FROM IDEAS TO IMPLEMENTATION
By the beginning of the twentieth century, many of the
pieces of the physics puzzle seemed to be falling into place.
The wave model of light had successfully explained interference and
diffraction, and wavelengths at the extremes of the visible spectrum had been
estimated. The invention of a pump
that could evacuate tubes to 10-4 of an atmosphere allowed the
investigation of cathode rays. X-rays
would soon be confirmed as electromagnetic radiation and patterns in the
Periodic Table appeared to be nearly complete.
The nature of cathode rays was resolved and the measurement of the charge
on the electron was soon to follow. There were some experimental observations still unexplained but
to many scientists the understanding of the world of the atom seemed almost complete.
This belief was about to be challenged seriously.
The exploration of the atom was well and truly inward bound
by this time and as access to greater amounts of energy became available,
physics moved further into the study of sub-atomic particles.
Careful observation, analysis, imagination and creativity throughout the
early part of the twentieth century developed a more complete picture of the
nature of electromagnetic radiation and matter.
The journey taken into the world of the atom has not remained isolated in
laboratories. The phenomena
discovered by physicists have been translated with increasing speed into
technologies, such as computers, to which society has ever-increasing access.
These technologies have often assisted physicists in their search for
further knowledge and understanding of natural phenomena at the sub-atomic
This module increases students’ understanding of the
history, nature and practice of Physics and the applications and uses of
Physics, the implications of Physics for society and the environment and the
current issues, research and developments in Physics.
ELECTRIC FIELDS REVISITED
Recall from the “Electrical
Energy in the Home” topic from the Preliminary Course, the nature of the electric
field around single point charges and around positive and negative charges
in proximity to one another.
Remember that the magnitude of
the electric field strength at a particular point in space is defined as
the force per unit charge at that point.
where E = electric
field strength, q = size of the charge and F
= force experienced by q at the point
in question. The SI units of
electric field strength are NC-1.
of the electric field at any point is defined as the direction in which a positive
test charge would move if placed in the field at that point.
since the electric field is strongest where the field lines are closest
together, the strength of the field around isolated charges decreases with
increasing distance from the charges.
Recall also, that two oppositely
charged parallel metallic plates separated by a distance, d, can be used to
produce an electric field as shown below:
Note that the strength of the field is uniform between
the plates but non-uniform towards the edges.
The magnitude, E, of the
electric field between the plates can be shown to be:
where V is the potential
difference between the plates.
Charges In A Magnetic Field Revisited
Recall from the “Motors & Generators” topic
that a moving electric charge carries with it an associated magnetic
field. Thus, an electric charge
moving through a magnetic field experiences a force, due to the interaction
of the two magnetic fields present. The
size of this force is given by:
= q v B
where q = size of charge, v = velocity of charge
perpendicular to the field and B = magnetic flux density vector.
If the charge enters the field at an angle q
to the field direction, instead of perpendicular to it, we must use the
component of v that is at right angles to the field direction.
Thus the formula becomes:
= q v B sin q.
The direction of the force on a charge in a magnetic field may be
determined by using Fleming’s
Left Hand Rule.
Hold the thumb, first finger and second finger of the LEFT hand mutually
at right angles. Point the first
finger in the direction of the magnetic field.
Point the second finger in the direction of conventional current flow (ie
in the direction of flow of positive charge).
The thumb then points in the direction of the force on the charged
THE INVESTIGATION OF CATHODE RAYS
In 1855 the German inventor and
glassblower Heinrich Geissler, invented a vacuum pump that could remove enough
gas from a glass tube to reduce the pressure to 0.01% of normal air pressure at
sea level. (normal air pressure at
sea level = 1 atmosphere = 760 mm of Hg = 101 325 N/m2)
This provided his friend, Julius Plucker, with the
apparatus to experiment with electrical current through gases at low pressure.
Plucker sealed electrodes into a glass tube and then evacuated the tube
to very low pressure. When Plucker applied very high voltage to the electrodes,
current flowed through the tube and he noticed that the glass tube itself
glowed with a pale green glow, mainly in the vicinity of the anode (positive
terminal). He concluded that rays
of some form were emanating from the cathode (negative electrode) and that these
rays caused the glass to glow. These
rays were eventually named cathode rays, as they appeared to come from
the cathode (negative electrode) of the tube. Plucker also showed that the rays were deflected by an
external magnetic field.
When we repeat Plucker’s
investigations in the laboratory, we find that if air is in the tube and the air
pressure is reduced to a few centimetres of mercury, then electrical
discharge occurs. Flickering
red streamers are observed. If
the pressure is further reduced the discharge beams become steady and a pink
glow fills the tube. On further
reducing the pressure, the anode glows, Faraday’s dark spaces are observed
and the glow becomes striated.
The following diagram shows a cathode ray tube with the
various glows and dark spaces labelled.
The voltage applied between the cathode and
anode is a high voltage and is usually supplied by an induction coil. The
diagram is not to scale.
By 1875, William
Crookes had designed new tubes for studying the glow produced when an
electric current passes through an evacuated tube.
When he used a bent tube, the most intense green glow appeared on the
part of the tube opposite the cathode. This
suggested that the green glow was caused by something that came out of the
cathode and then travelled down the tube until it hit the glass. Eugen Goldstein suggested the name cathode
did other ingenious experiments with gas tubes.
He placed a metallic Maltese cross in the path of the rays from
the cathode. This produced a sharp
shadow of the cross on the glass at the end of the tube.
Crookes concluded that cathode rays travelled in straight lines and could
not penetrate metal. See this Maltese
Cross tube or this
used a magnet near the tube to produce a horizontal magnetic field for the rays
to pass through. The path of the
rays was made visible by placing a fluorescent screen lengthways down the tube
and arranging a small aperture near the cathode to collimate the rays into a
thin beam. He observed that the
rays were deflected by the magnetic field as if they were negatively charged
Using a tube
containing a paddle wheel supported by glass rails, Crookes showed that the
cathode rays possessed energy and momentum.
The rays striking the paddle wheel moved it along the rails. See these
many other experiments led Crookes to conclude that cathode rays:
- were always the same regardless of which metal was used
as the cathode;
- always travelled in straight lines perpendicular to the surface
- are deflected by a magnetic field as if they were negatively charged
- cause glass to fluoresce;
- carry energy and momentum; and
- produce some chemical reactions similar to the
reactions produced by light – some silver salts change colour when struck by
Crookes also believed that cathode rays could be deflected by an electric field
but never succeeded in demonstrating this experimentally.
