# Wave-Particle Duality

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```					       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?
• 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
• 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!!!

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 views: 2 posted: 1/29/2012 language: pages: 26