The Atomic Theory and
Electronic Structure
A Visual-Historical Approach
David A. Katz
Department of Chemistry
Pima Community College
Tucson, AZ U.S.A.
Voice: 520-206-6044 Email: dkatz@pima.edu
Web site: http://www.chymist.com
Theories of Matter
• The Greeks and Hindus appear to have developed
theories on matter.
• Most of the writings are attributed to the Greeks due to
the amount of recorded information that has survived to
the present.
• Greeks thought substances could be converted or
transformed into other forms.
• They observed the changing of states due to heat and
equated it with biological processes.
• The Greeks were philosophers and thinkers, not
experimentalists, so they did not conduct experiments to
verify their ideas.
• Thales of Miletus (about 624-about 527 B.C.)
– Proposed that water is the primal matter from which
everything originated.
– He is also credited with defining a soul as that which
possesses eternal motion.
• Anaximander (610-546 B.C.)
– The primary substance, the apeiron, was eternal and
unlimited in extension. It was not composed of any known
elements and it possessed eternal motion (i.e., a soul).
• Anaximenes (585-524 B.C.)
– Stated that air is the primary substance
– Suggested it could be transformed into other substances
by thinning (fire) or thickening (wind, clouds, rain, hail,
earth, rock).
• Heraclitus of Ephesus (544-484 B.C.)
– fire is the primeval substance
– Change is the only reality.
• The Pythagoreans (Pythagoras (570-490 B.C.))
– Reduced the theory of matter to a mathematical and
geometric basis by using geometric solids to represent the
basic elements:
•
•
•
•
•
cube = earth
octahedron = air
tetrahedron = fire
icosahedron = water
dodecahedron = ether
• Empedocles of Agrigentum (492-432 B.C.)
– Credited with the first announcement of the concept of
four elements: earth, air, fire, and water, which were
capable of combining to form all other substances.
– Elements combined by specific attractions or repulsions
which were typified as love and hate.
• Anaxagoras of Klazomenae (c. 500-428 B.C.)
– Considered the universe to be composed of an infinite
variety of small particles called seeds.
– These seeds were infinitely divisible and possessed a
quality which allowed "like to attract like" to form
substances such a flesh, bone, gold, etc.
• Leucippus (5th century B.C.) and Democritus (460370 B.C.)
– First atomic theory.
– All material things consisted of small indivisible particles,
or atoms, which were all qualitatively alike, differing
only in size, shape, position and mass.
– Atoms, they stated, exist in a vacuous space which
separates them and, because of this space, they are
capable of movement. (This can be considered at the
first kinetic theory.)
• Pierre Gassendi (1592-1655)
– Revived the atomic theory (1650)
• Atoms are primordial, impenetable, simple,
unchangeable, and indestructible bodies
• They are the smallest bodies that can exist
• Atoms and vacuum, the absolutely full and the
absolutely empty, are the only true principles
and there is no third principle possible.
• Atoms differ in size, shape and weight
• Atoms may possess hooks and other
excrescences
• Atoms possess motion
• Atoms form very small corpuscles, or
molecules, which aggregate into larger and
larger bodies
• Robert Boyle (1627-1691)
– Hypothesized a universal matter, the concept
of atoms of different shapes and sizes
– Defined an element (The Sceptical Chymist,
1661)
• And, to prevent mistakes, I must advertise
You, that I now mean by Elements, as those
Chymists that speak plainest do by their
Principles, certain Primitive and Simple, or
perfectly unmingled bodies; which not
being made of any other bodies, or of one
another, are the Ingredients of which all
those call’d perfectly mixt Bodies are
immediately compounded, and into which
they are ultimately resolved.
– He could not give any examples of elements
that fit his definition.
• Sir Isaac Newton (1642 -1727)
– Modified atomic theory to atoms
as hard particles with forces of
attraction between them
Events Leading to the Modern Atomic Theory
• Stephen Hales (1677-1761)
– Devised the pneumatic trough,
1727
– Allowed for generation and
collection of gases
• Joseph Black (1728-1799)
– Mass relationships in chemical
reactions, 1752
• Magnesia alba and fixed air.