Some of the
properties above suggested to Physicists that cathode rays were a wave similar
to light. For instance, they
produced fluorescence, they travelled in straight lines, they produced similar
chemical reactions to those produced by light and they were not deflected by
electric fields. Yet cathode rays
were deflected by a magnetic field as if they were negatively charged particles.
This apparently inconsistent behaviour of cathode rays led to much
controversy over whether the rays were a stream of negatively charged particles
or a form of EM wave like light.
By the end of the 19th Century, the argument
in favour of cathode rays being charged particles had become much stronger.
By then, it had been shown by Eugen Goldstein that the rays could be
deflected by electric fields and by Jean Perrin that the charge on the rays was
negative. The final piece of evidence was provided by Joseph
John Thomson in a brilliant experiment conducted in 1897.
OF CHARGE TO MASS RATIO OF CATHODE RAYS
subjected beams of cathode rays to deflection by known electric and magnetic
fields set at right angles to each other (crossed fields) in order to measure the
charge to mass ratio of the cathode rays.
diagram of Thomson's
tube or this one Thomson's
tube or these photos & diagrams Thomson's
The tube used
by J.J. Thomson contained a cold cathode that produced cathode rays by using a strong electric
field in the vicinity of the cathode to cause gas discharge. The cathode rays so formed were accelerated towards the anode
by the potential difference between the anode and cathode.
At the anode, some of the cathode rays were collimated into a thin beam
by passing through a slit and then travelled with constant velocity to produce a
bright spot on the phosphorescent screen. An
electric field could be applied between the metallic plates and a magnetic field
at right angles to the electric field was produced by two Helmholtz induction coils
sitting on either side of the tube.
experimental procedure was to set E and B to zero and note the position on the
screen where the undeflected beam of cathode rays struck.
Then a known magnetic field was applied and the position of the deflected
beam noted. Finally, an electric
field E (=V/d) was applied and its value adjusted until the deflection of the
beam returned to zero.
particles curving in the B field: mv2/R = qvB
which can be
re-arranged to give: q/m = v/BR
Note that q/m,
the charge to mass ratio of the cathode rays, is the value we are after.
The value of B
was known from the arrangement of the Helmholtz coils. R, the radius of curvature of the particles in the magnetic field, was
found geometrically from the displacement of the beam spot on the screen.
To determine v, the velocity of the particles, Thomson applied the
B fields simultaneously and adjusted the E field value until the deflection of
the beam returned to zero. This
meant that the magnetic force (qvB) on the particles was exactly balanced by the
electric force (qE) on the particles:
qE = qvB
So we have
v = E/B (equation
The value of E
was known from the arrangements of the charged plates (E = V/d, where
voltage between plates & d = distance between plates).
equations 1 & 2 we have:
all of the quantities on the RHS are known.
Thomson determined q/m for cathode rays
as 1.76 x 1011 C/kg regardless of the material used for the cathode.
This determination effectively confirmed the particulate nature of
experiments, Thomson showed that the charge on the cathode ray particles was the
same size as the charge on the hydrogen ion.
This combined with the fact that the q/m ratio for cathode rays was
times larger than that for the hydrogen ion (determined in electrolysis
experiments) meant that the mass of the cathode ray particles had to be 1800
times smaller than that of the hydrogen ion.
On the basis of all these results, Thomson suggested that the cathode ray
particle was a fundamental constituent of the atom.
Although he originally referred to the particles as “corpuscles”,
the name “electron” slowly became accepted as the official name.
an aside, it is an interesting historical point that Sir Joseph John Thomson was
awarded the 1906 Nobel Prize in Physics for proving that the electron is a
particle and his son, Sir George Paget Thomson was awarded the 1937 Nobel Prize
for Physics for showing that the electron is a wave.)
THE CATHODE RAY TUBE
The cathode ray tube (CRT)
consists of three main components:
The end of the
CRT is coated on the inside surface with some fluorescent material such as zinc
sulfide (ZnS). When an electron
strikes the end of the tube, the material fluoresces, that is gives off light.
This enables a spot of light to appear wherever an electron (from the
electron gun) strikes the end of the tube.
Phosphorescent material can be used in place of the fluorescent material.
This produces a
narrow beam of electrons.
It consists of a filament enclosed in a cylindrical cathode
electrode, a ring-shaped electrode called the “grid” and two
cylindrical anode electrodes. The
filament is heated by passing electric current through it.
Electrons are then produced by thermionic emission from the heated
filament. These electrons are
accelerated towards the anodes by the electric field set up between the
cathode and anodes. The dual anode system helps to focus the electron beam.
The grid is placed between the cathode and anodes and is made
negative with respect to the cathode. This
enables the intensity of the electron beam to be controlled – the more
negative the grid, the fewer electrons are emitted from the electron gun and the
less the brightness of the spot on the end of the tube.
This allows the
electron beam to be deflected from the straight-line trajectory with which it
leaves the electron gun.
The deflection system consists of two sets of parallel plates, one set in
the horizontal plane, and the other in the vertical plane.
When potential differences are applied between each set of plates, electric
fields are set up between the plates. The
electrons in the beam then experience forces vertically while passing between
the horizontal plates and horizontally while passing between the vertical
plates. Thus, applying
appropriate voltages to the deflection plates can control the position of the
spot on the end of the screen.
A good diagram & some explanatory notes are at the following
link. Just page down a little for the diagram when you get there.
allow the manipulation of a stream of charged particles they are very useful for
a number of applications.
We will now examine some of these.
APPLICATIONS OF CATHODE RAYS
The Cathode Ray
The cathode ray oscilloscope (CRO)
is used to measure potential differences that change too rapidly with time to be
measured using a simple voltmeter. Since
many physical and biological effects can be converted into an electrical signal,
the CRO has become an extremely useful tool in physics, electronics, biology,
medicine and many other fields.
The CRO uses a CRT to produce a
graph of how an input signal voltage varies with time. The electrodes in
the CRT's electron gun produce a narrow beam of electrons, which produces a
bright spot on the CRO's fluorescent screen. The screen has a centimetre grid painted on it.
