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					  Wave Particle Duality

Advanced Higher Mechanics Topic 9
By the Fantastic Four
                     Introduction

Wave-Particle duality shows:
– Light can act like a wave and like a particle.
– Other particles can act as waves
Main experiment for showing light as particles is
the photoelectric effect.
           The Photoelectric Effect

Cathode and anode in a
vacuum.
Quartz window to illuminate
the cathode using an
ultraviolet light.
Sensitive ammeter shows
photocurrent
Potentiometer provides
stopping potential to reduce
photocurrent to zero.
      The Photoelectric Effect cont…
Energy of photoelectrons depends on the frequency of the light.
Below the threshold frequency, no electrons are emitted
Hence, light cannot be considered as waves in this case but as a
stream of particles, called photons (1905 Einstein’s quantum
theory of light)
Energy E of a photon:
                            E = hf

Where f = frequency of beam of light
        h = Planck’s constant (6.6310^34 Js)
This can also be written as E = hc        (v=f )
                                  
      The Photoelectric Effect cont…
When a photon is absorbed by the cathode, its energy
is used in exciting an electron.
Photoelectron is emitted when the energy is sufficient
for an electron to escape from an atom
Conservation of energy relationship for the photoelectric
effect:
                    hf = hf + ½ mv²
     hf is the energy of incident photon
     hf is the work function (min. energy required to
                               produce photoelectron)
     ½ mv² is the kinetic energy of photoelectron
       Compton Scattering




E=hf
       Compton Scattering


Conservation of linear momentum
    Wave-Particle Duality of particles

We know light can behave as particles.
The equation  = h/ρ links a property of waves
(wavelength) with a property of particles (momentum).
In 1924, Louis de Broglie suggested particles have a
wavelength.
Using the above equation, we can work out the ‘de
Broglie’ wavelength of particles.
In most cases, this wavelength is VERY small.
                         Example
Find the de broglie wavelength of an electron travelling
at 4 x 105 ms-1.
– The momentum of the electron is
   ρe = meve = 9.11 x 10-31 x 4 x 105 = 3.64 x 10-25 kgms-1
– The de Broglie wavelength is therefore:
   e = h / ρe = 6.63 x 10-34 = 1.82 x 10-9 m
               3.64 x 10-25
– If the velocity is above about 0.1c, then relativistic
  calculations are needed to be done. This is not needed for
  this course.
People like Jannik can also use this to work out the
wavelength of a bowel of Shreddies.
                  Wave Properties

Two properties of waves are:
– Interference
   • If you hit a ball in snooker, the balls don’t combine to
     make one big ball, nor do they disappear altogether.
– Diffraction
   • If a train travels through a tunnel, it does not spread out
     when it leaves the tunnel, it continues along the track.
– We have seen these effects before.
             Electron Diffraction

An object like a train has a wavelength many
times smaller than the width of the tunnel.
However, as shown before, electrons have a
very small wavelength.
This wavelength is about the same size as the
spacing between atoms on a crystalline solid.
Therefore, an electron can diffract when passing
through a crystal.
                Diffraction Pattern

Here is a typical pattern
from an electron
diffracting through a
crystalline solid.
The different diffraction
amounts is due to the
atomic spacing in the
solid and the wavelength
of the incident beam.
Electron Microscope
         What you NEED to know.

The equations, E = hf and ρ = h/λ
How to use the above equations.
Describe and explain the photoelectric effect.
Describe and explain electron diffraction.
Know that a de Broglie wavelength of a particle
is extremely small, other than on an atomic or
sub-atomic level.

				
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