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Physics Unit 4 2005
5. Wave-Particle Properties of Light
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1. The Electromagnetic Spectrum
In a vacuum, all electromagnetic waves move at the
same speed, c, the speed of light. They differ from
one another in their wavelength (and thus
frequency). The electromagnetic spectrum includes
waves with an enormous range of wavelengths,
from hundreds of kilometres to smaller than the size
of the nucleus of an atom.
Visible light, (~4.3  10-7m to ~6.9  10-7m) is
detected by the retina of the eye. The longer
wavelengths (lower frequency waves) appear red,
and the shorter wavelengths (higher frequency
waves) appear violet. The limits of the visible
spectrum are not well defined, because eye
sensitivity drops off gradually at both long and short
wavelengths.
Visible light makes up less than 10-6% of the
measured electromagnetic (EM) spectrum.
By 1864 the Scottish physicist, James Maxwell, had
worked out a mathematical theory of
electromagnetism. He developed a series of
equations to show that the energies of heat, light
and electricity are propagated in free space
(vacuum) as electromagnetic waves, their different
properties being due to differences in wavelength
and frequency. Such waves travel at the same
speed - the speed of light. They are transverse waves in which the disturbance is a time variation in both an
electric and a magnetic field set at right angles to each other.
Maxwell suggested that the vibrating electric charges that produced light were the electric charges in the atom.
Maxwell’s theory also did not require, as a necessity, the idea that light had to have a medium through which to
travel. For years scientists had been searching for the medium or ‘aether’ through which light travelled.
Maxwell’s work only assumed light to be travelling in an electromagnetic field and not necessarily a ‘particle
medium’. This explained why light appeared to be able to travel through what scientists thought was a vacuum,
but had been reluctant to believe was a complete vacuum because they thought some sort of medium was
essential for light’s propagation.
The shorter the wavelength (hence higher frequency) the more energy associated with the ray. From the
diagram, Gamma rays have more energy than radio-waves.
Physics Unit 4 2005
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5. Wave-Particle Properties of Light
Creation of Electromagnetic Waves
Name
Gamma-rays
X-rays
UV
Visible light
Infra-red
Generated by
Changes of energy levels in
the nucleus
Rapid deceleration of fast
moving electrons (e.g. by
tungsten target)
Orbital electrons of atoms.
E.g. the Sun
Re-arrangement of outer
orbital electrons in atoms
and molecules. (e.g.
incandescent solids)
Outer electrons in atoms and
molecules
Detected by
a) Photography
b) Ionisation
chamber
a) Photography
b) Photoelectric cell
a) Eye
b) Photography
c) Photocell
a) Photography by
special plate
b) Heating effect
Micro-waves
Micro-wave generators
Micro-wave receivers
Radio Waves
Oscillating electrons in radio
aerials
Tuned electric circuit
Properties
a) Penetrates matter
b) Ionise gases
c) Causes photo-electric
emission
a) Absorbed by glass
b) Can cause many
chemical reactions
c) (e.g. the tanning of
human skin)
d) Ionise atoms in the
atmosphere resulting in
the ionosphere
Can cause chemical action
a) Useful for ‘seeing’
molecular structures
b) Less scattered than
visible light by
atmosphere
a) Microwave ovens
b) Radar communication
Different wavelengths find
specialised uses in radio
communications
Some Common Visible Spectra
Spectrum of an incandescent
Intensity
light globe
Here are some graphs showing the
intensity of light emitted at different
wavelengths for common sources
of light. They are not to scale.
frequency
Spectrum of a fluorescent
light globe
Spectrum of the Sun
Intensity
Intensity
frequency
frequency
Physics Unit 4 2005
5. Wave-Particle Properties of Light
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2. Wave Properties
The distance between any two identical points is called the wavelength  .