When the potential difference across the horizontal & vertical
deflection plates is zero, the spot on the screen is at the origin of the set of
axes. A sawtooth voltage
from within the electronics of the CRO is applied across the horizontal
deflection plates. This causes the
spot to move horizontally, at a constant speed, from left to right across the
screen as viewed by the user. The
sawtooth voltage automatically switches the spot off when it reaches the right
side of the screen and moves it back to the left side of the screen to repeat
its motion. The time base
control on the CRO enables the speed with which the spot moves horizontally to
be accurately controlled.
The voltage signal to be measured
is applied to the vertical deflection plates. So, as the spot is scanned across the screen horizontally,
the vertical position of the spot changes in response to the input signal
voltage. The vertical grid scale on
the CRO is calibrated to represent the voltage of the applied signal.
A varying potential difference across the vertical deflection plates can
be synchronised with the time base on the horizontal deflection plates, to
produce an apparently motionless picture on the screen.
here for a photograph of a cathode ray oscilloscope.
An explanation of what an oscilloscope is and what it is used for can be
To produce television images in
Australia, the image formed by the optical lens system of the camera is scanned
electronically as a sequence of 625 vertically displaced horizontal lines.
This is called raster
scanning. The varying light
value along each line is converted into a fluctuating electrical signal. The voltage drops to a negative value at the start of each
new line to indicate the start of the line scan.
The whole scan is repeated 25 times every second, which is fast enough to
trick the brain of the viewer into thinking she is seeing continuous motion
without noticeable flicker.
In television receivers, a CRT
called a picture tube translates the television signal back into the picture we
see on the screen. The electrodes in the electron gun produce a beam
of electrons, which produces a bright spot on the fluorescent television
fields are used to deflect the electron beam in this CRT, since the magnetic
fields allow for a wider-angle beam than would be possible with electric fields
from charged plates. Two pairs of
magnetic field coils lie on either side of the neck of the picture tube.
One pair of coils provides a magnetic field to produce horizontal
deflection. The other pair produces
deflection in the vertical direction.
Both the horizontal and vertical
deflection plates are supplied with a continuously increasing time base voltage.
The horizontal time base moves the spot from left to right across the
screen, while the vertical time base moves the spot down the screen at a much
slower rate. At the end of each line of the image, the horizontal
deflection plates force the spot to “fly back” to the start of the next
line. Thus, the electron beam
zigzags down the screen from the top left corner to the bottom right and then
repeats its motion.
The brightness of the image on the
screen is controlled by the signal voltages applied to the grid in the electron
gun of the picture tube. In black
and white TV the brightness of the spot on the screen determines whether that
pixel is white, grey or black. In
colour TV there are three electron guns, each one able to activate only one of
the primary colours (red, green or blue) on the screen.
The coloured image is the result of the combination of coloured pixels of
See the "How TV Works" page:
and follow the links from there to get the full story.
This section of notes is no longer required by the
Syllabus but has been left here as a matter of interest.
The electron microscope uses a
beam of electrons rather than light to study objects too small for
conventional light microscopes. First
constructed by Max Knoll and Ernst Ruska around 1930, the instrument now
consists typically of an evacuated column of magnetic lenses with an electron
gun at the top and a fluorescent screen or photographic plate at the bottom.
It can thus be thought of as a kind of cathode ray tube.
The various magnetic lenses
(basically electromagnets) allow the operator to see details almost at the
atomic level (0.2 nm resolution) at up to a million times magnification and to
obtain diffraction patterns from very small areas. In the transmission electron microscope (TEM), electrons are
transmitted through the sample and form an image on the fluorescent screen or
photographic plate. In the scanning
electron microscope (SEM), the beam is focussed to a point and scanned over the
surface of the sample. Detectors
collect the backscattered and secondary electrons coming from the surface and
convert them into a signal that in turn is used to produce an image of the
For excellent diagrams & information on both TEM’s & SEM’s
see the links below.
Electron microscopy: http://www.unl.edu/CMRAcfem/em.htm
Scanning electron microscope: http://www.mse.iastate.edu/microscopy/highschool.html
- this site provides information at various levels of complexity. The
current link will give you the "High School" level. The more
complex "College" level can be obtained by clicking on the tab at the
bottom of the page.
In 1865 James
Clerk Maxwell predicted the existence of electromagnetic waves.
He suggested that an accelerated charge
would produce a non-uniformly changing electric field that would in turn produce
a changing magnetic field. By
Faraday’s Law, this non-uniformly changing magnetic field would in turn
produce a changing electric field and so on.
showed mathematically that such fields would propagate through space as a wave
motion with a speed of 3 x 108 m/s.
This speed agreed so closely with values of the speed of light measured
by Fizeau in 1849 and Foucault in 1862 that Maxwell became convinced that light
was a form of electromagnetic wave.
Hertz, a German physicist, achieved the first experimental demonstration of
electromagnetic waves in 1887.
Hertz used an induction coil to produce oscillating electric sparks
between two brass balls connected to two brass plates.
The brass plates acted as an aerial system.
He used a small loop of wire with a tiny gap in it as the receiver.
See diagram below.
As sparks jumped across the gap between the balls,
sparks were also observed jumping the gap in the receiver.
Hertz reasoned that the spark discharge oscillating backwards and
forwards between the brass balls set up changing electric and magnetic fields
that propagated as an electromagnetic wave, as postulated by Maxwell.
When these waves arrived at the receiver, the changing electric
field component caused charges in the loop to oscillate, thus producing the
spark across the gap in the receiver.
Hertz carried out a thorough investigation of these
waves and showed that they did indeed possess properties similar to light –
reflection, refraction, interference, diffraction and polarisation.
By setting up an experiment in which he allowed the waves to reflect
from a metal sheet and interfere with themselves to produce standing waves,
Hertz was able to determine their wavelength.
He calculated the frequency of oscillation of the sparks in his
transmitter from knowledge of the parameters of the circuit.
v = f
he calculated the speed of the waves as 3 x 108 m/s, as predicted by
Maxwell. Thus, Hertz’s experiment
confirmed Maxwell’s prediction of EM waves and provided strong experimental
support for the idea that light was a form of transverse EM wave.
The waves produced by Hertz eventually became known as radio
waves and his research led to the development of radio communications.
As Hertz suspected it was indeed oscillating charges that produced the
EM waves. Today we know that
radio waves are produced when an oscillating voltage applied to an antenna
causes free electrons to oscillate along that antenna.
