Atomic Structure

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Atomic Structure
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Wave-Particle Duality
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The Wave Nature of Light

• All waves have a characteristic wavelength, l,
  and amplitude, A.
• Frequency, n, of a wave is the number of cycles
  which pass a point in one second.
• Speed of a wave, c, is given by its frequency
  multiplied by its wavelength
• For light, speed c 3.00x108 m s-1 .
• The speed of light is constant!
• Higher Quality video (230 sec into video).

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The Wave Nature of Light
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The Wave Nature of Light
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The Wave Nature of Light
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Quantized Energy and Photons

• Planck energy can only be absorbed or released
  from atoms in certain amounts called quanta.
• The relationship between energy and frequency is
• where h is Plancks constant ( 6.626 ? 10-34 J s
  ) .

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Quantized Energy and Photons

• The Photoelectric Effect and Photons
• Einstein assumed that light traveled in energy
  packets called photons.
• The energy of one photon is

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Nature of Waves Quantized Energy and Photons
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Line Spectra and the Bohr Model

• Line Spectra
• Radiation composed of only one wavelength is
  called monochromatic.
• Radiation that spans a whole array of different
  wavelengths is called continuous.
• White light can be separated into a continuous
  spectrum of colors.
• Note that there are no dark spots on the
  continuous spectrum that would correspond to
  different lines.

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Line Spectra and the Bohr Model

• Bohr Model
• Colors from excited gases arise because electrons
  move between energy states in the atom.
  (Electronic Transition)

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Line Spectra and the Bohr Model

• Bohr Model
• Since the energy states are quantized, the light
  emitted from excited atoms must be quantized and
  appear as line spectra.
• After lots of math, Bohr showed that
• where n is the principal quantum number (i.e., n
  1, 2, 3, and nothing else).

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Line Spectra and the Bohr Model

• Bohr Model
• We can show that
• When ni gt nf, energy is emitted.
• When nf gt ni, energy is absorbed

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Line Spectra and the Bohr Model
Bohr Model
Mathcad (Balmer Series)
CyberChem (Fireworks) video
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Line Spectra and the Bohr Model Balmer Series
Calculations
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Line Spectra and the Bohr Model Balmer Series
Calculations
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Line Spectra and the Bohr Model

• Limitations of the Bohr Model
• Can only explain the line spectrum of hydrogen
  adequately.
• Can only work for (at least) one electron atoms.
• Cannot explain multi-lines with each color.
• Electrons are not completely described as small
  particles.
• Electrons can have both wave and particle
  properties.

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The Wave Behavior of Matter

• Knowing that light has a particle nature, it
  seems reasonable to ask if matter has a wave
  nature.
• Using Einsteins and Plancks equations, de
  Broglie showed
• The momentum, mv, is a particle property, whereas
  ? is a wave property.
• de Broglie summarized the concepts of waves and
  particles, with noticeable effects if the objects
  are small.

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The Wave Behavior of Matter

• The Uncertainty Principle
• Heisenbergs Uncertainty Principle on the mass
  scale of atomic particles, we cannot determine
  exactly the position, direction of motion, and
  speed simultaneously.
• For electrons we cannot determine their momentum
  and position simultaneously.
• If Dx is the uncertainty in position and Dmv is
  the uncertainty in momentum, then

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Energy and Matter
E m c2
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Quantum Mechanics and Atomic Orbitals

• Schrödinger proposed an equation that contains
  both wave and particle terms.
• Solving the equation leads to wave functions.
• The wave function gives the shape of the
  electronic orbital. Shape really refers to
  density of electronic charges.
• The square of the wave function, gives the
  probability of finding the electron ( electron
  density ).

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Quantum Mechanics and Atomic Orbitals
Solving Schrodingers Equation gives rise to
Orbitals. These orbitals provide the electron
density distributed about the nucleus. Orbitals
are described by quantum numbers.
Sledge-O-Matic- Analogy
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Quantum Mechanics and Atomic Orbitals

• Orbitals and Quantum Numbers
• Schrödingers equation requires 3 quantum
  numbers
• Principal Quantum Number, n. This is the same as
  Bohrs n. As n becomes larger, the atom becomes
  larger and the electron is further from the
  nucleus. ( n 1 , 2 , 3 , 4 , . )
• Angular Momentum Quantum Number, ?. This quantum
  number depends on the value of n. The values of
  ? begin at 0 and increase to (n - 1). We usually
  use letters for ? (s, p, d and f for ? 0, 1,
  2, and 3). Usually we refer to the s, p, d and
  f-orbitals.
• Magnetic Quantum Number, m?. This quantum number
  depends on ? . The magnetic quantum number has
  integral values between - ? and ? . Magnetic
  quantum numbers give the 3D orientation of each
  orbital.

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Quantum Numbers of Wavefuntions
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Quantum Mechanics and Atomic Orbitals
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Quantum Mechanics and Atomic Orbitals

• Orbitals and Quantum Numbers

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Representations of Orbitals
The s-Orbitals
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Representations of Orbitals
The p-Orbitals
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d-orbitals
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Orbitals and Their Energies
Orbitals CD
Many-Electron Atoms
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Many-Electron Atoms
Electron Spin and the Pauli Exclusion Principle
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Many-Electron Atoms

• Electron Spin and the Pauli Exclusion Principle
• Since electron spin is quantized, we define ms
  spin quantum number ? ½.
• Paulis Exclusions Principle no two electrons
  can have the same set of 4 quantum numbers.
• Therefore, two electrons in the same orbital must
  have opposite spins.

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Figure 6.27
Orbitals CD
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Orbitals CD
Figure 6.28
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Orbitals and Their Energies
Orbitals CD
Many-Electron Atoms
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Electron Configurations
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Electron Configurations
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Metals, Nonmetals, and Metalloids
Metals
Figure 7.14
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Periodic Trends

• Two Major Factors
• principal quantum number, n, and
• the effective nuclear charge, Zeff.

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Figure 7.5 Radius video Clip
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Figure 7.6
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Figure 7.10 IE clip
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Figure 7.9
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Electron Affinities

• Electron affinity is the opposite of ionization
  energy.
• Electron affinity the energy change when a
  gaseous atom gains an electron to form a gaseous
  ion
• Cl(g) e- ? Cl-(g)
• Electron affinity can either be exothermic (as
  the above example) or endothermic
• Ar(g) e- ? Ar-(g)

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Figure 7.11 Electron Affinities
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Group Trends for the Active Metals
Group 1A The Alkali Metals
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Group Trends for the Active Metals
Group 2A The Alkaline Earth Metals
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Group Trends for Selected Nonmetals
Group 6A The Oxygen Group
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Group Trends for Selected Nonmetals
Group 7A The Halogens
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Group Trends for the Active Metals

• Group 1A The Alkali Metals
• Alkali metals are all soft.
• Chemistry dominated by the loss of their single s
  electron
• M ? M e-
• Reactivity increases as we move down the group.
• Alkali metals react with water to form MOH and
  hydrogen gas
• 2M(s) 2H2O(l) ? 2MOH(aq) H2(g)

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Group Trends for the Active Metals

• Group 2A The Alkaline Earth Metals
• Alkaline earth metals are harder and more dense
  than the alkali metals.
• The chemistry is dominated by the loss of two s
  electrons
• M ? M2 2e-.
• Mg(s) Cl2(g) ? MgCl2(s)
• 2Mg(s) O2(g) ? 2MgO(s)
• Be does not react with water. Mg will only react
  with steam. Ca onwards
• Ca(s) 2H2O(l) ? Ca(OH)2(aq) H2(g)

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Atomic Structure