Variation

Frequency
The frequency of the wave determines the pitch of the sound. Frequency is a measure of how rapidly the source
of the wave is vibrating. The frequency (f) is defined as the number of complete waves that pass a point in one
second. The units for frequency are Hertz, Hz, which are cycles per second.
Wave equation
The wave equation links the velocity of the wave to the frequency and the wavelength. v = f 
where v is the velocity in m/s, f is the frequency in Hz and  is the wavelength in metres. When we do this with
light we replace v with c to get c = f  .
Transverse waves
When waves vibrate up and down in a direction perpendicular to the direction of motion of the wave, it is referred
to as a transverse wave. e.g. water waves, where the motion of the water particles is at right angles (up and
down) to the direction of the wave (forward).
Superposition
The displacement of two waves
combing with each other is
calculated by the vector addition
of the two components. The
displacement of the combined
pulse is the sum of the separate
displacements.
The two pulses pass through each
other without being altered. To find
the total wave disturbance at any
time, the individual displacements of
each wave are added at each point.
When different sound waves
pass through the same region of
space, the individual waves add
together to produce the resultant
sound wave. This is called
superposition.
There are some good applets at http://smcc.edu.hk/phy/Virtual%20lab.htm
Physics Unit 4 2005
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5. Wave-Particle Properties of Light
3. Diffraction
Diffraction is the bending of waves around obstacles in the path of the waves, or as waves pass through narrow
openings. In diffraction, the wave remains in the same medium and so its speed, frequency and wavelength are
unchanged. The only thing that changes is the direction of the wave as it passes through gaps or around
obstacles.
long wavelengths, low frequencies
short wavelengths, high frequencies
When the obstacle is small compared with the wavelength of the light, there is very little disturbance. Larger
'shadows' occur when the obstacle is much larger than the wavelength of the incident wave. When light travels
through a narrow opening the waves bend around both sides of the opening and are diffracted into the region
beyond the barriers on both sides.
Circular wavefronts
Narrow gap c) λ  w
Wavefronts straight, except for slight bending at ends.
large gap   w
The amount of diffraction (bending) is given by the value of the
ratio  where w is either the width of the object or the width of
w
the opening.
If the ratio  ≥ 1, then it is complete diffraction, i.e. bending
w
through 1800.
If the ratio  << 1, then there is very little diffraction.
w
Physics Unit 4 2005
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5. Wave-Particle Properties of Light
4. Interference
When waves pass through each other, they can add together so that the reinforce each other; or they can cancel
each other out. When the waves add together this is called constructive interference, and will lead to a bright
point. When the cancel each, this is called destructive interference and this leads to a dark point. On the
diagram below the blue lines represent the bright spots and the red lines represent the dark areas.
Two dimensional representations
S1
This is a diagram of two point
sources in phase. The dark lines
represent troughs and the green
lines represent crests, coming from
the sources. The blue line in the
central position is the central
antinode, because everywhere along
this line, there are two waves in
phase. The 'red' lines are the nodal
lines. It is along these that the path
difference between the two sources
is ½ 
S2
The path difference between these two lines is zero. I.e. they are the same length, both are 4  .
The distance from S1 to P is 3.5  while
the distance from S2 to P is 4  . So the
difference between these two lengths,
called the path difference is 0.5  .
Everywhere along the first nodal line (on
either side of the central maximum) the
path difference will always be 0.5  .
If we consider the point Q. The path
difference is S2Q - S1Q = 5  - 3.5  =
1.5  .
P
Q
S1
S2
For any nodal line the path difference is summarise by P.D. = (n - ½)  where n = 1, 2, 3….
For the anti-nodal lines the path difference P.D. = n  where n= 0, 1, 2…..
Physics Unit 4 2005
5. Wave-Particle Properties of Light
5. Young’s Double Slit Experiment
In 1801, Thomas Young, revived the wave model with an
experiment that demonstrated the wave nature of light. He
allowed the light from a distant source to pass through two narrow
parallel slits with a screen placed some distance behind them.
