The Atomic Theory and Electronic Structure A Visual-Historical Approach

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The Atomic Theory and Electronic StructureA
Visual-Historical Approach

• David A. Katz
• Department of Chemistry
• Pima Community College
• Tucson, AZ U.S.A.
• Voice 520-206-6044 Email dkatz_at_pima.edu
• Web site http//www.chymist.com

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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.

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• 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).

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• 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.

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• 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
  (460-370 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.)

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• 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

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• 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 calld 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.

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• Sir Isaac Newton (1642 -1727)
• Modified atomic theory to atoms as hard particles
  with forces of attraction between them

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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

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• 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

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• Antoine Laurent Lavoisier (1743-1794) (and
  Marie-Anne Pierrette Paulze Lavoisier
  (1758-1836)?)
• Nature of combustion, 1777
• Elements in Traité élémentaire de chemie, 1789

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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.

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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

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Daltons symbols, 1808
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Daltons atomic weights, 1808
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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
Muriatic radicle (chlorine) M Columbium (nioblium) Cl Copper Cu Glucinum (beryllium) Gl
Fluoric radicle 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 Ch Gold Au Manganese Ma
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Pieces of Atoms the electron

• Heinrich Geissler (1814-1879)
• Julius Plücker (1801-1868)
• Evacuated tube glowed, 1859
• Rays affected by a magnet

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• Johann Wilhelm Hittorf (1824-1914)
• Maltese cross tube, 1869
• Rays travel in straight line
• Cast shadows of objects

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• William Crookes (1832-1919)
• Verified previous observations, 1879
• Caused pinwheel to turn
• Composed of particles
• Have negative charge

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• Joseph John Thomson (1846-1940)
• e/m -1.759 x 108 coulomb/gram - 1897

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• Robert Millikan (1868-1923)
• Oil drop experiment 1909
• e -1.602 x 10-19 coulomb
• N 6.062 x 1023 molecules/g-molecule

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Pieces of Atoms the proton

• Eugen Goldstein (1850-1930)
• Canal rays - 1886

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Pieces of Atoms the neutron

• James Chadwick (1891-1974)
• Discovered the neutron 1932

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The Subatomic Particles
Particle Symbol Charge coulomb Mass g Relative Charge Relative Mass amu
electron -1.602 x 10-19 9.109 x 10-28 -1 0.0005486 0
proton 1.602 x 10-19 1.673 x 10-24 1 1.0073
neutron 0 1.675 x 10-24 0 1.0087
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Models of the Atom

• Philipp Lenard (1862-1947)
• Dynamids 1903
• Hantaro Nagaoka (1865-1950)
• Saturnian model - 1904

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• J. J. Thomson
• Plum pudding 1904
• Partly based on A. M. Mayers (1836-1897)
  floating magnet experiment

A. M. Mayer
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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 liquidair interface,
Nature 405, 1033-1036 (29 June 2000)
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• 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
alpha-particles 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
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• 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 a-particles
  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 a 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)

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• 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

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• 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

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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)
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Radioactivity and Stability of the nucleus
Wilhelm Conrad Roentgen 1845-1923 Discovered
x-rays - 1895
Barium platinocyanide
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• Henri Becquerel (1852-1908)
• Radiation activity, 1896

Uranium nitrate
Image of potassium uranyl sulfate
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Pierre Curie (1859-1906) Marie Curie
(1867-1934) Radioactivity- 1898 Polonium -
1898 Radium - 1898
pitchblende
Radium bromide

• Marie Curie with inset photo of Pierre Curie

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• Ernest Rutherford (1871-1937)
• a, ß, ? - 1903

In his lab at McGill University, 1903
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Glenn T. Seaborg (1912-1999)
Extending the periodic table
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Spectra
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The Electromagnetic Spectrum
Viewing spectra using holographic diffraction
grating (Flinn Scientific C-Spectra)
Hydrogen spectrum
Helium spectrum
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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
• Where m an integer, 3, 4, 5,
• In 1888, Johannes Rydberg generalized Balmers
  formula to calculate all the lines of the
  hydrogen spectrum
• Where RH 109677.58 cm-1

