This document discusses the wave-particle duality of light and matter. It explains how experiments demonstrating the photoelectric effect and electron diffraction show that electromagnetic radiation and electrons exhibit both wave-like and particle-like properties depending on the situation. De Broglie hypothesized that all particles can behave as waves, and he formulated an equation showing that particles are associated with a wavelength determined by their momentum and Planck's constant.

1. Quantum Phenomena
Wave-particle duality
De Broglie wavelength
Thursday, 03 November 2011

2. The Particle nature of EM radiation
Look at this example.
Current
detected
Lithium
Cathode
Anode
Dim Blue
Light

3. The Particle nature of EM radiation
Look at this example.
No Current
detected
Lithium
Cathode
Anode
Bright Red
Light

4. The Particle nature of EM radiation
Explain why a current is detected when dim blue light is shone on the
lithium cathode, but not when bright red light is used.
• Blue light is made of photons with enough energy to eject the
electrons from the lithium
• Red light is made of photons with low energy (not enough to cause
photoelectric emission)
• The energy of EM radiation depends on its frequency, not on its
intensity (amplitude)
What does this example suggest about the nature of EM radiation?
• EM radiation has a particle nature, because photoelectricity can only
be explained with photons, i.e. “lumps” of electromagnetic
radiation/energy called Quanta.

5. The dual nature of EM radiation
In conclusion, we can say that light (and all EM radiation) can behave in
some occasions like a wave and in others like a particle.
Properties
• Diffraction
• Wavelength
• Refraction
• Frequency
Wave • Massless
nature Phenomena
Properties
• Photoelectric
• Kinetic Energy effect
Particle • Linear Momentum
nature Phenomena

6. The Wave-Particle duality
We say that light (EM radiation) has a wave-particle nature because it
features properties of both waves and particles. But, is this true of
particles too, like electrons? Look at this experiment.
Fluorescent
Electron beam screen
Electron gun
Graphite foil

7. The Wave-Particle duality
Where have you seen a similar pattern?
• Light can be diffracted by a pin hole
• This diffraction pattern is very similar to the pattern left by the
electrons through the graphite foil
Diffraction of
light through a
pin hole

8. The Wave nature of electrons
But if electrons can be diffracted like light, what does this suggest?
• Electrons behave like a wave through a graphite foil
• Electrons must have a wavelength just like any other wave
What is the condition for diffraction to occur?
• The wavelength of the wave (particle) must be similar in size to the
gap the wavelength goes through
What is the atomic spacing of the graphite then?
• The atoms of carbon are at the same distance apart as the
wavelength of the incident electrons
Click here for
flash activity

9. De Broglie’s Equation
Latching on the ideas of EM waves behaving like particles in the
photoelectric effect, De Broglie suggested that particles could behave
like waves under certain conditions and, therefore, have a
wavelength and be subject to wave phenomena like diffraction. He
formulated this equation later proven correct by effects like electron
diffraction:
h
mv
• = wavelength of the particle
• mv = linear momentum of particle
• h = Planck’s constant

10. De Broglie’s Equation
Work out the wavelength of an electron of mass 0.9 x
10-30 kg travelling at a speed of 106 m/s, and a tennis
ball of mass 0.05 kg travelling at a speed of 10 m/s.
e = 7 x 10-10 m b = 10-33 m
What EM wave has a similar wavelength?
X-rays.