The particle model of light predicts that two bright lines will be
formed on the screen, one for each slit. In fact, Young actually
observed a series of alternating bright and dark lines or fringes.
Young explained this result, using Huygens’ principle and
assuming that each narrow slit acted as a source of secondary
waves which spread out behind the slits and interfered with each
other to form the bright and dark bands. Antinodes where crests
met crests and troughs met troughs and constructively interfered
with each other to form the bright lines. Nodes were formed
where crests met troughs and troughs met crests and the
displacements cancelled each other out by deconstructive
interference, producing lines of minimum intensity.
This experiment showed that light
would produce an interference pattern,
because it diffracted when passing
through very small slits if the sources
were close enough together. The
pattern produced has a pattern of
nodes and antinodes just like sound or
water. A series of light and dark lines
were observed on the screen. Dark
lines correspond to cancellation, or
nodes, bright lines to antinodes.
The following applet is designed to
demonstrate two slit interference
effects with light.
Young’s experiment (2)
6
Physics Unit 4 2005
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5. Wave-Particle Properties of Light
Effect of wavelength
Small wavelength
Med. wavelength
Large wavelength
As the wavelength is increased the pattern spreads out.
Effect of the gap size
Small Gap
Med. Gap
Large Gap
As the gap size is increased the number of lines increases.
Physics Unit 4 2005
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5. Wave-Particle Properties of Light
6. Photoelectric Effect
In the region between charged plates, the electric field E is constant, and so a constant electric force FE acts on
any electrons between the plates. This causes them to accelerate towards the positive plate. Electrons moving
directly between the plates will have a uniform force acting on them. The electric force does work on these
electrons and they gain kinetic energy as they move towards the positive plate.
e-
The change in kinetic energy of the electrons is given by:
Work =  KE = q.  V
Unit of work and energy = joules (J)
Where q = charge of electron (C)
 V potential difference electron moves through (V).
A convenient unit of energy when dealing with electrons is the electron volt (eV).
An electron gains 1eV of energy when it is accelerated across a potential difference of 1 volt.
1 eV = 1.6 × 10-19 J
To convert from J to eV, divide the energy (in Joules) by 1.6  10-19.
One application that this is used in is the photoelectric effect. We can use the voltage to stop electrons and thus
we would know how much kinetic energy the electrons had. Imagine energy was given to an electron and it
came out of side A. Assume it took 2.3V to stop an electron from travelling from side A to side B. Then the
electrons that came out of Side A must have had 2.3ev of energy.
++++++++++++++++
e-
Side A
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Side B
The Photoelectric Effect
In 1887, Hertz, while detecting electro-magnetic waves, found that sparks could jump larger gaps if the metal
surface was illuminated by ultraviolet light. It was soon shown that the ultraviolet light was liberating negatively
charged particles from the metal. In 1899, J.J. Thomson showed that the charge to mass ratio of these particles
was the same as that of cathode rays and they were, in fact electrons. The process by which electrons are
ejected from matter by light was named the photoelectric effect.
Physics Unit 4 2005
5. Wave-Particle Properties of Light
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According to Maxwell’s electromagnetic theory, light waves carry energy and so it was conceivable that light
falling on a metal surface could supply sufficient energy to eject some of the electrons. However, this model was
shown to conflict with the detailed experimental evidence.
Detailed experiment
In 1902, Lenard carried out a detailed study of the
photoelectric effect, particularly examining the kinetic
energies of the photoelectrons (Electrons that have been
emitted from a metal using light). He did this by allowing
light of different frequencies to fall on a clean metal
surface in a vacuum. Electrons which left the
photocathode and reached the anode, produced a small
current in the ammeter. When the anode was at a
sufficiently high positive potential relative to the cathode,
all the photoelectrons were collected and the current was
a maximum. When the anode potential was zero, the
photoelectric current was not zero because many of the
electrons were emitted from the cathode with enough
kinetic energy to travel to the anode. When the anode
potential was made slightly negative with respect to the
cathode, the electrons were repelled and only those
electrons with sufficiently high kinetic energy could reach
the anode. The reverse voltage at which the current is reduced to zero, the ‘Stopping potential’ V o, gives a
measure of the maximum kinetic energy of the emitted photoelectrons.
