Review: Why Atoms?

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Review Why Atoms?

• Chemical combination rules (Dalton)
• Success of kinetic theory in describing behavior
  of matter
• Predictions that follow from the theory are
  confirmed, although atoms are not directly
  observed
• Brownian motion
• A way of seeing atoms directly
• Again, predictions based on atomic theory are
  confirmed by experiments
• X-ray diffraction
• Studied in detail in the early 20th century

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How Big are They?

• Clearly, very small!
• Too small to be visible in the best optical
  microscopes
• Microscopes can only resolve an object that is
  comparable in size or larger than the wavelength
  of the light used to illuminate it
• For visible light, the smallest structures that
  can be seen are about 400 nanometers, or 4 ? 107
  m
• Atoms must be smaller than this!

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What is Light?

• Light is a type of wave
• Other common examples water waves, sound
• A wave is a disturbance in a medium (water, air,
  etc.) that propagates
• Typically the medium itself does not move much

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Anatomy of a Wave
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Electromagnetic Waves

• Medium the electric and magnetic field
• Speed 3 ? 105 km/sec (about 186,000 mi/sec)

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The Electromagnetic Spectrum
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Visible Light

• The color of visible light is determined by its
  wavelength
• White light is a mixture of all colors
• We can separate out individual colors with a prism

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Visible Light

• 400440 nm Violet
• 440480 nm Blue
• 480530 nm Green
• 530590 nm Yellow
• 590630 nm Orange
• 630700 nm Red
• 1 nm 1 nanometer
• 109 m

Longer wavelength
Shorter wavelength
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Superposition and Interference

• When several waves pass through the same place,
  the total wave is obtained by adding together the
  individual wave displacements (Principle of
  Superposition)

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X-Ray Diffraction

• X-rays have wavelengths comparable to atomic
  sizes
• We can see atoms and molecules by bouncing
  X-rays off them
• Crystals and molecules reflect X-rays in patterns
  depending on their structures
• From the reflection pattern one can figure out
  the structure!

X-ray diffraction pattern of DNA
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Interaction of X-Rays with Atoms

• Involves the electrons, primarily

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More Information

• Intensities (brightness) of diffraction maxima
  can vary more information about detailed
  structure
• The symmetry of the crystal structure is
  reflected in the diffraction pattern

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So, How Big are They?

• Earliest estimate Johann Loschmidt (1865)
• Used results from kinetic theory to estimate the
  size of an air molecule
• We no know there are several types of molecules
  present in air
• They are roughly the same size, though!
• His result was about one millionth of a
  millimeter
• In other words, about 103 m/106 or 109 m
• This is about 400 times smaller than the smallest
  object visible in an optical microscope

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Brownian Motion

• Discovered in 1828 by Robert Brown, a Scottish
  botanist
• He observed that microscopic pollen grains
  suspended in a liquid move around erratically,
  even though the liquid itself has no observable
  motion
• Explanation the grains are being jostled and
  buffeted by unseen atoms
• The smaller the grain, the more violently it is
  agitated

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Size of Atoms

• In 1905, Einstein worked out several predictions
  regarding Brownian motion using atomic theory
• Confirmed by Jean Perrin (1908)
• Nobel Prize for Physics 1926
• Based on his measurements, Perrin gave an
  accurate estimate of the size of atoms about 1-2
  ? 1010 m
• The atomic scale is about a tenth of a nanometer

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Avogadros Hypothesis

• Equal volumes of gases under the same conditions
  of temperature and pressure have equal numbers of
  molecules
• Derived from the observations by Gay-Lussac and
  others
• gases unite in simple proportions by volume
• if a reaction of two gases produces a gas, the
  volume of gas produced is also related by a
  simple proportion
• He also proposed that some gases (like oxygen and
  hydrogen) are not made up of single atoms
• Why werent his idea quickly accepted?
• they indicated that Daltons atomic weights were
  wrong
• there was no agreement as to what a molecule
• he was not a particularly accomplished
  experimentalist

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Loschmidts Number

• Avogadros Hypothesis predicts that one cubic
  centimeter of any gas under standard conditions
  will always contain the same number of molecules
• Avogadro, however, never calculated this number
  (he had neither the experimental or theoretical
  background to accomplish this)
• The first estimate of this quantity was made by
  Loschmidt in 1865 from the kinetic theory of
  gases
• (Cannizzaro first promoted Avogadros ideas at
  the Karlsruhe Conference of Chemists in 1860)

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Avogadros Number

• Chemists prefer to use what we now call
  Avogadros Number for many calculations
• Avogadros number is the number of oxygen (O2)
  molecules in 32 grams of oxygen, or the number of
  H2 molecules in 2 grams of H2or the number of
  molecules per mole of molecules
• It is an honorary name (first used by Perrin in
  1909) still called Loschmidts Number in
  Germany
• NA 6.022 x 1023 (atoms or molecules) per mole

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Estimating Avogadros Number