Electromagnetic Radiation

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Electromagnetic Radiation

• Radiant energy that exhibits wave-like behavior
  and travels through space at the speed of light
  in a vacuum.

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Å (Angstrom)
?m
cm
m
km
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Waves

• Waves have 3 primary characteristics
• 1. Wavelength distance between two peaks in a
  wave.
• 2. Frequency number of waves per second that
  pass a given point in space.
• 3. Speed speed of light is 2.9979 ? 108 m/s.

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(No Transcript)
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Wavelength and frequency

• ? c/?
• ? frequency (s?1)
• ? wavelength (m)
• c speed of light (m s?1)

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Matter and Energy

• 1800s Matter can absorb or emit any quantity or
  energy
• Plancks discovery (1900) Energy can be gained
  or lost only in whole-number multiples of the
  quantity h?

DE h?
h Plancks constant 6.626 ? 10-34 J?s ?
frequency of electromagnetic radiation DE
energy step, quantum
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Quantized Electromagnetic Radiation

• Einstein proposed that electromagnetic radiation
• is quantized
• is a stream of particles called photons
• exhibits wave properties, wavelength and
  frequency
• exhibits particle properties, mass

hc ?
Ephoton h?
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Quantized Electromagnetic Radiation
Wave-like
Particle-like
hc ?
Ephoton h?
E mc2
Combining these to find mass with wave properties
h ?c
E c2
hc/ ? c2
m


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de Broglies Equation
Electromagnetic Radiation exhibits particle
properties
h ?c
m
Particles exhibit wave properties
A particle with velocity (?) has
h ??
h m?
m
?
rewritten
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Matter
All matter exhibits both particle and wave
properties

• Large pieces of matter (baseballs) exhibit
  predominantly particle properties

• Very small pieces of matter (photons) exhibit
• predominantly wave properties

• Medium pieces of matter (electrons) exhibit
  qualities of particles and waves

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H2 spectrum
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Bohr Model

• Electrons in a hydrogen atom move around the
  nucleus only in certain allowed circular orbits
• Energy levels of these orbits available for the
  electrons is

Z2 n2
E -2.178 ? 10-18 J
n 3
n 2
RH (Rydberg constant) 2.178 ? 10-18 J n
integer corresponding to orbit (larger orbit
larger number) Z nuclear charge ( of protons),
Z 1 for H
n 1
Bohr model for H
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Change in energy for electrons

• Excited electrons move to higher orbits and then
  fall back to lower orbits
• Lowest orbit is ground state, n1
• If electron is removed from the atom, n ?,
  therefore E? ? 0
• DE energy of final state energy of initial
  state

For hydrogen DE (-2.178? 10-18 J)
12 ninitial2
12 nfinal2
-
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H2 spectrum
Limitations of Bohr Model

• Spectral lines are broad (actually multiple
  wavelengths)
• Suggest finer division for electron energy/steps
• Some atoms showed continuous spectrum (nitrogen)
• Multiple electron atoms gave varying results in
  the visible spectrum

Hydrogen Visible Spectrum
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Heisenberg Uncertainty Principle

• Dx uncertainty in position
• D(mv) uncertainty in momentum
• h Plancks constant
• The more accurately we know a particles
  position, the less accurately we can know its
  momentum.

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Quantum Mechanics

• Schrödinger proposed an equation that contains
  both wave and particle terms.
• Solving the equation leads to wave functions
• The wave function is the shape of the electronic
  orbital (home of electron).
• The square of the wave function ?2, gives the
  probability of finding the electron.
• That is, it gives the electron density for the
  atom.