Ek max = eVo
The main experimental results were:
 The rate at which photoelectrons are emitted is proportional to the intensity of the light (for light above
the threshold frequency)
 The maximum kinetic energy of the photoelectrons is independent of the intensity of the light.
 The maximum kinetic energy of the photoelectrons depends on the frequency of the light.
 Below a certain frequency, different for different metals, light cannot eject photoelectrons at all. This is
called the cut-off or threshold frequency.
The discovery of the photoelectric effect dramatically changed the way scientists were thinking about light. The
particle model had lost most of its supporters, especially since Young’s double slit interference experiments. In
1897 Heinrich Hertz observed an interaction between light and matter, now known as the photoelectric effect.
After further work by Philip Lenard between 1899 and 1902, led Albert Einstein to conclude that light does in fact
behave like a particle. The wave model could not explain the photoelectric effect.
It sometimes happens that when light falls on certain metals, electrons are ejected from the metal. These
electrons are known as photoelectrons and can be shown to be electrons by measuring their charge mass ratio.
A photocell can be used to investigate the photoelectric effect. Photoelectrons ejected from the cathode are
pulled across to the anode. These moving electrons are a current that may be measured by an ammeter.
Physics Unit 4 2005
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5. Wave-Particle Properties of Light
Dim light
Photocell
+
eA
Small i flows
Metal plate
The experiment can be used to show that the number of electrons ejected depends upon the light intensity. As
the light intensity increased, so too did the size of the current. More electrons were escaping from the metal
when the light was brighter.
When the frequency (i.e. colour) of the light shining on the metal changes, there is a frequency at which the
electrons begun to be emitted from the metal. This is called the THRESHOLD or CUT-OFF FREQUENCY (fc).
Below this frequency, no emission occurs, even for very intense light.
Red light (low frequency)
Bright Red light
No electrons emitted
No electrons emitted
+
+
A
A
i = 0A
i = 0A
Green light. Electron emission starts
+
e-
Green light. Electron emission starts
+
A
e-
A
Small current
Bigger current
Violet light. Electron emission continues
+
e-
Violet light. Electron emission continues
+
A
Small current
e-
A
Bigger current
Physics Unit 4 2005
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5. Wave-Particle Properties of Light
When the battery is reversed, some important results are obtained.
Dim Light
-
Dim Light


e-
+
-
e- +

 
A
No current
A
Small current
Small retarding voltage
More negative retarding voltage
 As the anode is made more negative fewer electrons get across the tube- this means that the ejected
electrons must have a range of kinetic energies. Electrons with little or no KE are stopped as soon as the
anode becomes negative - those with the most KE being stopped by Vc volts. Energetic electrons come from
the surface, less energetic electrons from below the metal surface.
 The value of Vc, the cut off voltage, depends upon the colour, not the intensity of the light. With most metals,
low frequency light will not generate electrons.
 The time lag between the light striking the photo-cathode and the emission of electrons is less than 3 x 10-9
secs, even for the lowest light intensity.
 More intense light generates more electrons, but does not increase their energy.
Failure of the wave model
The electromagnetic wave model describes the energy in the light beam as arriving continuously and uniformly
over the metal surface. If the intensity of the light beam in increased, then the energy available to the electrons
is also increased and so the maximum kinetic energy available to the electrons is also increased and so the
maximum kinetic energy of the photoelectrons should increase. This does not, in fact, happen! The theory also
predicts that the energy in a light beam is described entirely by its intensity, so the maximum kinetic energy of
the photoelectrons should be independent of the frequency of the light – this again contradicts the facts!
