Wave-Particle Duality

							       Wave-Particle Duality
• Last time we discussed several situations in
  which we had to conclude that light behaves
  as a particle called a photon with energy
  equal to hf
• Earlier, we discussed interference and
  diffraction which could only be explained
  by concluding that light is a wave
• Which conclusion is correct?
        Wave-Particle Duality
• The answer is that both are correct!!
• How can this be???
• In order for our minds to grasp concepts we build
  models
• These models are necessarily based on things we
  observe in the macroscopic world
• When we deal with light, we are moving into the
  microscopic world and talking about electrons and
  atoms and molecules
       Wave-Particle Duality
• There is no good reason to expect that what
  we observe in the microscopic world will
  exactly correspond with the macroscopic
  world
• We must embrace Niels Bohr’s Principle of
  Complementarity which says we must use
  either the wave or particle approach to
  understand a phenomenon, but not both!
        Wave-Particle Duality
• Bohr says the two approaches complement
  each other and both are necessary for a full
  understanding
• The notion of saying that the energy of a
  particle of light is hf is itself an expression
  of complementarity since it links a property
  of a particle to a wave property
       Wave -Particle Duality
• Why must we restrict this principle to light
  alone?
• Might microscopic particles like electrons
  or protons or neutrons exhibit wave
  properties as well as particle properties?
• The answer is a resounding YES!!!
       Wave Nature of Matter
• Louis de Broglie proposed that particles
  could also have wave properties and just as
  light had a momentum related to
  wavelength, so particles should exhibit a
  wavelength related to momentum

                  h
               
                  mv
      Wave Nature of Matter
• For macroscopic objects, the wavelengths
  are terrifically short
• Since we only see wave behavior when the
  wavelengths correspond to the size of
  structures (like slits) we can’t build
  structures small enough to detect the
  wavelengths of macroscopic objects
       Wave Nature of Matter
• Electrons have wavelengths comparable to
  atomic spacings in molecules when their
  energies are several electron-volts (eV)
• Shoot electrons at metal foils and amazing
  diffraction patterns appear which confirm
  de Broglie’s hypothesis
        Wave Nature of Matter
• So, what is an electron? Particle? Wave?
• The answer is BOTH
• Just as with light, for some situations we need to
  consider the particle properties of electrons and
  for others we need to consider the wave properties
• The two aspects are complementary
• An electron is neither a particle nor a wave, it just
  is!
Electron Microscopes
         Models of the Atom
• It is clear that electrons are components of
  atoms
• That must mean there is some positive
  charge somewhere inside the atom so that
  atoms remain neutral
• The earliest model was called the “plum
  pudding” model
Plum Pudding Model
       We have a blob of positive charge
       and the electrons are embedded in
       the blob like currants in a plum
       pudding.
       However, people thought that the
       electrons couldn’t just sit still
       inside the blob. Electrostatic forces
       would cause accelerations. How
       could it work?
       Rutherford Scattering
• Ernest Rutherford undertook experiments to
  find out what atoms must be like
• He wanted to slam some particle into an
  atom to see how it reacted
• You can determine the size and shape of an
  object by throwing ping-pong balls at the
  object and watching how they bounce off
• Is the object flat or round? You can tell!
         Rutherford Scattering
• Rutherford used alpha particles which are the
  nuclei of helium atoms and are emitted from some
  radioactive materials
• He shot alphas into gold foils and observed the
  alphas as they bounced off
• If the plum pudding model was correct, you would
  expect to see a series of slight deviations as the
  alphas slipped through the positive pudding
       Rutherford Scattering
• Instead, what was observed was alphas were
  scattered in all directions
        Rutherford Scattering
• In fact, some alphas scattered through very
  large angles, coming right back at the
  source!!!
• He concluded that there had to be a small
  massive nucleus from which the alphas
  bounced off
• He did a simple collision model conserving
  energy and momentum
        Rutherford Scattering
• The model predicted how many alphas
  should be scattered at each possible angle
• Consider the impact parameter
        Rutherford Scattering
• Rutherford’s model allowed calculating the
  radius of the seat of positive charge in order
  to produce the observed angular distribution
  of rebounding alpha particles
• Remarkably, the size of the seat of positive
  charge turned out to be about 10-15 meters
• Atomic spacings were about 10-10 meters in
  solids, so atoms are mostly empty space
Rutherford Scattering
      From the edge of the atom, the nucleus
      appears to be 1 meter across from a
      distance of 105 meters or 10 km.
      Translating sizes a bit, the nucleus
      appears as an orange viewed from a
      distance of just over three miles!!!
      This is TINY!!!
Rutherford Scattering
      Rutherford assumed the electrons must
      be in some kind of orbits around the
      nucleus that extended out to the size of
      the atom.
      Major problem is that electrons would
      be undergoing centripetal acceleration
      and should emit EM waves, lose
      energy and spiral into the nucleus!
      Not very satisfactory situation!
           Light from Atoms
• Atoms don’t routinely emit continuous
  spectra
• Their spectra consists of a series of discrete
  wavelengths or frequencies
• Set up atoms in a discharge tube and make
  the atoms glow
• Different atoms glow with different colors
           Atomic Spectra
• Hydrogen spectrum has a pattern!
            Atomic Spectra
• Balmer showed that the relationship is
      1     1 1 
         R 2  2  for n  3, 4,5,...
          2   n 
           Atomic Spectra
                   1     1 1 
                      R 2  2 for n  2,3,4,...
• Lyman Series         1 n 
                   1     1 1 
• Balmer Series    
                      R 2  2  for n  3, 4,5,...
                        2   n 
                   1     1 1 
• Paschen Series   
                      R 2  2  for n  4,5,6,...
                        3 n 
            Atomic Spectra
                   1     1 1 
                      R 2  2 for n  2,3,4,...
• Lyman Series         1 n 
                   1     1 1 
• Balmer Series    
                      R 2  2  for n  3, 4,5,...
                        2   n 
                   1     1 1 
• Paschen Series   
                      R 2  2  for n  4,5,6,...
                        3 n 
• So what is going on here???
• This regularity must have some
  fundamental explanation
• Reminiscent of notes on a guitar string
            Atomic Spectra
• Electrons can behave as waves
• Rutherford scattering shows tiny nucleus
• Planetary model cannot be stable classically
• What produces the spectral lines of isolated
  atoms?
• Why the regularity of hydrogen spectra?
• The answers will be revealed next time!!!