This generates an EM wave that spreads out from the transmitter at 3 x 108
m/s. When the EM wave strikes a
receiving antenna it forces charges in the antenna to oscillate at the frequency
of the wave. This oscillating
electrical signal is then converted into an audio-frequency signal by
diodes in appropriately tuned electronic circuits.
Applications of the production of EM waves by
oscillating electric charges in radio antennae started with the
demonstration of “wireless” telegraphy by Sir Oliver Lodge in 1894. Marconi accomplished the first trans-Atlantic transmission in
1901. The invention of the triode
valve amplifier in 1906 enabled radio transmission of speech and music over long
distances. The invention of the
transistor in 1948 eventually resulted in further improvements in radio
transmission and reception and decrease in size of transmitters and receivers.
Today, radio communications networks, citizen-band radio, mobile phone
networks and television image transmission are examples of applications of EM
wave production. (This information in this last paragraph is no longer required by the
OF PHOTOELECTRIC EFFECT
While conducting his initial experiments, Hertz often
placed the receiver in a darkened box to make it easier to see the tiny sparks
in the gap. He noticed that the
sparks across the gap in the receiver were distinctly weaker when the receiver
was in the box. After much
effort Hertz discovered that the sparks jumping the gap in the receiver were
more vigorous when the receiver was exposed to the ultraviolet light coming from
the sparks in the gap of the transmitter.
Although this was a most amazing discovery, Hertz did not further
investigate the phenomenon but confined his research to the production and study
of EM waves. What Hertz had
discovered in fact was the photoelectric effect.
We will examine this effect shortly.
AND BLACK BODY RADIATION
we saw in the Cosmic Engine topic physicists use black body cavity radiators
to approximate perfect
absorbers and emitters of radiation. A “black body” by definition is a body whose surfaces
absorb all the thermal radiation incident upon them and allow none to be
reflected. All black bodies at the
same temperature emit thermal radiation with the same spectrum, independent of
their composition. The
intensities of the colours in the spectrum depend only on the temperature.
The energy density of black body radiation inside a
cavity radiator at various temperatures as a function of wavelength is shown on
the Cosmic Engine page.
Note that the intensity versus wavelength plot for the radiation emitted
from the hole connecting the cavity to the outside has the same shape.
The radiation inside a cavity whose walls are at temperature T has the
same character as the radiation emitted by the surface of a blackbody at
The shape of these energy density curves was determined
experimentally as early as 1899. Theoretical
physicists, however, could not satisfactorily explain the shape of these curves
using classical electromagnetic theory.
In fact, two physicists, Rayleigh and Jeans derived an equation for black
body radiation that suggested that at low wavelengths (high frequencies) the
energy density approaches infinity. Historically,
the grossly unrealistic prediction at high (ultraviolet) frequencies became
known as the “ultraviolet catastrophe”.
Clearly, a new approach was needed.
This came in 1900 when a German physicist, Max Planck, suggested a
revolutionary idea. Planck
suggested that radiation was emitted or absorbed by a black body in discrete
quanta (packets of energy) rather than continuously, as suggested by classical
physics. This daring hypothesis
led to the successful explanation of the shape of the energy density curves for
black body radiation. With time and the contributions of many physicists,
Planck’s hypothesis led to the development of a whole new branch of Physics
called Quantum Physics.
Mathematically, Planck expressed the quantisation
of energy emitted from a black body as:
= n h n
where E = the energy of the radiation emitted, h
= a constant, now called Planck’s constant with a value of 6.626 x 10-34 Js,
= the frequency of the radiation emitted and n = 0, 1, 2, 3, ….. to represent the
different multiples of allowed energy coming from the black body at a particular
temperature. Conversely, the energy
inside a black body cavity is quantised, the allowed energy states are
called quantum states and the integer n is called the quantum number.
(As an aside, the formula that Planck obtained for the
energy density in the black body spectrum is:
Cute, eh? This can be
expressed in terms of l by using c =
n l. This is how the plots of energy density shown above were
AND THE PHOTOELECTRIC EFFECT
As mentioned previously, Hertz stumbled across a curious effect of light
when conducting his EM wave experiments. Sparks
jumping the gap in his receiver were more vigorous when the receiver was exposed
to ultraviolet light. Because both
light and electricity were involved in this phenomenon, it was called the
In 1900, Philipp Lenard showed that the photoelectric effect is actually
the emission of electrons from the surface of material when the material is
illuminated by light of high frequency. In a series of experiments Lenard found that:
The number of electrons released (the photocurrent) is
proportional to the light intensity.
The emission of photoelectrons was virtually instantaneous (if it
Emission was frequency dependent.
There is a certain threshold frequency below which no
photoelectrons were emitted.
As the intensity of the light increased, the maximum kinetic
energy of emitted electrons remained constant.
The maximum kinetic energy of emitted electrons was found to depend on
the frequency of the light used and the type of surface.
The last three of these experimental results
could not be explained by the classical wave theory of
theory for instance predicted that electrons in a surface absorbing low
intensity radiation of any frequency should accumulate energy for several
seconds and then have sufficient energy to be ejected.
Electrons absorbing higher intensity radiation should be ejected more
quickly. Experimental results
showed, however, that emission was almost immediate for all frequencies above
the threshold frequency and was independent of intensity.
Inspired by the work of Planck, Albert
Einstein proposed the radical idea that light energy is transmitted in
discrete packets of energy rather than as a spreading wave.
The amount of energy in each packet is a quantum and represents
the smallest quantity of light energy of a particular frequency.
Einstein gave the name photon to a quantum of radiant energy
and expressed the energy, E,
of this photon as:
= h f
where h = Planck’s constant = 6.626
x 10-34 Js & f = the frequency of the radiation emitted.
This model of light is referred to as the particle model.
Einstein used his particle model
of light to explain the photoelectric effect in the following way:
Light striking a surface consists of photons.
Each photon carries an energy hf into the surface.
Each photon gives up all its energy to a single electron.
Part of that energy (f) is used
in causing the electron to pass through the metal surface.
The rest of the energy (hf - f)
is given to the electron as kinetic energy.
This is the kinetic energy the electron will have outside the surface if
it does not suffer any internal collisions on the way out.
In other words, (hf - f) is
the maximum kinetic energy, Kmax,
of the photoelectron.
This explanation is summarised in Einstein’s
where f is called the work
function for the surface and is the minimum energy required to remove an
electron from the surface. Thus, f
= hf0 where f0 is the threshold
frequency below which no photoelectrons are emitted.
