Section 5.3 Physics and Quantum Mechanical Model

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Section 5.3Physics and Quantum Mechanical Model

• The study of light led the development of the
  quantum mechanical model by Schrödingers.
• Isaac Newton believed that light consisted of
  particles.
• Scientists in the beginning of the 1900s
  believed that light consisted of waves.

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Parts of a Wave

• Amplitude height from zero to the crest.
• Wavelength (?) the distance between the crests.
• Frequency (?) the number of wave cycles to pass
  a given point per unit of time.
• Speed of light (c) equals the wavelength times
  the frequency

c ? ?
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• The wavelength and frequency of light are
  inversely proportional to each other.
• According to the wave model, light consists of
  electromagnetic waves.
• Electromagnetic radiation includes radio waves,
  microwaves, infrared waves, visible light
  ultraviolet waves, X-rays, and gamma rays.
• All electromagnetic waves travel in a vacuum at a
  speed of 2.998 X 108m/s.

c ? ?
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Color Spectrum

• Sunlight (white light) is a continuous range of
  wavelengths and frequencies.
• A prism, or rain droplets in the case of a
  rainbow, can separate each frequency of light
  into a spectrum of colors.
• Each color bends into the other in the order of
  red, orange, yellow, green, blue, and violet.
• ROY G BIV
• Which color in the visible spectrum has the
  longest wavelength?

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Practice ProblemCalculating the Wavelength of
Light

• Question
• What is the frequency of radiation which has a
  wavelength of 7.00 X 10-5 cm?
• In what region of the electromagnetic spectrum is
  this radiation?

• Answer
• 4.29 X 1014 s-1
• Infrared Spectrum

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Atomic Spectra

• When atoms absorb energy, electrons move into
  higher energy levels, and these electrons lose
  energy by emitting light when they return to
  lower energy levels.
• Unlike white light, the light emitted by atoms
  consists of a mixture of only specific
  frequencies, each of a particular color.
• Therefore, when light emitted by an element
  passes through a prism, it separates into
  discrete lines to give the atomic emission
  spectrum of that element.

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Atomic Emission Spectrum

• Each discrete line in an emission spectrum
  corresponds to one exact frequency of light
  emitted by the atom.
• Each emission spectrum is unique to that element.
  No two elements have the same spectrum.

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Niels Bohr

• The Bohr Model, was on of the first models to
  explain the emission spectrum of hydrogen, and
  predicted specific values of these frequencies.

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• In the Bohr models the lone electron of hydrogen
  can have only certain specific energies.
• The lowest energy is its ground state
• In the ground state the principle quantum number
  (n) is 1.
• Excitation of the electron by absorbing energy
  raises it from quantum from the ground state to
  an excited state with n 2, 3, 4, and so forth.

Ground State
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Emission of Light

• When the electron looses energy and drops back to
  a lower energy level, energy (in the form of
  light) is released.
• This happens in a single abrupt step called an
  electronic transition.

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Energy Equation

• The light emitted by an electron moving from a
  higher to a lower energy level has a frequency
  directly proportional to the energy change of the
  electron.
• Therefore, each each transition produces a line
  of specific frequency (?) in the spectrum

• Energy is related by
• E (h)(?)
• where h 6.626 X 10-34 J s plan
• ? frequency

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3 Groups of Lines Observed in the Emission
Spectrum of HydrogenRefer to Page 143 Figure 5.14

• Lyman Series
• Ultraviolet
• Energy value of electrons from higher energy
  levels to n 1
• Balmer Series
• Visible
• transitions from higher energy levels to n 2
• Paschen Series
• Infrared
• transitions from higher energy levels to n 3

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Questions

1. What is the name of the series of visible lines
   in the hydrogen spectrum?
2. Suppose an electron, in its ground state at n
   1, absorbs enough energy to jump to n 2. What
   type of radiation will it emit when it returns to
   the ground state?
3. If you observe a hydrogen gas discharge tube
   through a diffraction grating, could you see the
   line corresponding to this emission?
4. Which series of lines could human detect with our
   eyes?
5. Compare the energy of the Paschen and the Balmer
   series.
6. What do you notice about the spacing of the
   energy levels from n 1 to n 7?

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Quantum Mechanics

• Light is it a wave or a particle?
• Dual Wave-Particle Behavior of light
• The particle aspect (as explained by Einstein) of
  light, could be describe as a quanta of energy.
• Light quanta are called photons

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Photoelectric Effect

• Metals eject electrons called photoelectrons when
  light shines on them.
• Red light (? 4.3 X 1014 s-1 to 4.6 X 1014 s-1),
  will not cause the ejection of photoelectrons
  from potassium metal.
• Yellow light (? 5.1 X 1014 s-1 to 4.3 X 1014
  s-1) will.
• Intensity does not matter.

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De Broglie

• Reasoned that if light behaves as waves and
  particles, than particles of matter can also
  behave as waves.
• ? h (m)(?) where h
  planks constant (6.626 X 10-34 J s)
  m mass ? frequency
• Classical mechanics adequately describes the
  motions of bodies much larger than atoms, while
  quantum mechanics describes the motion of
  subatomic particles and atoms as waves.
• Using the above equation, the wavelength of a
  moving electron (mass of an electron is 9.11 X
  10-28g) and (moving at the speed of light) has a
  wavelength of about 2 X 10-10cm. (this is the
  size of a typical atom)

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Major Differences between Classical Mechanics and
Quantum Mechanics

1. Classical mechanics adequately describes the
   motions of bodies much larger than the atoms they
   comprise. It appears that such a body gains or
   loses energy in any amount.
2. Quantum mechanics describes the motions of
   subatomic particles and atoms as waves. These
   particles gain or lose energy in packages called
   quanta.

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Heisenberg Uncertainty Principle

• It is impossible to know exactly both the
  velocity and the position of a particle at the
  same time.
• Schrödinger used the wavelike motion of matter
  and the uncertainty principle in his electron
  cloud model of an atom which lead to the concept
  of electron orbitals and configurations.