WaveParticle Duality

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Wave-Particle Duality
JJ Thomson won the Nobel prize for describing the
electron as a particle.
His son, George Thomson won the Nobel prize for
describing the wave-like nature of the electron.
The electron is a particle!
The electron is an energy wave!
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• Properties of Light as a wave
• Light is called electromagnetic radiation
• Electromagnetic radiation form of energy which
  exhibits wave-like behavior as it goes through
  space
• Electromagnetic spectrum continuum of all of
  the forms of electromagnetic radiation
• Light has the characteristics of waves
• Wavelength distance between two crests or two
  troughs (symbol - ?, unit meters)
• Frequency the numbers of waves which passes a
  certain point in a certain amount of time (symbol
  ?, unit Hz (1 cycle/sec) (Hertz)
• All electromagnetic radiation has the same
  velocity which is 3.00 X 108 m/s (speed of light
  c)
• Therefore, c ? x ? indirect relationship

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Electromagnetic radiation moves through space as
a wave moving at the speed of light.
c ? ?
C speed of light, a constant (3.00 x 108 m/s)
? frequency, in units of hertz (Hz, cycles/sec)
(nu)
? wavelength, in meters (lambda)
As frequency increases, wavelength decreases and
vice versa.
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Types of electromagnetic radiation
Wavelength increases ?

• Frequency increases
• Energy Increases

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• The Photoelectric Effect (Light as a Particle)
• Certain interactions between light and matter
  could not be explained by the wave theory of
  light
• 1900, Max Planck performed experiments with the
  light coming off hot objects which showed us that
  light does not emit energy continuously as would
  be expected from a wave and proposed
• Energy is lost or gained in whole number
  multiples
• ?E nh? (energy of a quantum of electromagnetic
  radiation)
• (h Plancks constant 6.626 X 10-34 J-s)
• Planck said that light emitted energy in small
  packets called a quanta
• Quantum min. quantity of energy that can be
  lost or gained by an atom
• 1905, Albert Einstein showed us that the
  Photoelectric Effect revealed that light was
  indeed not just a wave, but was a particle of
  energy with a particle frequency which determined
  the energy of that particle

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• Electromagnetic radiation was now not just a wave
  but also a particle (wave-particle duality)
• Photon a particle of light (electromagnetic
  radiation) that has zero mass and the energy of a
  quantum
• Ephoton h? hc/? (energy of a photon) same a
  quantum)
• Photons can only be absorbed in whole number
  ratios basically all or none
• In order for an electron to be ejected from the
  surface of a metal, one photon alone must have
  the min. energy to knock the electron loose.

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The energy (E ) of electromagnetic radiation is
directly proportional to the frequency (?) of the
radiation.
E h?
E Energy, in units of Joules (kgm2/s2)
h Plancks constant (6.626 x 10-34 Js)
? frequency, in units of hertz (Hz)
The high the frequency of light or EM radiation,
the greater the energy of the waves.
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Energy and Mass

• Einstein Energy and mass are inter-related
• E mc2 h? hc/?
• de Broglie
• Light travels through space as a wave
• Light transmits energy as a particle
• Particle have a wavelength, exhibited by
  diffraction patterns (Davison and Germer
  electrons through a Nickel atom)
• ? h/mv (v velocity)
• Large particles have very short wavelengths but
  have a larger mass (such as a baseball)
• Small particle have a larger wavelength and a
  smaller mass (such as a electron)
• All matter exhibits both particle and wave
  properties

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Spectroscopic analysis of the visible spectrum
white light produces all of the colors in a
continuous spectrum
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Spectroscopic analysis of the hydrogen spectrum
produces a bright line spectrum or emission
spectrum
Each line in bright line spectrum represents a
different transition of electrons from an excited
state to the ground state
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• Hydrogen Atom Line-Emission Spectra
• Ground state lowest energy state of an atom
• Excited state energy level of higher potential
  energy
• When electricity is passed through a gas at low
  pressure, the electrons in the atoms move to
  excited states. When they return to the ground
  state, the excess energy is given off a light
  (ER) in the form of a photon
• When this light was sent through a prism, the
  scientists expected a continuous spectrum, but
  only got certain distinct wavelengths and
  frequencies of light made up the emitted light.
• This revealed that the energy states of a
  hydrogen electron must be distinct energy levels
  (specific values for the hydrogen atom)

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Electron transitionsinvolve jumps of definite
amounts ofenergy.
This produces bands of light with
definite Wavelengths each bands represents a
different transition
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The Bohr Model of the Atom
I pictured electrons orbiting the nucleus much
like planets orbiting the sun.
Niels Bohr

• Bohr's Hydrogen atom has an electron which runs
  like a train on isolated circular tracks.
• Photons are emitted or absorbed when the electron
  jumps from one track to another.