MgCO3  MgO + CO2
• Henry Cavendish (1731-1810)
– Inflammable air, “Hydrogen”, 1766
– Later: H2 + O2 → H2O
• Joseph Priestley (1733-1804)
and
Carl Wilhelm Scheele (1742-1786)
– Dephlogisticated air/ feuer luft
“Oxygen”, 1774
• Antoine Laurent Lavoisier
(1743-1794) (and MarieAnne Pierrette Paulze
Lavoisier (1758-1836)?)
– Nature of combustion, 1777
– Elements in Traité
élémentaire de chemie, 1789
The Atomic Theory
• John Dalton (1766-1844)
– New System of Chemical
Philosophy, 1808
– All bodies are constituted of a vast
number of extremely small
particles, or atoms of matter bound
together by a force of attraction
– The ultimate particles of all
homogeneous bodies are perfectly
alike in weight, figure, etc.
The Atomic Theory
– Atoms have definite relative weights “expressed in
atoms of hydrogen, each of which is denoted by
unity”
– Atoms combine in simple numerical ratios to form
compounds
– Under given experimental conditions a particular
atom will always behave in the same manner
– Atoms are indestructible
Dalton’s symbols, 1808
Dalton’s atomic weights,
1808
Jon Jakob Berzelius, 1813: Letters for element symbols
Name
Symbol
Name
Symbol
Name
Symbol
Name
Symbol
Oxygen
O
Tungsten
Tn
Palladium
Pa
Uranium
U
Sulphur
S
Antimony
Sb
Silver
Ag
Cerium
Ce
Phosphorus
P
Tellurium
Te
Mercury
Hg
Yttrium
Y
M
Columbium
Cl
(nioblium)
Copper
Cu
Glucinum
(beryllium)
Gl
F
Titanium
Ti
Nickel
Ni
Aluminum
Al
Boron
B
Zirconium
Zr
Cobalt
Co
Magnesium Ms
Carbon
C
Silicium
Si
Bismuth
Bi
Strontium
Sr
Nitric radicle N
Osmium
Os
Lead
Pb
Barytium
Ba
Hydrogen
H
Iridium
I
Tin
Sn
Calcium
Ca
Arsenic
As
Rhodium
Rh
Iron
Fe
Sodium
So
Molybdenum Mo
Platinum
Pt
Zinc
Zn
Potassium
Po
Chromium
Gold
Au
Manganese Ma
Muriatic
radicle
(chlorine)
Fluoric
radicle
Ch
Pieces of Atoms – the electron
• Heinrich Geissler
(1814-1879)
• Julius Plücker
(1801-1868)
– Evacuated tube
glowed, 1859
– Rays affected by a
magnet
• Johann Wilhelm Hittorf (1824-1914)
– Maltese cross tube, 1869
• Rays travel in straight line
• Cast shadows of objects
• William Crookes (1832-1919)
– Verified previous observations, 1879
– Caused pinwheel to turn
• Composed of particles
– Have negative charge
• Joseph John Thomson (1846-1940)
e/m = -1.759 x 108 coulomb/gram - 1897
• Robert Millikan (1868-1923)
– Oil drop experiment – 1909
e = -1.602 x 10-19 coulomb
N = 6.062 x 1023 molecules/g-molecule
Pieces of Atoms – the proton
• Eugen Goldstein (1850-1930)
– Canal rays - 1886
Pieces of Atoms – the neutron
• James Chadwick (1891-1974)
Discovered the neutron – 1932
The Subatomic Particles
Particle
Symbol
Charge
coulomb
Mass
g
Relative
Charge
Relative Mass
amu
electron
0
1
e or e 
-1.602 x 10-19
9.109 x 10-28
-1
0.0005486 ≈ 0
proton
p  or 11H
1.602 x 10-19
1.673 x 10-24
+1
1.0073
neutron
n or 01n
0
1.675 x 10-24
0
1.0087
Models of the Atom
• Philipp Lenard (1862-1947)
– Dynamids – 1903
• Hantaro Nagaoka (1865-1950)
– Saturnian model - 1904
• J. J. Thomson
– Plum pudding – 1904
• Partly based on A. M.
Mayer’s (1836-1897)
floating magnet experiment
A. M. Mayer
“We suppose that the atom consists of a
number of corpuscles moving about in a
sphere of uniform positive
electrification…
when the corpuscles are constrained to
move in one plane …the corpuscles will
arrange themselves in a series of
concentric rings.
