The Atomic Theory and Electronic Structure

A Visual-Historical Approach

David A. KatzDepartment of ChemistryPima 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 (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.)

• 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 Marie-Anne 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

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

Jon Jakob Berzelius, 1813: Letters for element symbols

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 Chargecoulomb

Massg

Relative Charge

Relative Massamu

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

01 ore e−

−

11orp H+

10orn n

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

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)

“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

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

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 α-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 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 Roentgen1845-1923

Discovered x-rays - 1895

Barium platinocyanide

Henri Becquerel (1852-1908)Radiation activity, 1896

Image of potassium uranyl sulfate

Uranium nitrate

Marie Curie with inset photo of Pierre Curie

pitchblende

Radium bromide

Pierre Curie (1859-1906)Marie Curie (1867-1934)

Radioactivity- 1898Polonium - 1898Radium - 1898

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

Where m = an integer, 3, 4, 5, …

• In 1888, Johannes Rydberg generalized Balmer’s formula to calculate all the lines of the hydrogen spectrum

Where RH = 109677.58 cm-1

2

2 2364.56

2( )m

mλ =

−

2 22 1

1 1 1( )HR n nλ= −

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

Rearrange to

Substitute into Planck’s equation

From general relativity: e = mc2

Substitute for e and solve for λ

Light is composed of particles called photons

h

mcλ =

cνλ

=

ehc

λ=

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 byn = 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”

2( )hp n

π=

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

r = 53 pm

Bohr’s calculated radii of hydrogen energy levels r = n2A0

r = 4(53) pm = 212 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

r = 9 (53) pm = 477 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:

where RH = the Rydberg constant, 2.18 × 10−18 J,

and n1 and n2 are the initial and final energy levels of the electron.

2 22 1

1 1( )HE Rn n

∆ = −

• 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

and rewrote it as

where m = mass of an electron v = velocity of an electron

The Wave Nature of the Electron

h

mcλ =

h

mvλ =

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

The Wave Nature of the Electron

• 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

4

hx p

π∆ ×∆ ≥

4

hx p π∆×∆≥

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

d2Ψdy2

d2Ψdx2

d2Ψdz2

+ +8π2mΘ

h2(E-V(x,y,z)Ψ(x,y,z) = 0+

how ψ changes in space

mass of electron

total quantized energy of the atomic system

potential energy at x,y,zwave function

Quantum Mechanics

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.

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.)

magnetic mlintegers from -l to 0 to +l orbital orientation

spin ms+1/2 or -1/2 direction of e- spin

Solutions to the Schrodinger Wave EquationQuantum Numbers of Electrons in Atoms

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.

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

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 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

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

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

Em

pty su

bsh

ellsV

alence

sub

shells

Fu

ll su

bsh

ells

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 RuleFriedrich 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. 2008http://www.atto.fysik.lth.se/