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• Bohr Model of the Atom
• 1913, Niels Bohr proposed that the electrons of
  an hydrogen atom have distinct energy states
  called orbits
• Electrons in these orbits have definite, fixed
  energies.
• En -RH (1/n2)
• n energy level (principle quantum )
• RH Rydberg constant 2.178X10-18 J
• Lowest energy level is closest to the nucleus
  lowest potential energy
• Potential energy is negative because it is less
  than if the electron were at an infinite distance
  or n 8
• Bohr said the at n 8, where there is no
  interaction with the nucleus and E 0

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• Bohr Model of the Atom
• Depending on the amount of energy absorbed by
  the atom, this would determine to what excited
  state that the electron would jump.
• The difference between the higher state and the
  ground state determined the energy, and
  therefore, the frequency and wavelength of the
  photons given off.
• ? hc/?E
• where
• Rydberg Equation -
• ?E -2.178X10-18 J (1/n2final 1/n2initial)
• Shortcomings of the Bohr Model
• Bohrs model only applied to Hydrogen
• Electrons do not move in circular orbits

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The Wave-like Electron
The electron moves through space as an energy
wave. To understand the atom, one must understand
the behavior of electromagnetic waves.
Quantum Mechanics study of electron moving as
waves with a specific amount of energy called a
quantum
Louis deBroglie
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The electron acts as a standing wave

• Standing waves do not move through space
• Standing waves are fixed at both ends like the
  strings on a guitar

Only certain sized orbits can contain the
electrons standing waves whole number energy
levels goes along with the idea of a quantum of
energy
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Wave-like Electrons
Electrons are confined to certain spaces in the
atom called orbitals Electrons travel around in
these spaces in a wave-like pattern.
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Schrödinger Wave Equation

• Electrons exist in regions called orbitals (? -
  wave function) 3D region around the nucleus
  that indicates the probable location of an
  electron
• His equation only provide the probability of
  finding an electron in a certain area.
• Orbitals are not circular orbits

Erwin Schrödinger
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Heisenberg Uncertainty Principle
One cannot simultaneously determine both the
position and momentum/velocity of an electron.

• ? x ?(mv) (h/4p)
• ? x uncertainty of position
• ?(mv) uncertainty of momentum
• The more accurately we know the position of any
  particle or electron, the less accurately we know
  it momentum and vice versa

Werner Heisenberg
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Quantum Numbers
Each electron in an atom has a unique set of 4
quantum numbers which describe its energy,
location, orientation, and spin in the atom.

• Principal quantum number energy level
• Angular momentum quantum number
• location/type of orbital
• Magnetic quantum number orientation
• Spin quantum number type of spin
• (/- ½)

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Pauli Exclusion Principle
No two electrons in an atom can have the same
four quantum numbers.
Each electron has a unique combination of quantum
numbers describing its energy level, type of
orbital, orientation, and spin.
Wolfgang Pauli
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Principal Quantum Number, (n)
Generally symbolized by n, it denotes the shell
(energy level) in which the electron is located.
Ex. n 1 , 1st energy level, lowest energy
Number of electrons that can fit in a shell
2n2
Number of orbitals that can fit in a shell
n2
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Principal Quantum Number, (n)

• Principal Quantum Number (n) indicates the
  main energy level occupied by the electron (n
  1, represents the lowest energy level)
  (1,2,3,4,)
• More than one electron can have the same n value
  they are said to be in the same electron shell
• Total of orbitals in a shell is equal to n2

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Angular Momentum Quantum Number, (l)
The angular momentum quantum number, generally
symbolized by l, denotes the orbital (subshell or
sublevel) in which the electron is located.
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Angular Momentum Quantum Number, (l)

• Angular Momentum Quantum Number - (l)
  indicates the shape of each orbital called
  sublevels (0, 1, 2, 3, n-1)
  Sublevel
• l 0 s
• 1 p
• 2 d
• 3 f

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Magnetic Quantum Number, (ml )
The magnetic quantum number, generally symbolized
by ml, denotes the orientation of the electrons
orbital with respect to the three axes in space.
(x, y, and z axes 3D coordinates)
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Magnetic Quantum Number, (ml )