When the corpuscles are not constrained
to one plane, but can move about in all
directions, they will arrange themselves in
a series of concentric shells”
J. J. Thomson, 1904
Photo Reference: Bartosz A. Grzybowski,
Howard A. Stone and George M. Whitesides,
Dynamic self-assembly of magnetized,
millimetre-sized objects rotating at a liquid–air
interface, Nature 405, 1033-1036 (29 June 2000)
Ernest Rutherford (1871-1937)
Hans Geiger and Ernest Marsden – 1908
Geiger and Marsden were running
“experiments on scattering of alpha
particles when passing through thin foils of
metals such as aluminum, silver, gold,
platinum, etc. A narrow pencil of alphaparticles under such conditions became
dispersed through one or two degrees and
the amount of dispersion,…,varied as the
square root of the thickness or probable
number of atoms encountered and also
roughly as the square root of the atomic
weight of the metal used.
Recollections by Sir Ernest Marsden, J. B. Birks,
editor, Rutherford at Manchester, W. A. Benjamin
Inc., 1963
In a discussion with Geiger, regarding Ernest Marsden,
Rutherford stated that “I agreed with Geiger that young
Marsden, whom he had been training in radioactive methods,
ought to begin a research. Why not let him see if any αparticles can be scattered through a large angle? I did not
believe they would be…”
Recollections by Ernest Rutherford, J. B. Birks, editor, Rutherford at Manchester, W. A. Benjamin
Inc., 1963
“The observations, however, of Geiger and Marsden** on the
scattering of a rays indicate that some of the α particles, about
1 in 20,000 were turned through an average angle of 90 degrees
in passing though a layer of gold-foil about 0.00004 cm. thick, …
It seems reasonable to suppose that the deflexion through a
large angle is due to a single atomic encounter, …”
** Proc. Roy. Soc. lxxxii, p. 495 (1909)
*** Proc. Roy. Soc. lxxxiii, p. 492 (1910)
From the experimental results, Rutherford deduced that the
positive electricity of the atom was concentrated in a small
nucleus and “the positive charge on the nucleus had a
numerical value approximating to half the atomic weight.”
Recollections by Sir Ernest Marsden, J. B. Birks, editor, Rutherford at Manchester, W. A.
Benjamin Inc., 1963
“It was quite the most incredible event that has ever happened
to me in my life. It was almost as incredible as if you had fired
a 15-inch shell at a piece of tissue-paper and it came back and
hit you.”
Recollections by Ernest Rutherford, J. B. Birks, editor, Rutherford at Manchester, W. A.
Benjamin Inc., 1963
The
Rutherford
Atom Model
The atom is mostly empty space with a dense nucleus
Protons and neutrons in are located in the nucleus.
The number of electrons is equal to the number of
protons.
Electrons are located in space around the nucleus.
Atoms are extremely small: the diameter of a hydrogen
atom is 6.1 x 10-11 m (61 pm)
Radioactivity and
Stability of the nucleus
Wilhelm Conrad Roentgen
1845-1923
Discovered x-rays - 1895
Barium
platinocyanide
Henri Becquerel (1852-1908)
Radiation activity, 1896
Uranium nitrate
Image of potassium uranyl
sulfate
Pierre Curie (1859-1906)
Marie Curie (1867-1934)
Radioactivity- 1898
Polonium - 1898
Radium - 1898
pitchblende
Marie Curie with inset photo
of Pierre Curie
Radium bromide
Ernest Rutherford (1871-1937)
α, β, γ - 1903
In his lab at McGill University, 1903
Glenn T. Seaborg (1912-1999)
Extending the periodic table
Spectra
The Electromagnetic Spectrum
Viewing spectra using holographic diffraction
grating (Flinn Scientific C-Spectra)
Hydrogen spectrum
Helium spectrum
The Balmer Series of Hydrogen Lines
• In 1885, Johann Jakob Balmer (1825 - 1898),
worked out a formula to calculate the positions
of the spectral lines of the visible hydrogen
spectrum
m2
  364.56 2 2
m 2
(
)
Where m = an integer, 3, 4, 5, …
• In 1888, Johannes Rydberg generalized
Balmer’s formula to calculate all the lines of
the hydrogen spectrum
1
1
1
 RH


n22 n12
(
Where RH = 109677.58 cm-1
)
The Quantum Mechanical Model
• Max Planck (1858 -1947)
– Blackbody radiation – 1900
– Light is emitted in bundles called
quanta.
e = hν
h = 6.626 x 10-34 J-sec
As the temperature
decreases, the peak of the
black-body radiation curve
moves to lower intensities
and longer wavelengths.
