Chapter 7: Quantum theory of the atom

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Chapter 7 Quantum theory of the atom
Chemistry 1061 Principles of Chemistry I Andy
Aspaas, Instructor
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Atomic emission and line spectra

• When different compounds are burned, they give
  off surprisingly different colors of light
• It can be used to identify certain compounds
• If the emitted light is sent through a prism so
  the colors are separated, only certain discrete
  colors of light are given off (atomic line
  spectrum)
• The color of light can be related to the amount
  of energy that light contains

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The wave nature of light

• Electromagnetic radiation energy that is in the
  form of a wave, (visible light, x-rays, radio
  waves, etc)
• Wavelength, ? distance between any two adjacent
  identical points of a wave
• Visible light, wavelength measured in nm
• Radio waves can be measured in m
• Frequency, ? (nu) number of wavelengths that
  pass a fixed point in one unit of time (usu. 1
  second)

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Electromagnetic spectrum
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Frequency and wavelength

• All electromagnetic waves travel at the speed of
  light, c 3.00 x 108 m/s
• c ??, if ? is in m, and ? is in sec-1
• Visible light wavelengths are always given in nm,
  between 400 and 800 nm
• Frequency is usually given in sec-1, or Hz

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The particle nature of light

• While light has wave-like properties, it also has
  particle-like properties
• Photon discreet particles of energy which make
  up light (or any electromagnetic radiation)
• The energy of one photon of light is related to
  the frequency of that light
• E h?
• (where h is Plancks constant, 6.63x10-34 Js)
• This relates the wave-like and particle-like
  properties of light

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More about atomic line spectra

• Heated solid metals emit light of all
  wavelengths, or a continuous spectrum
• Would form a rainbow if sent through a prism
• Heated gases emit light of only particular
  wavelengths, or a line spectrum
• Would form only lines of particular colors if
  sent through a prism
• These lines are associated with energy level
  transitions

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Energy levels

• Electrons can have only specific energy values in
  an atom (energy levels)
• Energy levels are quantized (only specific
  allowed values)
• When an electron absorbs energy from the
  environment, it can be promoted to a higher
  energy level
• In order for it to return to a lower level,
  energy must be released in the form of a single
  photon
• Depending on which levels this transition
  involves, the photon will have a different amount
  of energy

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H atom energy level calculations

• Energy levels are numbered with integers starting
  with 1, symbol is n
• n 1, 2, 3,
• The energy of a particular level is given by
• E -(RH) / (n2) where RH 2.179 x 10-18 J
• The energy of a photon given off can be
  calculated by subtracting the lower energy level
  from the higher energy level (energy of a photon
  is positive)

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Quantum mechanics

• Just like light can be wave-like and
  particle-like, so can electrons
• The most accurate description of an electrons
  behavior is using a wave-like interpretation,
  this is known as quantum mechanics
• An electron can be described by a wavefunction
  an equation for the wave that represents an
  electron
• Only the probability of an electron appearing in
  a certain place can be calculated
• Heisenberg uncertainty principle says the more
  precisely you know the position of a small
  particle, the less precisely you know its momentum

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Atomic orbitals

• The 3-dimensional space in which there is a high
  probability of finding an electron in an atom is
  referred to as an atomic orbital
• Can be described by three quantum numbers
• Principal quantum number, n refers to the energy
  of an electron, it also associates with the size
  of an orbital (n 1, 2, 3, 4,)

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Atomic orbitals

• Angular momentum quantum number, l indicates
  shape of orbital (l 0, 1, 2, 3, . n-1)
• Usually shown by letters s, p, d, f, and g
• Magnetic quantum number, ml Distinguishes
  orbitals of same shape but different position
  (ml integers from l to l)
• Spin quantum number, ms indicates which of 2
  possible spin states an electron is in, equal to
  either -1/2 or 1/2

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Permissible atomic orbitals for n 1, 2, 3
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Atomic orbital shapes