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The Quantum Mechanical Model

• Max Planck (1858 -1947)
• Blackbody radiation 1900
• Light is emitted in bundles called quanta.
• e h?
• 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.
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The Quantum Mechanical Model

• Albert Einstein (1879-1955)
• The photoelectric effect 1905
• Plancks equation e h?
• Equation for light c ??
• Rearrange to
• Substitute into Plancks equation
• From general relativity e mc2
• Substitute for e and solve for ?
• Light is composed of particles called photons

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The Bohr Model - 1913

• Niels Bohr (1885-1962)

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The Bohr Model Bohrs 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

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The Bohr Model Bohrs Postulates

• The Angular momentum is given by
• n an integer 1, 2, 3,
• h Plancks constant
• Two different states of the electron in the atom
  are involved. These are called allowed
  stationary states

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The Bohr Model Bohrs Postulates

• The Planck-Einstein equation, E h? 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
• h? E1 E2
• ? frequency of the spectral line
• E energy of the allowed stationary state
• 8. We cannot visualize or explain, classically
  (i.e., according to Newtons Laws), the behavior
  of the active electron during a transition in the
  atom from one stationary state to another

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Bohrs 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 r 49(53) pm 1908
pm 2597 pm
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• Lyman Series
• 
  Balmer Series
• 
  Paschen Series
• 
  
• 
  Brackett Series
• 
  Pfund
  Series
• 
  Humphreys Series

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The Bohr Model

• The energy absorbed or emitted from the process
  of an electron transition can be calculated by
  the equation
• where
• RH the Rydberg constant, 2.18 ? 10-18 J,
• and
• n1 and n2 are the initial and final energy
  levels of the electron.

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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 Einsteins equation
• and rewrote it as
• where m mass of an electron
• v velocity of an electron

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The Wave Nature of the Electron

• Clinton Davisson (1881-1958 ) and Lester Germer
  (1886-1971)
• Electron waves - 1927

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• 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.
• 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

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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 ?

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Quantum Mechanics

• The square of the wave equation, ?2, gives a
  probability density map of where an electron has
  a certain statistical likelihood of being at any
  given instant in time.

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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.

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Solutions to the Schrodinger Wave
Equation Quantum Numbers of Electrons in Atoms
Name
Symbol
Permitted Values
Property
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Looking at Quantum NumbersThe 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.

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Looking at Quantum NumbersThe Azimuthal Quantum
Number, l

• The azimuthal (or angular momentum) quantum
  number tells the electrons 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
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Looking at Quantum NumbersThe 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.

Value of l Orbital (subshell) Letter designation Orbital Shape Name
0 s sharp
1 p principal
2 d diffuse
3 f fine
From emission spectroscopy terms
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Looking at Quantum NumbersThe 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 designation Number of 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
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Quantum Numbers and Subshells

• Orbitals with the same value of n form a shell
• Different orbital types within a shell are called
  subshells.

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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)

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A Summary of Atomic Orbitals from 1s to 3d
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Empty subshells
Valence subshells
Full subshells

• Approximate energy levels for neutral atoms.
• From Ronald Rich, Periodic Correlations, 1965

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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.

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• Otto Stern (1888-1969) and Walther Gerlach
  (1889-1979)
• Stern-Gerlach experiment, 1922

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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.

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• 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.

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Hunds Rule

• Friedrich Hund (1896 - 1997)
• For degenerate orbitals, the lowest energy is
  attained when the electrons occupy separate
  orbitals with their spins unpaired.

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J. Mauritsson, P. Johnsson, E. Mansten, M.
Swoboda, T. Ruchon, A. LHuillier, and K. J.
Schafer, Coherent Electron Scattering Captured by
an Attosecond Quantum Stroboscope,
PhysRevLett.,100.073003, 22 Feb.
2008http//www.atto.fysik.lth.se/