So, the equation above becomes:
(f - f0) = Kmax
Robert Millikan, an
American physicist, experimentally verified Einstein’s explanation of the
photoelectric effect in 1916. Einstein
received the 1921 Nobel Prize in Physics for his work on this effect.
Today, we view light as having
a dual character. Light behaves
like a wave under some circumstances and like a particle, or photon, under
others. When we consider the
propagation of light or its interaction with other EM radiation we usually find
it convenient to consider light as a wave motion.
When we deal with the interaction of light with matter we usually find it
convenient to think of light as a stream of particles.
On some occasions we need to
consider the wavelength and frequency properties of light, on others we need to
consider the energy or momentum aspects. The
energy is related to the frequency, the frequency is related to the speed of
= f l and E = h f
Clearly, these equations can be
rearranged as needed.
Note also that the Syllabus requires you to summarize
the use of the photoelectric effect in both photocells and solar cells. We
will look at this a little later, after we have dealt with thermionic and solid
THE DE BROGLIE MODEL OF THE
section on the de Broglie model of the atom is no longer required by the From
Ideas To Implementation Syllabus but is useful background to the Band Theory of
Solids and so has been left in this topic.
Most physics students at senior
high school level picture the atom as consisting of electrons in
planetary-like orbits around a tiny central nucleus that contains protons and
neutrons. Roughly speaking, this is
the model of the atom as described by Niels Bohr.
One of the assumptions Bohr made in creating his model was that electrons
could rotate in what he called “stationary states” around the nucleus
without losing energy. This
assumption was necessary to explain why the electrons undergoing circular motion
around the nucleus did not radiate energy as predicted by Maxwell’s Theory of
Electromagnetism. Exactly how the
stationary states enabled the electrons to orbit without losing energy was not
In 1924, Louis de Broglie, a
French physicist, explained how this could be so.
He suggested that the wave-particle dualism that applies to EM
radiation also applies to electrons and other atomic particles.
In other words, electrons can be thought of as either particles or
De Broglie reasoned that the
electrons in an atom existed as matter waves in standing wave orbits
around the nucleus. No energy
would be lost from such an orbit. De
Broglie showed mathematically that for such orbits to exist the angular momentum
of the electron could only have certain values. We say that the angular momentum of the electron is quantized.
In other words, there are only certain discrete energy levels that an
electron can occupy within the atom.
CLASSICAL MECHANICS VERSUS
is non-examinable but may be of interest to you.
Ever wondered what the basic difference is between
classical physics and quantum mechanics? Well, take a detour for a minute
and investigate the paradox of Schrodinger's Cat. This link takes you to
the Brainteasers page of this site & to the description of the Schrodinger's
Cat paradox that resides there. After reading the paradox, follow the
links to the discussion of the paradox and then, if you are still interested, to
a description of the domain of quantum mechanics itself. Use the back
button of your browser to get back here. Go
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BAND THEORY OF
The de Broglie model of the atom
was the stimulus for further research that eventually led to the wave and matrix
formulations of Quantum Mechanics, proposed by Erwin Schrodinger
and Werner Heisenberg respectively in 1925.
According to modern quantum theory, only certain discrete energy
levels or energy states are permissible in a given atom and an
electron must therefore absorb or emit discrete amounts of energy, or quanta,
in passing from one level to another. A
normal atom at absolute zero temperature has an electron occupying every one of
the lower energy levels, starting outward from the nucleus and continuing until
all electrons have been placed.
Quantum theory shows that when two
atoms are brought close enough together to interact, each of the allowed
electron energy levels within the atoms splits into two distinct but closely
spaced energy levels as the atoms combine to form the two-atom system.
In a six-atom system, each allowed electron energy level is split
into a set of six separate but closely spaced energy levels.
Clearly then, as we pack more and more atoms closely together each set of
split energy levels contains more and more levels spread over the same energy
range allowed at that particular radius from the nuclei.
So, in a crystalline solid, such as a metal or a diamond, where
billions upon billions* of atoms are packed closely together, the energy levels
within each set become so closely spaced in energy that they form a practically
continuous energy band. (*6.023
x 1023 atoms /mole of substance, to be precise.)
In solids, the bands of
permissible energy levels are called the allowed bands. These may either be filled with electrons or empty depending
on whether they correspond to filled or empty energy levels in the isolated
atoms. The energy bands between
these allowed bands are called forbidden bands. These bands correspond to the gaps between electron energy
levels within the isolated atoms. The
highest energy band that is occupied by electrons is the valence band.
A higher energy band called the conduction band lies above the
valence band. See the diagram
In insulators the valence band is completely filled and
the energy gap between it and the conduction band is very large as shown in
diagram (c) below. Thus, electrons cannot move under the influence of an applied
potential difference. Insulators
therefore have very high electrical resistance and do not conduct electric
current. Note that if an
appropriately large amount of energy was supplied to electrons in the valence
band to enable them to reach the conduction band, conduction would then occur.
This is what happens when an insulator “breaks down”.
Also note that in reality some electrons in insulators are free to move
but their numbers are extremely small compared with those of metallic
In semiconductors there is a
small forbidden gap between the valence band and the conduction band as shown in
diagram (b) above. At absolute
zero the valence band is completely full with electrons and the material acts as
an insulator. As the temperature
increases some electrons gain sufficient thermal energy to escape from the
valence band and cross the forbidden gap into the conduction band.
Once sufficient electrons have crossed the gap conduction of electric
current becomes possible and conductivity increases with temperature.
Semiconductors have electrical resistances between those of conductors
At room temperature the valence
band of a semiconductor is almost completely full. Very few electrons have gained enough thermal energy to move
to the conduction band. When an
electron does move from the valence band to the conduction band it leaves behind
a vacancy or hole. Since this hole
represents the absence of an electron from the valence band, it can be treated
as a positive charge. A nearby
electron can move into the hole, creating a new hole at the position from which
it moved. In a sense the hole
has moved within the valence band. Thus,
both electrons and holes are responsible for carrying current in a semiconductor.
