WaveParticle Duality

1
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?

2
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

3
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 Bohrs Principle of
  Complementarity which says we must use either the
  wave or particle approach to understand a
  phenomenon, but not both!

4
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

5
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!!!

6
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

7
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 cant build structures small
  enough to detect the wavelengths of macroscopic
  objects

8
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
  Broglies hypothesis

9
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!

10
Electron Microscopes
11
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

12
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 couldnt just sit still inside the
blob. Electrostatic forces would cause
accelerations. How could it work?
13
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!

14
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

15
Rutherford Scattering

• Instead, what was observed was alphas were
  scattered in all directions

16
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

17
Rutherford Scattering

• The model predicted how many alphas should be
  scattered at each possible angle
• Consider the impact parameter

18
Rutherford Scattering

• Rutherfords 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

19
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!!!
20
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!
21
Light from Atoms

• Atoms dont 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

22
Atomic Spectra

• Hydrogen spectrum has a pattern!

23
Atomic Spectra

• Balmer showed that the relationship is

24
Atomic Spectra

• Lyman Series
• Balmer Series
• Paschen Series

25
Atomic Spectra

• Lyman Series
• Balmer Series
• Paschen Series
• So what is going on here???
• This regularity must have some fundamental
  explanation
• Reminiscent of notes on a guitar string

26
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!!!