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Orbitals and Quantum Numbers

• Wave functions or orbitals describe a specific
  distribution of electron density in space
• Each orbital has characteristic shape and energy

Lowest energy orbit for hydrogen atom has an
energy of 2.18 ? 10-18 J (same as Bohr predicted)
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Quantum Mechanics and Atomic Orbitals

• If we solve the Schrödinger equation, we get wave
  functions and energies for the wave functions.
• We call wave functions orbitals.
• To solve Schrödingers equation, it requires 3
  quantum numbers and eventually a fourth quantum
  number was added
• Principal Quantum Number, n (energy steps)
• Angular Momentum Quantum Number, l (orbit shape)
• Magnetic Quantum Number, ml (orbit orientation)
• Electron Spin Quantum Number, ms (electron spin)

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Quantum Numbers (QN)The electrons address

• 1. Principal QN (n 1, 2, 3, . . .) - related
  to size and energy of the orbital.
• 2. Angular Momentum QN (l 0 to n ? 1) -
  relates to shape of the orbital.
• 3. Magnetic QN (ml l to ?l) - relates to
  orientation of the orbital in space relative to
  other orbitals.
• 4. Electron Spin QN (ms 1/2, ?1/2) - relates
  to the spin states of the electrons.

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Probability of finding an electron at a distance
from the nucleusNote Discrete breaks in
probability as you move out from nucleus
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Principle Quantum Number (n)

• Represents shells of electrons
• Related to size and energy of the orbital
• Larger number of electrons require more energy
  shells
• each row in the periodic table represents a new
  shell of electrons (n)

ie. Aluminum (Al) has three shells of electrons n
1, 2, 3
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Angular Momentum QN (l)
Relates to shape of orbital (subshell) l 0 to
(n-1)
l 0 s orbit
l 1 p orbit
l 2 d orbit
l 3 f orbit
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Angular Momentum QN (l)

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Magnetic QN (ml)

• Relates to orientation of orbital in space
  relative to other orbitals of equal energy
• ml l to -l

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Magnetic QN (ml)
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Electron Spin QN (ms)

• Relates to spin states of the electrons
• Two electrons per orbital one ½ and one ½

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Pauli Exclusion Principle

• In a given atom, no two electrons can have the
  same set of four quantum numbers (n, l, ml, ms).
• Therefore, an orbital can hold only two
  electrons, and they must have opposite spins.

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Aufbau Principle

• electrons are added from the inner shells out
  (low energy to high)
• Subshells with the same principle QN have equal
  energy degenerate orbitals

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Hunds Rule

• The lowest energy configuration for an atom is
  the one having the maximum number of unpaired
  electrons allowed by the Pauli principle in a
  particular set of degenerate orbitals.
• Pairing requires energy (repulsion)

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Quantum Numbers
Total electrons 28 Nickel has 28 es
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Practice with Quantum snote undefined s can
be anything within rule limits

• a.      How many electrons can be described by
  the quantum numbers n 4, l 4?
• b.      How many electrons can be described by
  the quantum numbers n 3, ml 1, ms½ ?
•  
• c.      How many orbitals can be described by the
  quantum numbers n 5, l 4?

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Orbital Energy Map
H 1 electron He 2 electrons Li 3
electrons Be 4 electrons B 5 elelctrons C 6
electrons N 7 electrons O 8 electrons F 9
electrons Ne 10 electrons Na 11 electrons Ar
18 electrons Ca 20 electrons Sc 21 electrons
d orbitals hold 10 e-
p orbitals hold 6 e-
s orbitals hold 2 e-
Note Each electron gets unique address
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Orbitals for outer electrons
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Writing Electron Configurations for Atoms

• Determine the of electrons
• Fill orbitals according to rules (periodic table
  as guide)
• Write out notation
• Number in front of letter indicates shell
• Letter indicates subshell
• Superscripted number indicates of electrons in
  that subshell
• Shorthand notation example
• examples N, Ne, Ca, Ni, Kr

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Valence Shell Electrons

• Outermost shell of electrons
• Usually involved in chemical reactions
• Ions are formed by adding or removing electrons
  from outershells
• Typically, all electrons after the last noble gas
• d and f blocks have exceptions
• Before full, 3d is higher in energy than 4s so we
  fill 4s first
• Once full, 3d is lower is energy than 4s so
  remove 4s first making the 4s electrons valence
  and not the 3d.
• examples N, Ne, Ca, Ni, Kr