In a semiconductor, under the influence of an external
electric field, holes move within the valence band in the direction of the
electric field, while electrons move within the conduction band in the opposite
direction. See the diagram
In a pure semiconductor the number
of holes in the valence band is exactly equal to the number of electrons in the
conduction band. Despite the
duplication in the number of charge carriers, the conduction of a piece of pure
silicon (semiconductor) is very low compared with copper, since so few charge
carriers are actually available. When
conduction happens in a pure semiconductor, the material is called an intrinsic
The introduction of small
amounts of certain “impurities” into germanium or silicon can markedly
increase their conductivity. The
process is known as doping. When
conduction occurs in a doped semiconductor, the material is called an extrinsic
Both germanium and silicon atoms
have four electrons in their valence shell.
When these atoms combine with others of their species, each atom shares
one valence electron with each of its four neighbours.
The introduction of atoms that have five electrons in their valence shell
means that where such atoms replace the germanium or silicon in the crystal
lattice, there is a surplus electron that is not used for bonding.
This surplus electron thus becomes available for conduction.
Semiconductors doped in this way contain more electrons than holes and
are called n-type semiconductors, since conduction takes place mainly by
electrons – negative charges. Group
V elements from the Periodic Table, such as phosphorus (P), arsenic (As) and
antimony (Sb) are used to dope germanium or silicon and produce n-type material. The pentavalent element used is called a donor atom
because it donates an electron.
Where an atom that has only three
electrons in its valence shell replaces a germanium or silicon atom in the
crystal lattice, there is a shortage of one electron to complete the bonding.
Effectively a hole has been added to the lattice.
This hole thus becomes available for conduction.
Semiconductors doped in this way contain more holes than electrons and
are called p-type semiconductors, since conduction takes place mainly by holes
– positive charges. Group III
elements from the Periodic Table, such as boron (B), aluminium (Al), gallium (Ga)
and indium (In) are used to dope germanium or silicon and produce p-type
material. The trivalent element
used is called an acceptor atom because it accepts an electron.
The fact that we can control
the number and type of charge carriers in semiconductor material by adding
impurity atoms makes semiconductors extremely useful in electronics.
The other exciting feature of semiconductors is that when a crystal is
produced consisting of p-type and n-type material in contact, the resulting p-n
junction has the following useful properties:
were discovered in the 1930’s. Semiconductor
crystals were used as rectifiers in radio and radar receivers.
These rectifiers took the high frequency alternating signal of the radio
wave and extracted the low frequencies necessary for the headphones.
In 1942-43, during World War II, Seymour Benzer, a graduate student at
Purdue University accidentally discovered that a crystal of germanium (Ge) could
withstand higher voltage than any rectifier that was then in use.
Benzer went on to discover that mixing trace elements of tin into the
germanium could produce rectifiers that were ten times more resistant to damage
than was standard at the time. Germanium
became the experimental physicists’ choice of material for research into
semiconductor properties and devices.
The production of semiconductor
devices requires semiconductor material with almost perfect crystalline
structure. Due to the
interest in germanium at that time, techniques for its purification were
developed and improved throughout the 1940’s. Although silicon (Si) was also
known to be a semiconductor at that time, techniques for its purification were
not developed until the 1950’s. For
this reason germanium was the first semiconductor material used to produce
semiconductor devices. Most notably
germanium was used to produce the first transistors in 1948.
Today, silicon is the most
commonly used semiconductor material in the world.
Other semiconductors used for particular applications include germanium,
selenium, gallium arsenide, zinc selenide, lead telluride and indium antimonide.
Silicon is the preferred material for manufacturing solid-state
devices such as transistors, integrated circuits, solid-state memories and so on
section in blue (on why silicon is the preferred semiconductor material for
transistors) is no longer examinable.
VERSUS THERMIONIC DEVICES:
When a metal or carbon filament
is heated to high temperatures electrons are emitted from the filament.
This process is called thermionic emission.
Thermionic devices consist of an evacuated tube (vacuum tube)
containing a cathode and at least one other electrode.
Vacuum tubes called diode
valves are the simplest thermionic device, containing a cathode and only
one other electrode. In the
simplest diode valve, thermionic emission from the cathode releases electrons
that are then attracted to the anode, producing a flow of current through the
tube. If an alternating potential
difference is applied across a diode a current only occurs when the potential
difference is such that the anode is positive with respect to the cathode.
The diode is said to rectify alternating current.
Triode valves contain three
electrodes, a cathode, an anode and a control grid that lies between them.
Because the grid is between the cathode and anode, all electrons have to
pass through it in their paths to the anode.
Small changes in the potential difference between the grid and the
cathode produce changes in the current between the cathode and the anode that
would have required much larger changes in the anode-cathode potential
difference. The triode therefore
amplifies small potential differences.
In a radio receiver for instance, the signal voltage applied to the grid
of the triode valve modulates the tube current passing from the cathode to the
anode. A small change in the signal
voltage produces a much larger change in the tube current and hence in the
circuitry connected to the anode.
Prior to 1948 vacuum tubes were
the state of the art amplifiers used in radio equipment to increase signal
voltages to levels that could drive loudspeakers.
Triodes and more complex vacuum tubes such as tetrodes (4
electrodes) and pentodes (5 electrodes) were widely used in amplifying
circuits even up until the 1960’s.
A solid-state device is an
electronic component or device that is composed chiefly or exclusively of solid
materials, usually semiconducting, and that depends for its operation on the
movement of charge carriers within it. The
development of simple solid-state devices such as semiconductor diodes in
the 1930’s eventually led to the development of the point contact
transistor by Walter Brattain and John Bardeen in 1948.
In the same year William Shockley proposed the idea of the junction
(sandwich) transistor and by 1950 had turned the idea into reality.
Shockley’s transistor turned out to be the more
useful of the two. It consisted of
a sandwich structure in which two n-type semiconductor layers were
separated by a p-type semiconductor layer, as shown below.
The two n-type layers are known as
the emitter and collector. The
p-type layer is called the base. Transistors can be connected in a number of different ways in
circuits. In a typical connection
small variations in the base current result in much larger changes in the
collector current for a constant potential difference between the collector and
emitter. In other words, the
transistor can be used as an amplifier.
From the 1960’s onwards
solid-state devices such as transistors, and later integrated circuits
and microprocessors, replaced thermionic devices for the following
Modern day transistors are usually
either bipolar junction transistors or field-effect transistors (FET’s).
They are used worldwide in a huge range of electronics applications –
computers, medical equipment, telecommunications, industrial equipment,
household devices such as stereos and so on.
USE OF PHOTOELECTRIC
EFFECT IN PHOTOCELLS
Syllabus point 9.4.2 Column 3 Dot Point
3 requires students to gather, process and present information to summarize the use of the photoelectric effect in photocells.
