Quantum Model of the Atom

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Quantum Model of the Atom
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Waves

• Waves are an oscillation that moves outward from
  a disturbance
• Waves transfer energy
• Example ripples moving away from a pebble
  dropped into a pond

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Electromagnetic Radiation
James Maxwell developed an elegant mathematical
theory in1864 to describe all forms of radiation
in terms of oscillating or wave-like electric and
magnetic fields in space.
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Wavelength (?) length between two successive
crests Frequency (?) number of cycles per
second that passes a certain point in space. (Hz
cycles per second) Amplitude maximum height
of a wave as measured from the axis of
propagation Nodes points of zero amplitude
always occur at ?/2 for sinusoidal waves
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Velocity speed of wave velocity ?? C
the speed of light 2.99792458 just call it 3 x
108 m/s ALL EM RADIATION TRAVELS AT THIS SPEED!
Notice that ? and ? are inversely proportional.
When one is large, the other is small.
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Properties of Waves
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Albert Einstein's Conclusions

• Einstein explained the photoelectric effect by
  concluding that energy travels as "packets" of
  energy called quanta.
• In other words, energy is not continuous.
• brighter light has more photons, but bluer light
  has higher energy photons
• frequency-to-energy conversion factor is h
  (Planck's constant, 6.62610-34 J/s)
• The energy of a photon in joules (J) may be
  calculated by using E h x ?

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Summary

• Energy is quantized.
• It can occur only in discrete energy units called
  quanta (h?).
• EM radiation (light, etc.) ehhibits wave and
  particle properties.
• This phenomenon is known as the dual nature of
  light.

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The collapsing atom paradox

• what's the electron doing in an atom?
• electrons within the atom can't be stationary
• positively charged nucleus will attract the
  negatively charged electron
• electron will accelerate towards the nucleus
• if electrons within the atom move,
• moving charges emit electromagnetic radiation
• emission will cause electrons to lose energy and
  spiral into the nucleus
• the atom will collapse!
• why don't atoms collapse?
• classical physics has no answer!
• key electrons have wave/particle duality

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Electrons as Waves

• DeBroglie came along and said if energy can
  behave like matter, matter should behave like
  energy, also known as the wave-particle duality
  of matter.
• When the calculations where done, the wave
  properties of matter could only be seen with very
  small bits of matter, i.e. an electron. Larger
  samples of matter had wavelengths too small to be
  observed.

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The de Broglie hypothesis

• connect wave and particle nature of matter using
  a relationship that applies to photons ? h/p
• where p is the momentum of the particle (p mass
  times velocity)

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Heisenburg's Uncertainty Principle

• It's impossible to know both the exact position
  and momentum of an electron at the same time.
• The location given for an electron is only
  PROBABLE (90)

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Electrons in Atoms

• the quantum theory is used to explain the origin
  of spectral lines and to describe the electronic
  structure of atoms.

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Emission Spectra

• experimental key to atomic structure analyze
  light emitted by high temperature elements. The
  example below emits a continuous spectrum which
  is not very useful. However..

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• samples single elements emit a characteristic
  set of discrete wavelengths- not a continuous
  spectrum!
• Atomic spectra can be used as a "fingerprint" for
  an element

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Hydrogens Atomic Line Spectra and Neils Bohr
Emission spectrum the collection of frequencies
of light given off by an excited electron Line
spectrum isolate a thin beam by passing through
a slit then a prism or a diffraction grating
which sorts into discrete frequencies or lines.
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Hydrogen Spectra
emission
absorption
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Why atoms emit or absorb only certain wavelengths

• if atoms emit only discrete wavelengths, maybe
  atoms can have only discrete energies
• an analogy A turtle sitting on a ramp can have
  any height above the ground- and so, any
  potential energy

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• A turtle sitting on a staircase can take on only
  certain discrete energies
• energy is required to move the turtle up the
  steps (absorption)
• energy is released when the turtle moves down the
  steps (emission)
• only discrete amounts of energy are absorbed or
  released (energy is said to be quantized)

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• bottom step is called the ground state
• higher steps are called excited states
• Atoms absorbing energy causes electrons to jump
  to the excited state. When they return to the
  ground state, they emit energy (light).

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The Quantum model of the Atom

• The study of how atoms emit light when excited,
  lead to the quantum model.
• Like the Bohr model, the quantum model has energy
  levels that contain electrons.
• However, these electrons do not follow a fixed
  path but occupy a 3D volume called an orbital
  based on a probability of 90. The exact position
  of a particular electron is unknown.

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Schroedingers Wave equation

• To find the probable location of an electron
  Schroedinger treated the electron as if it
  traveled as a wave. His wave equation showed
• 1) Electrons probable locations known as
  ORBITALS
• 2) The motion of the electron covers an area
  called an ELECTRON CLOUD.

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• To "solve" Schroedinger's wave equation 4
  parameters must be known. These are called
  QUANTUM NUMBERS (n, l, m, s)
• These four numbers are like the address of an
  electron and may be used to identify any electron
  in an atom.

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• 1) principle quantum number (n)
• what energy level the electron is in and
  probable distance from the nucleus
• the larger the number, the farther away from the
  nucleus
• Each principle energy level is composed of
  sub-energy levels. There are the same number of
  sub-energy levels as the principle energy level
• n1 one sub-energy level
• n2 two sub-energy levels
• n3 three sub-energy levels

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• 2) Sub-energy (orbital) quantum number (l)
• Indicates the shape of the orbital an electron
  occupies.
• lowest energy s sphere
• p dumbbell
• d x-shaped or figure eight
• highest energy f complex

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Orbital shapes

• s orbital (one possible orientation)

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• P orbital ( three possible orientations)

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• d orbital ( five possible orientations)

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• f orbital (seven possible orientations)

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• 3) Magnetic quantum number (m)
• indicates how the orbital is arranged in space.
• Each sub-energy level may have the following
  number of arrangements (orientations).
• s has 1 orbital arrangements
• p has 3 orbital arrangements
• d has 5 orbital arrangements
• f has 7 orbital arrangements
• (notice a pattern?)

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• 4) Spin quantum number (s)
• indicates the direction an electron spins.
  (clockwise or counterclockwise)
• allows 2 electrons into each orbital

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• The maximum number of electrons in a principle
  energy level is found by 2n2
• The maximum number of orbitals in a principle
  energy level is found by n2.
• Pauli exculsion principle - an atomic orbital
  may contain at most 2 electrons (some may have
  only 1) this is the basis of the spin quantum
  number
• Hund's rule When electrons enter orbitals of
  equal energy (same n,l), one electron enters each
  orbital until all the orbitals contain one
  electron with parallel spins.

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Writing electron configurations

• When writing electron configurations for atoms,
  the aufbau principle must be used.
• Aufbau literally means build-up in German. This
  means electrons fill atoms from the lowest to
  highest energy levels.

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• The diagonal rule tells you the order in which to
  place (or build) the electrons in an atom

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Periodic Table and Electron Configuration