A further difficulty for the wave theory is that the energy in the light beam is delivered in a smooth continuous
fashion and is spread out over the whole wave front. Consequently, it should take some appreciable time after
the light is turned on, before any one of the electrons absorbs enough energy to escape from the surface. This
time delay should be longer for dim light. Experimentally, it turns out that there is no measurable time delay,
even with the weakest light source!
Physics Unit 4 2005
5. Wave-Particle Properties of Light
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The Photon Model
In 1901, Max Plank was attempting to solve a puzzling discrepancy between the observed spectrum of light from
a black body and the theoretical predictions of Maxwell’s electromagnetic theory. He postulated that
electromagnetic energy was emitted and absorbed in packets or quanta, each one carrying a definite amount of
energy. The energy was proportional to the frequency, f, and given by the equation: E = hf where h is Plank’s
constant
Plank’s radical suggestion produced a better fit between theory and experiment but was not widely accepted
since it disagreed with the essentially continuous nature of radiation as described by Maxwell’s theory.
In 1905, Albert Einstein extended Plank’s idea and suggested that light was not merely emitted in discrete
amounts or quanta, but that it retained its identity, travelled through space as a particle of light energy or photon
and was ultimately absorbed by matter as a complete quantum of energy.
So, in the photoelectric effect, one electron could absorb exactly one photon and receive the full
quantum of energy, hf. Since it will require a certain minimum amount of energy, W, to remove the electron from
the surface, the maximum kinetic energy of the photoelectron will be:
Ek max = photon energy – minimum energy to remove electron
= hf – w
The minimum energy required to remove an electron from
the metal is called the work ‘function’ and the symbol W is
used for this. Photoelectrons from below the surface will
lose further energy by collisions before they escape, so
there will be a range of energies for the emitted
photoelectrons.
The photon model of light, suggested by Einstein, explained
the observed facts:
 Since the photon energy E = hf, then the maximum energy of the photoelectron would obviously depend on
the frequency of the light, f.
 No electron will be emitted until the energy of the incoming photon is at least equal to the work function of the
surface. This means that the frequency of the light must be above a minimum value fo, such that hfo = W.
This explains the existence of a threshold frequency – light with lower frequency than the threshold frequency
will not eject photoelectrons, no matter how intense the light.
 Increasing the intensity of the light means that the number of photons is increased but the energy of the
individual photons is unchanged. So more electrons may be ejected but the maximum energy will be
unchanged. A very weak light source with a frequency that is greater then the threshold frequency will eject
electrons.
Experimental confirmation of the photon model
In 1916, Robert Millikan published experimental results which completely verified Einstein’s photoelectric theory.
He prepared clean surfaces of lithium, sodium, and potassium and measured the maximum energy of the
photoelectrons emitted when the surface was exposed to light of different frequencies. The graph of maximum
kinetic energy versus frequency for each metal was a straight line, with the same gradient in each case. The
intercept of the frequency axis represents the threshold frequency, fo. The intercept on the energy axis is –W,
the negative of the work function. The values were different for each material, though the gradients were the
same.
Physics Unit 4 2005
5. Wave-Particle Properties of Light
13
If a graph of the KE of the ejected electrons is plotted against the frequency of the incoming light the following
can be deduced:
 There is a threshold frequency below which the electrons are not emitted.
 Different metals have different threshold frequencies
 The gradient of the graph is the same for all metals.
 The equation of the graph, an energy equation, is Ek = hf - W where Ek is the Kinetic Energy of the
ejected electrons, h a universal constant and W a constant for the material.
This can be written as
hf = Ek + W
 The constant h is called Planck's constant and has the value of 6.626 x 10-34 Js. or 4.136 x 10-15 eVs.
hf
h
 Other experiments show that photons have a momentum given by p =
=
c

 W is either called the work function or the binding energy of the metal.