In essence the summary of the
use of the photoelectric effect in photocells should contain information similar
to the following.
Photocells consist of a cathode and anode in an evacuated
glass tube. The photoelectric
effect is used in photocells to free electrons from the cathode, thus enabling a
current of electrons to flow from the cathode to the anode. The cathode is usually coated with a photosensitive compound
that emits electrons when light falls upon it.
If a photon of light with frequency above the threshold
frequency for the photosensitive compound strikes an atom of the compound it
will be absorbed and will cause the atom to emit an electron.
This electron leaves the cathode and moves towards the positive potential
of the anode. In this same way a
continuous beam of light shining on the cathode produces sufficient electrons
via the photoelectric effect to enable a continuous current of electrons to flow
between the cathode and anode. The
size of this photocurrent is proportional to the intensity of the light incident
on the cathode.
EFFECT OF LIGHT
ON SEMICONDUCTORS IN SOLAR CELLS
Syllabus point 9.4.3 Column 3 Dot Point
4 requires students to gather, process and present information to summarize the
effect of light on semiconductors in solar cells.
In essence the summary of the
effect of light on semiconductors in solar cells should contain information
similar to that in the following example.
Solar cells are photovoltaic devices composed of
semiconductor material such as silicon. Usually
a p-n junction is used. This is a
junction formed between a piece of n-type silicon and a piece of p-type silicon.
An electric field is set up at the junction and this forms a potential
barrier that forces any free electrons in the silicon to move to the n-type
silicon and any holes to move to the p-type silicon.
Light shining on the semiconductor material
frees electrons from
the valence band to the conduction band of the semiconductor material, thus
producing electron-hole pairs in the semiconductor.
A photon of light with energy greater than the band gap energy between
the valence and conduction bands but less than the work function energy for the
semiconductor strikes an electron and is absorbed.
This gives the electron sufficient energy to jump the forbidden energy
gap from the valence to the conduction band.
Once the electron is free it is forced by the barrier
potential to move to the n-type material, while the hole left behind is forced
to move to the p-type material. If
an external circuit is supplied, the electron will move out of the n-type
material, around the external circuit through a load and back into the p-type
material to recombine with the hole. Clearly,
as many electrons undergo the same process, an electric current has been
produced by the solar cell. The
size of the current produced is proportional to the light intensity incident on
the solar cell. Overall, light
energy has been transformed into electrical energy.
PHOTOCELLS AND SOLAR CELLS
By way of general information, solar cells are actually one type of
photocell. The few basic differences that exist between the two can be
stated as follows:
are often thermionic whereas solar cells are always solid state;
are usually used as detectors
or switches whereas solar cells are usually used for practical power
photocells use the photoelectric effect directly to knock electrons out of a
metal surface (the cathode) whereas solar cells being photovoltaic devices
use light energy to free electrons from the valence band to the
conduction band of the semiconductor material but not to kick them out of
that semiconductor material;
photocells require an external potential difference to be applied between
the anode and cathode to attract the photoelectrons released from the
cathode to the anode, whereas solar cells do not require an external
potential difference to be applied in order for them to produce a current.
Crystalline solids consist of a regular, three-dimensional arrangement
of atoms in a periodic pattern called a crystal lattice.
The internal structure of such solids can be determined using a technique
called X-ray diffraction.
As you will recall from the Preliminary Course, diffraction
is the name given to the phenomenon in which a wave spreads out as it passes
through a small aperture or around an obstacle. Diffraction
patterns are most intense when the size of the aperture or obstacle is
comparable to the size of the wavelength of the wave. Since the wavelength of X-rays is of the order of 10-10m
and since the interatomic spacing in solids is of the same order, X-rays produce
strong diffraction patterns from crystals.
(Note that both neutrons and electrons can be used in place of X-rays.)
The British physicists William and Lawrence Bragg
(father & son) applied X-ray diffraction to the study of crystals from
about 1912 onwards. A beam of
X-rays with a wide range of wavelengths was collimated and directed onto the
single crystal specimen under study. A
flat film behind the specimen received the diffracted beams. The diffraction pattern consisted of a series of spots of
light that indicated the symmetry of the crystal.
William Bragg presented a simple explanation of the
diffracted beams from a crystal. He
suggested that the X-ray waves incident on parallel planes of atoms in the
crystal are reflected, with each plane reflecting only a very small fraction of
the radiation. The diffracted beams
are formed when the reflections from parallel planes of atoms interfere
constructively, as in the diagram below.
Bragg derived the following formula, now called the Bragg
Law, which enables the determination of the interatomic spacing, d, of
the atoms in the specimen or the wavelength, l, of the X-rays (depending on what is known):
where q = the angle of reflection at which
constructive interference occurs and n = the order of diffraction
(n = 1, 2 ,
3, ….. corresponding to occasions when the path difference between the two
reflected rays in the diagram is an integral number, n, of wavelengths, allowing
constructive interference to occur).
The Braggs’ contribution to our understanding of
crystal structure has had a lasting beneficial impact in many areas of science
and engineering. They were
pioneers in a field which has allowed us to greatly increase our knowledge and
understanding of materials and which has assisted tremendously in the
development of new materials. The
Braggs received the 1915 Nobel Prize for Physics in recognition of their
important contribution to science.
Metals possess a crystal
lattice structure. As mentioned
previously, metals are composed of atoms that have some weakly bound valence
electrons. As these atoms come
together to form the crystal lattice, some of the weakly bound electrons are
freed from their atoms by the energy released in binding.
In very good conductors such as copper, aluminium and silver, all the
atoms are fully ionised, one electron becoming detached from each nucleus in the
lattice. These delocalised valence electrons are free to move from atom
to atom and are thus shared by all atoms in the lattice. In this
sense, they behave like a gas, an “electron gas”.
Thus, there are many valence electrons available for conduction in
metallic solids. Conduction in metals can be considered as a free
movement of electrons, relatively unimpeded by the crystal lattice.
Drift Velocity in Metals - Not Examinable:
In the absence of an electric field, thermal energy causes electrons in a metal to move
throughout the crystal lattice at speeds of up to 106
When an electric field is applied across a metallic conductor, the
electrons experience a net force in a direction opposite to the applied field
direction. This results in a net drift
of electrons towards the high potential end of the field.
This drift motion is superimposed on the random motion of the electron
and produces a net drift velocity of around 10-4
The net drift of electrons in one particular direction constitutes a current.