The Quantum Mechanical Model
• Albert Einstein (1879-1955)
The photoelectric effect – 1905
Planck’s equation: e = hν
Equation for light : c = λν
c
Rearrange to


Substitute into Planck’s equation
e
hc

From general relativity: e = mc2
Substitute for e and solve for λ
h

mc
Light is composed of particles called photons
The Bohr Model - 1913
• Niels Bohr (1885-1962)
The Bohr Model – Bohr’s Postulates
1. Spectral lines are produced by atoms one at a
time
2. A single electron is responsible for each line
3. The Rutherford nuclear atom is the correct
model
4. The quantum laws apply to jumps between
different states characterized by discrete values
of angular momentum and energy
The Bohr Model – Bohr’s Postulates
5. The Angular momentum is given by
h
p n
2
( )
n = an integer: 1, 2, 3, …
h = Planck’s constant
6. Two different states of the electron in the atom
are involved. These are called “allowed
stationary states”
The Bohr Model – Bohr’s Postulates
7. The Planck-Einstein equation, E = hν holds for
emission and absorption. If an electron makes
a transition between two states with energies
E1 and E2, the frequency of the spectral line is
given by
hν = E1 – E2
ν = frequency of the spectral line
E = energy of the allowed stationary state
8. We cannot visualize or explain, classically (i.e.,
according to Newton’s Laws), the behavior of
the active electron during a transition in the
atom from one stationary state to another
Bohr’s calculated radii of
hydrogen energy levels
r = n2A0
r = 53 pm r = 4(53) pm
= 212 pm
r = 9 (53) pm
= 477 pm
r = 16(53) pm
= 848 pm
r = 25(53) pm
= 1325 pm
r = 36(53) pm
= 1908 pm
r = 49(53) pm
= 2597 pm
Lyman Series
Balmer Series
Paschen Series
Brackett Series
Pfund Series
Humphrey’s Series
The Bohr Model
The energy absorbed or emitted
from the process of an electron
transition can be calculated by the
equation:
E  RH
(
1
1
 2
2
n2 n1
)
where
RH = the Rydberg constant, 2.18  10−18 J,
and
n1 and n2 are the initial and final energy
levels of the electron.
The Wave Nature of the Electron
• In 1924, Louis de Broglie (1892-1987)
postulated that if light can act as a particle,
then a particle might have wave properties
• De Broglie took Einstein’s equation
h

mc
and rewrote it as
h

mv
where m = mass of an electron
v = velocity of an electron
The Wave Nature of the Electron
• Clinton Davisson (1881-1958 ) and
Lester Germer (1886-1971)
– Electron waves - 1927
• Werner Heisenberg (1901-1976)
– The Uncertainty Principle, 1927
“The more precisely the position is
determined, the less precisely the
momentum is known in this instant, and
vice versa.”
x

p


h
4
h
 x p
4
– As matter gets smaller, approaching the
size of an electron, our measuring device
interacts with matter to affect our
measurement.
– We can only determine the probability of
the location or the momentum of the
electron
Quantum Mechanics
Erwin Schrodinger (1887-1961)
• The wave equation, 1927
• Uses mathematical equations of wave
motion to generate a series of wave
equations to describe electron behavior in
an atom
• The wave equations or wave functions are
designated by the Greek letter ψ
wave function
d2Y
dx2
+
d2Y
dy2
mass of electron
+
d2Y
dz2
how y changes in space
potential energy at x,y,z
82mQ
+
(E-V(x,y,z)Y(x,y,z) = 0
2
h
total quantized energy of
the atomic system
Quantum Mechanics
• The square of the wave
equation, ψ2, gives a
probability density map of
where an electron has a
certain statistical likelihood
of being at any given
instant in time.
Quantum Numbers
• Solving the wave equation gives a set of wave
functions, or orbitals, and their corresponding
energies.
• Each orbital describes a spatial distribution of
electron density.
• An orbital is described by a set of three quantum
numbers.
• Quantum numbers can be considered to be
“coordinates” (similar to x, y, and z coodrinates
for a graph) which are related to where an
electron will be found in an atom.