• Magnetic Quantum Number (m) indicates the
  orientation of the orbital around the nucleus
• s m 0 (centered around nucleus)
• p m -1, 0, 1
• d m -2, -1, 0, 1, 2
• f m -3, -2, -1, 0, 1, 2, 3

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Spin Quantum Number, (ms)
Spin quantum number (ms) denotes the behavior
(direction of spin) of an electron within a
magnetic field.
Possibilities for electron spin
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Assigning the Numbers

• The first three quantum numbers (n, l, and m) are
  integers.
• The principal quantum number (n) cannot be zero
  n must be 1, 2, 3, etc.
• The angular momentum quantum number (l) can be
  any integer between 0 and n - 1.
• For n 3, l can be either 0, 1, or 2.
• The magnetic quantum number (m) can be any
  integer between -l and l.
• For l 2, m can be either -2, -1, 0, 1, or 2.

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Principle, angular momentum, and magnetic quantum
numbers n, l, and ml
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s orbital shape
s Orbital shape
The s orbital has a spherical shape centered
around the origin of the three axes in space.
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Sizes of s orbitals
Orbitals of the same shape (s, for instance) grow
larger as n increases
Nodes are regions where electrons are not likely
to exist.
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p Orbital shapes
There are three dumbbell-shaped p orbitals in
each energy level except n1, each assigned to
its own axis or has its own orientation (x, y
and z) in space.
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d orbital shapes
d Orbital shapes
Things get a bit more complicated with the five d
orbitals that are found in the d sublevels
beginning with n 3. To remember the shapes,
think of double dumbbells and a dumbbell
with a donut!

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f Orbital Shapes
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Rules in Writing Electron Configurations

• Aufbau Principle an electron occupies the
  lowest energy orbital that can receive it.
• Pauli Exclusion Principle each orbital can hold
  2 electrons
• Hunds Rule Orbitals of equal energy are each
  occupied by one electron before any orbital is
  occupied by a second electron, and all electrons
  in orbitals with one electron must have the same
  spin.
• Ex. ?_ ?_ __ ?_ ?_ ?_ ?? ?_ ?_
• 2p 2p
  2p

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Orbital filling table
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Electron configuration of the elements of the
first three series
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Irregular confirmations of Cr and Cu
Chromium steals a 4s electron to half fill its 3d
sublevel
Copper steals a 4s electron to FILL its 3d
sublevel
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Types of Notation

• Electron Configuration Notation Fe (Iron)
• 1s2 2s2 2p6 3s2 3p6 4s2 3d6
• Orbital Notation
• ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ??
  ? ? ? ?_
• 1s 2s 2p 3s 3p
  4s 3d
• Noble Gas Notation
• Ar 4s2 3d6
• (Refers back to the noble gas with the last
  filled outside energy level Argon is the noble
  gas in the row above Iron (Fe))

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Electron Configuration of Ions- Ions are formed
by losing electrons in the valence energy level

• Main group elements (s and p block elements)
  generally lose or gain electrons to become like a
  noble gas
• Ex. Na (loses 1 e-) ? Na (same electron
  configuration as Ne)
• Na 1s2 2s2 2p6 3s1 ? Na 1s2 2s2 2p6
• Transition elements form positive ions by first
  losing their outer s electrons then their outer d
  electrons
• Ex. Fe Ar 4s2 3d6 ? Fe2 Ar 3d6

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History of the Periodic Table

• Aristotle 400BC - divided substances into four
  categories Earth, Wind, Fire, Water
• Lavoisier 1770 Wrote 1st extensive list of
  elements (33) distinguished between metals and
  non-metals
• John Dalton first atomic masses calculated
  based on Hydrogen
• Berzelius - 1828 developed table based on
  atomic weights 1st to use chemical symbols
• Dobereiner Newlands developed 1st groupings
  of elements (similar to groups and periods on
  modern PT) triads groups of 3 elements with
  similar properties (Cl,Br,I)(S,Se,Te)(Ca,Sr,Ba)

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Mendeleevs Periodic Table
Dmitri Mendeleev
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History of the Periodic Table

• Dmitri Mendeleev 1860 Russian chemist who
  developed 1st formal periodic table 63 known
  elements
• Organization
• Horizontal rows (periods) in order of atomic mass
• Elements with similar properties under each other
  noted the pattern of similarities
• Left spaces for undiscovered elements predicted
  the existence of these elements later Scandium,
  Gallium, and Germanium
• Rearranged the table to accommodate similarities
  in properties Te/I switched because properties
  even though Te is heavier

