: quarks, leptons, and bosons.
98
Exercises
1. What type of spectra are the electromagnetic radiation from a solid and a hot gas?
What are the features of absorption spectra?
2. Calculate the largest wave numbers for each of the Lyman series, the Balmer series, and the
Paschen series. What are the energies of the lines in eV units?
(8230299, 1524129, 533445 m–1 respectively; these lines are in the UV, visible, and IR regions. To calculate
the energies of the lines in eV, show that the Rydberg constant R = 2.1814x10–18 J = 13.6 eV, and then
calculate the energies of transitions.)
3. Estimate the wavelengths of characteristic X-rays of lithium, aluminum, lead, and uranium, by
applying the Moseley’s law.
4. What are the characteristics of alpha, beta, and gamma rays?
How can they be distinguished experimentally?
5. Describe Rutherford’s alpha scattering experiment. What did he observe, and what conclusion did
he reach? What are the radii of atoms and atomic nuclei?
6. Nickel has a density of 8.90 g cm–3. Calculate the volume occupied by each nickel atom. Assume
that nickel atoms as spheres, and they pack in such a way that only 75% of the volume is occupied
by the spheres (25 % of the space are gaps between spheres). Estimate the radius of nickel atoms.
(Assume the radius of the atom to be r, then (3/4) r 3 * 8.9 = 0.75*58.71 g /6.022x1023 and solve for r)
7. If the radius of an atomic nucleus is only 1/100000th of the radius of its atom, estimate the density of
the nucleus. Nickel density is 8.90 g cm–3. (8.9x1015 g/ cm3 = 8.9x1012 kg/cm3, a huge value)
8. How are X-rays generated? Why was their discovery such a significant contribution in science?
What properties of X-rays give their modern applications? Give the applications and indicate the
special properties making X-rays suitable for that particular application.
9. Table salt has a density of 2.165 g/cm3. If a cubic unit contains 4 Na and 4 Cl atoms, what is the
edge length of this cubic unit?
(Atomic weights of Na 22.99, Cl 35.45, Arvogadro’s number 6.0221 x 1023. If the cubic unit has edge length
of a, then
density = 4 (22.99 + 35.45) / (6.0221x1023 a3).
Solving this equation results in a = 0.564 nm. This problem illustrates that if the density is measured
accurately, the distances between planes can be evaluated, and the X-ray wavelength can be determined by
X-ray diffraction.)
10. Describe the Bohr atom.
11. Confirm the Bohr radius, the atomic energy unit hartree, and the Rydberg constant by calculation
using the formulas given in The Bohr Atom.
99
12. Assume that the transitions responsible for characteristic X-ray emission are from n =2 to n =1.
Estimate the wave number and wavelength for metals with Z = 23-30, 42, 47, and 79. Compare
these results with those given in the Table, earlier. What modifications should be made in the
assumption or for the Mosely's law? (Using the formula (Z -1)2(1-1/4) gets a better fit)
13. What are the rest masses of electrons, protons, neutrons, hydrogen, and deuterium?
14. Define and differentiate the following pairs of terms: isotopes, nuclides; atomic mass, atomic
weight; and atomic number, mass number.
15. In 1968, electron scattering experiments by protons at Standford gave hints that point-like particles
existed inside the proton. Other particle scattering experiments also indicated that protons and
neutrons had more than one center. Discuss the similarities and differences in principle between
these scattering experiments and Rutherford’s  scattering experiments.
16. Write an essay on one of these topics: Moseley's law, radioactivity, alpha particles, beta particles,
gamma rays, atomic number, atomic mass, nucleon, isotope and nuclide, electron, proton, neutron,
quark, fundamental particles, baryons, Rutherford atom, Bohr's atom, and the standard model.
Further reading and work cited
Bockhoff, F.J. (1969), Elements of quantum theory, Addison Welsley.
Gell-Mann, M. (1976), What are the building blocks of matter?, in The nature of the physical universe - 1976 Nobel
Conference, 27-45. Edited by Huff, D and Prewett, O. John Wiley & Sons.
Ihde, A.J. (1964), The development of modern chemistry, Harper & Row
Romer, A. (1964), Discovery of radioactivity and transmutation, Dover Publication
Sarton, G. (1954) Ancient Science and modern civilization, Univ. of Nebraska Press.
Sarton, G. (1970), A history of science, Norton & Company Inc.
Sidgwick, N.V. (1950), The chemical elements and their compounds, Oxford.
Interesting Web Sites
For stories of Niels Bohr, Marie Curie, Albert Einstein, Enrico Fermi, Galileo, and Isaac Newton, see
http://www2.lucidcafe.com/lucidcafe/library/95oct/nbohr.html
For information on the Standard Model and Fundamental Particles, see
http://pdg.lbl.gov/cpep/adventure.html,
http://www.hep.ph.rhbnc.ac.uk/hep/talk/small_parts1.html
For information on the Top Quark, visit http://www.fnal.gov/pub/top95/top_why_sixth.html
http://www.ph.ed.ac.uk/~pclark/top/template.html,
Here is a general article on nucleons with many links to other Internet sites
http://www.europe.apnet.com/inscight/07071997/graphb.htm
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