Solutions to the Schrodinger Wave Equation
Quantum Numbers of Electrons in Atoms
Name
Symbol
Permitted Values
Property
principal
n
positive integers(1,2,3,…) Energy level
angular
momentum
l
integers from 0 to n-1
orbital shape (probability
distribution)
(The l values 0, 1, 2, and 3
correspond to s, p, d, and f
orbitals, respectively.)
integers from -l to 0 to +l
orbital orientation
magnetic
spin
ml
ms
+1/2 or -1/2
direction of e- spin
Looking at Quantum Numbers:
The Principal Quantum Number, n
• The principal quantum number, n,
describes the energy level on which the
orbital resides.
• The values of n are integers ≥ 0.
n = 1, 2, 3, etc.
Looking at Quantum Numbers:
The Azimuthal Quantum Number, l
• The azimuthal (or angular momentum) quantum
number tells the electron’s angular momentum.
• Allowed values of l are integers ranging from 0 to
n − 1.
For example, if n = 1, l = 0
if n = 2, l can equal 0 or 1
Value of l
Angular momentum
0
None
1
Linear
2
2-directional
3
3-directional
Looking at Quantum Numbers:
The Azimuthal Quantum Number, l
• The values of l relate to the most probable electron
distribution.
• Letter designations are used to designate the different
values of l and, therefore, the shapes of orbitals.
Orbital Shape
Name*
Value
of l
Orbital (subshell)
Letter designation
0
s
sharp
1
p
principal
2
d
diffuse
3
f
fine
* From
emission
spectroscopy
terms
Looking at Quantum Numbers:
The Magnetic Quantum Number, ml
• Describes the orientation of an orbital with respect to a
magnetic field
• This translates as the three-dimensional orientation of
the orbital.
• Values of ml are integers ranging from -l to l:
−l ≤ ml ≤ l.
Values of l
Values of ml
Orbital
Number of
designation
orbitals
0
0
s
1
1
-1, 0, +1
p
3
2
-2, -1, 0, +1, +2
d
5
3
-3, -2, -1, 0, +1, +2, +3
f
7
Quantum Numbers and Subshells
• Orbitals with the same value of n form a shell
• Different orbital types within a shell are called subshells.
Pictures of s and p orbitals
Imaging the atomic orbitals of carbon atomic chains with
field-emission electron microscopy
I. M. Mikhailovskij, E. V. Sadanov, T. I. Mazilova, V. A. Ksenofontov, and
O. A. Velicodnaja, Department of Low Temperatures and Condensed
State, National Scientific Center, Kharkov Institute for Physics and
Technology, Academicheskaja, 1, Kharkov 61108, Ukraine
Phys. Rev. B 80, 165404 (2009)
A Summary
of Atomic
Orbitals from
1s to 3d
Empty subshells
Valence
Full
subshells subshells
Approximate energy levels for neutral atoms.
From Ronald Rich, Periodic Correlations, 1965
The Spin Quantum Number, ms
• In the 1920s, it was
discovered that two
electrons in the same
orbital do not have exactly
the same energy.
• The “spin” of an electron
describes its magnetic
field, which affects its
energy.
• Otto Stern (1888-1969) and
Walther Gerlach (1889-1979)
– Stern-Gerlach experiment, 1922
Spin Quantum Number, ms
• This led to a fourth
quantum number, the spin
quantum number, ms.
• The spin quantum number
has only 2 allowed values:
+1/2 and −1/2.
• Wolfgang Pauli (1900-1958)
– Pauli Exclusion Principle, 1925
“There can never be two or more
equivalent electrons in an atom for
which in strong fields the values of all
quantum numbers n, k1, k2, m1 (or,
equivalently, n, k1, m1, m1) are the
same.”
Hund’s Rule
Friedrich Hund (1896 - 1997)
For degenerate orbitals,
the lowest energy is
attained when the
electrons occupy
separate orbitals with
their spins unpaired.
J. Mauritsson, P. Johnsson, E. Mansten, M. Swoboda, T. Ruchon, A. L’Huillier, and K. J.
Schafer, Coherent Electron Scattering Captured by an Attosecond Quantum
Stroboscope, PhysRevLett.,100.073003, 22 Feb. 2008
http://www.atto.fysik.lth.se/