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History of the Periodic Table

• Problems
• Elements did not fit in atomic mass order
• Why did elements exhibit periodic behavior or why
  did they have similar properties
• Henry Moseley 1914 used x-ray experiments to
  show the number of protons in each element
  (atomic number)
• Organized the periodic table in order of atomic
  number better fit the properties of the
  elements
• Explained the Te/I problem
• Periodic Law the physical and chemical
  properties of elements are a product of their
  atomic number

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History of the Periodic Table

• Modern Periodic Table
• Elements with similar properties fell in columns
  or groups (families) periodic (or found at
  regular intervals)
• William Ramsay 1890s discovered the noble
  (inert) gases
• Lanthanides 1900s identification of the Ce
  through Lu
• Actinides Glenn Seaborg 1940 discovered
  and/or synthesized elements Th through Lr
• Many other periodic tables were developed to help
  explain trends in the elements that had been
  discovered or synthesized.

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Periodic Table with Group Names
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Determination of Atomic Radius
Half of the distance between nuclei of identical
atoms that are bonded together.
Periodic Trends in Atomic Radius

• Radius decreases across a period

Greater attraction by the nucleus due to an
increase in protons and pos. charge in the
nucleus.

• Radius increases down a group

Addition of principal quantum (energy) levels,
electrons are farther from the nucleus
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Table of Atomic Radii
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Ionic Radii
Cations

• Positively-charged ions lost electrons

• Smaller than the corresponding
• atom
• Protons outnumber electrons
• Less shielding by inner electrons

Anions

• Negatively-charged ions gained electrons

• Larger than the corresponding
• atom
• Electrons outnumber protons
• Greater electron-electron repulsion

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Table of Ion Sizes

• Tends to decrease across a period within each
  orbital block difference between numbers of
  protons and electrons
• Tends to increase down a group

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Ionization Energy
Ion an atom or group of atoms that has lost or
gained electrons ( or charge) Ionization
process by which an atom loses or gains an
electron Ionization Energy - the energy required
to remove an electron from an atom
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Periodic Trends in Ionization Energy

• Increases for successive electrons taken from
• the same atom

• Tends to increase across a period

Atoms are getting smaller, electrons are closer
to the nucleus stronger hold on electrons

• Tends to decrease down a group

Outer electrons are farther from the nucleus,
shielded from nucleus by inner electrons lesser
hold on electrons

• Metals low ionization energies easily removed
• Sea of Electrons electrons shared by all
  metals atom, therefore not very tightly held
• Non-metals high ionization energies strong
  hold
• Noble gases very high ionization energies

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Ionization of Magnesium
Mg 738 kJ ? Mg e-
Mg 1451 kJ ? Mg2 e-
Mg2 7733 kJ ? Mg3 e-
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Table of 1st Ionization Energies
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Another Way to Look at Ionization Energy
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Electron Affinity The energy change associated
with the addition of an electron
Periodic Trends in Electron Affinity

• Affinity tends to increase across a period

As you go towards the nonmetals, the addition of
an electron makes the atom more stable and the
atom loses a large amount of energy Metals lose
less energy when an electron is added

• Affinity tends to decrease as you go down
• in a group

Electrons farther from the nucleus experience
less nuclear attraction
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Electronegativity
A measure of the ability of an atom in a
chemical compound to attract electrons

• Electronegativities tend to increase across
• a period

• Electronegativities tend to decrease down a
• group or remain the same

• Nonmetals characteristically high
  electronegativity - (Fluorine greatest) (upper
  right corner greatest)
• Metals characteristically low electronegativity
  - (Francium lowest) (lower left corner
  lowest)

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Periodic Table of Electronegativities
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Periodic Trends across the d- and f- Block
Elements

• Atomic radii very little increase in atomic
  radius across d- and f-block elements
• Ionization energy tends to increase across the
  d- and f-block elements
• Ion Formation electrons are removed from the
  outermost shell first meaning the s-electrons
  most form 2 ions (lose 2 s electrons)
• Ionic radii smaller than the regular elements
  form pos. ions therefore losing electrons and
  lose the outside orbital
• Electronegativity generally low as are other
  metals, increases as atomic radius decreases as
  you go towards the nonmetals