The size, I, of this current can
be shown to be:
where n = electron density (number of electrons per unit volume of
= charge on the electron, v = drift velocity of electrons, and
= cross-sectional area of the conductor.
Causes of Electrical Resistance:
Electrons can move freely through a regular crystalline lattice, but any
disruptions in the regularity of the lattice will obstruct their flow and cause resistance.
There are two main sources of this electrical resistance.
The first is imperfections
in the crystal lattice, such as those caused by impurity atoms
or by vacancies,
where an atom is missing from a site in the lattice. Each time an electron collides with an imperfection, it loses
kinetic energy. This
energy is added to the vibrational energy of the lattice, which, in turn, is
measured as a rise in temperature of the conductor.
Secondly, every atom in a lattice vibrates. The thermal energy emitted
or absorbed by these lattice vibrations is quantized and the quanta are
called phonons. Every lattice contains rapidly moving phonons.
electrons collide with phonons, they are scattered and lose kinetic energy, which is again added
to the vibrational energy of the lattice and produces a rise in the temperature
of the conductor.
Note that collisions between electrons and phonons account
for most of the electrical resistance of a conductor. The higher the temperature of the conductor, the more
energetic the vibrations of ions in the lattice and the more phonons there are
present in the lattice. So, as
the temperature rises so too does the electrical resistance of the metallic
Hence, the electrical resistance
of a metallic conductor should decrease to a low but non-zero value as the
temperature decreases towards absolute zero.
We would still expect a residual resistance even near absolute zero due
to crystal lattice imperfections. The
fact is, however, the electrical resistance of some metals disappears completely
at sufficiently low temperatures.
In 1911, the Dutch physicist Heike Kamerlingh-Onnes found that the
electrical resistance of solid mercury drops to an immeasurably small value when
cooled to a temperature of 4.15 K (-269oC).
This phenomenon in which a conductor
loses all of its electrical resistance at a certain critical temperature
is called superconductivity.
Mercury goes from a normal state to a superconducting state
as the temperature drops below 4.15 K. Many
other elements, and many compounds and alloys have since been found to exhibit
similar behaviour. Up until 1986
the highest value of Tc discovered was
about 23 K. In 1986, Georg Bednorz
and Alex Muller discovered certain ceramic materials that became superconducting
at 30 K and since then other ceramics have been produced with Tc
values as high as 134 K. These new
ceramic materials are known as high temperature superconductors.
The German physicists Walther Meissner and Robert
Ochsenfeld discovered another exciting property of superconductors in 1933.
They found that when a superconducting material is cooled below its
critical temperature in the presence of an applied magnetic field, it expels
all magnetic flux from its interior. If
the field is applied after the material has been cooled below Tc
the magnetic flux is excluded from the superconductor.
This effect is now called the Meissner Effect
and lends itself to a startling demonstration of superconductivity.
A magnet can be made to float above a piece of superconducting material,
as shown in the diagram below. Supercurrents
induced by the magnet flow through the superconductor and produce a magnetic
field that exactly cancels out the magnet’s own field.
THE BCS THEORY
In 1957, John
Cooper and John
Schrieffer of the USA proposed a detailed quantum mechanical theory,
now known as BCS
Theory, to explain superconductivity. The
predictions of this theory are in excellent agreement with experimental results
for low temperature superconductors. Some adjustments or perhaps even a new theory are necessary
in order to fully explain high temperature superconductivity.
BCS Theory suggests that superconductors have zero
electrical resistance below their critical temperatures because at such
temperatures the electrons pass unimpeded through the crystal lattice and
therefore lose no energy. The
theory states that the supercurrent in a superconductor is carried by many
millions of bound electron pairs, called Cooper pairs. These pairs form when one electron passing between adjacent positive ions
in the lattice attracts the ions, causing them to move slightly inwards and to
create a region of increased positive charge density.
Due to the elastic properties of the lattice, this region of increased
positive charge density propagates through the lattice as a wave.
A second electron passing through the lattice is attracted into this
moving region of increased positive charge density and is effectively swept
along by the lattice wave created by the first electron.
Thus, by pairing off two by two, the electrons pass more smoothly through
the lattice. See diagram below.
Cooper pairs continually form, break and re-form.
Since random lattice vibrations break up Cooper pairs, the temperature
needs to be low enough to keep such vibrations to a minimum.
Note that the description of BCS Theory given above has
been greatly over-simplified. A
more detailed description is way beyond the scope of this course.
& LIMITATIONS OF SUPERCONDUCTORS:
Generation, Storage and Transmission
The electrical resistance of transmission lines
typically results in power losses of up to 5 %. If power lines could be made superconducting, the present
transmission losses could be reduced. Superconducting
generators could be used to produce electrical power more efficiently
than conventional generators. Since current can flow indefinitely in superconductors,
superconductor coils could be used to store electricity produced in
periods of low demand for use in periods of peak demand.
Many research laboratories around the world are working in this area.
to their lack of resistance, superconductors have been used to make electromagnets
that generate large magnetic fields with no energy loss.
Superconducting magnets are used in Magnetic Resonance Imaging (MRI) machines to
produce 3-D images of the internal structure of the human body.
They are used in other nuclear magnetic resonance instruments to study the
structure of materials and in the construction of powerful particle accelerators.
Superconducting magnets are also used in magnetic levitation (Maglev)
trains and in experimental nuclear
fusion reactors in which the hot plasma is confined by magnetic fields.
the quantum effects of superconductivity, devices have been developed
that measure electric current, voltage, and magnetic field with unprecedented
(Superconducting Quantum Interference Devices) are used to measure magnetic
fields that are less than a billionth of the earth’s magnetic field strength.
These devices have applications in medicine, materials science, geology
and other fields.
are built using Josephson junctions, superconducting electronic switches.
Such switches can switch current off or on very quickly – within a
picosecond (10-12 s). They
can thus be used instead of transistors in computers to produce machines that
operate many times faster than present day machines and that are much smaller,
since no space needs to left inside such machines for heat dissipation purposes.
of superconductors include:
superconductors still require temperatures close to absolute zero for their
operation. This requires the use of
liquid helium as the coolant. This
is very expensive and wasteful of helium, which is a non-renewable resource.
temperature ceramic superconductors are difficult to produce, brittle, difficult
to make into wires for electricity transmission and are chemically unstable in