Download - From Ideas to Implementatio n Core Module 9.4. Introduction A new dawn in physics had begun at the start of the twentieth century… …it appeared that the.

From Ideas to

ImplementationCore Module 9.4

Introduction

A new dawn in physics had begun at the start of the twentieth century…

…it appeared that the stage had been reached when all the disparate elements of scientific knowledge seemed to be

coming together…

…many scientists felt that the total knowledge about the universe lay just beyond their horizon…

…future generations of scientists, it was believed, would have nothing to discover…

…this idea was about to be challenged.

However, early in the twentieth century, physics, or classical physics as it is now known was to be shaken to the core by two remarkable new insights about the universe.

The first of these insights was was made by Albert Einstein when he proposed his now famous Theory of Special Relativity in which he showed that space and time were interrelated.

Until now, physicists believed that all phenomena could be broken down into fundamental interactions that were capable of being described by the laws of physics.

By extending the laws of quantum physics to large masses, distances and times, it was shown that it was possible to derive the laws of classical physics.

These insights lead to the development of quantum physics, which was primarily developed to explain atomic phenomena and eventually proved to be more fundamental than classical physics.

The second insight came when Max Planck realised that in spite of his best efforts to make the laws of classical physics fit natural phenomena on the atomic scale, these laws were simply incapable of resulting in an explanation.

We start with the discovery and identification of cathode rays and how this ultimately led to modern television.

We then look at how black body radiation and the photoelectric effect led to a new view of the nature of electromagnetic radiation with the quantum theory of Max Planck.

We conclude by looking at how the study of sub-atomic particles led to the invention of the transistor and to the discovery of superconductivity.

In this unit, we will investigate some of the fundamental ideas of quantum physics.

• explain why the apparent inconsistent behaviour of cathode rays caused debate as to whether they were charged particles or electromagnetic waves

• explain that cathode ray tubes allowed the manipulation of a stream of charged particles

• identify that moving charged particles in a magnetic field experience a force

• identify that charged plates produce an electric field

• describe quantitatively the force acting on a charge moving through a magnetic field

• discuss qualitatively the electric field strength due to a point charge, positive and negative charges and oppositely charged parallel plates

• describe quantitatively the electric field due to oppositely charged parallel plates

• outline Thomson’s experiment to measure the charge/mass ratio of an electron

• outline the role of:

– electrodes in the electron gun

– the deflection plates or coils

– the fluorescent screen in the cathode ray tube of conventional TV displays and oscilloscopes

• perform an investigation and gather first-hand information to observe the occurrence of different striation patterns for different pressures in discharge tubes

• perform an investigation to demonstrate and identify properties of cathode rays using discharge tubes:

– containing a maltese cross

– containing electric plates

– with a fluorescent display screen

– containing a glass wheel

– analyse the information gathered to determine the sign of the charge on cathode rays

• solve problem and analyse information using:

and

1. Increased understandings of cathode rays led to the development of television

Students learn to: Students:

F qvB sinF qE

E V

d

By the 1850’s, much was known about which solids and liquids were electric conductors or insulators, and it was thought that all gases were electric insulators.

Discharge Tubes

In 1855, Heinrich Geissler (a glass blower and maker of scientific equipment) had refined a vacuum pump that could evacuate a glass tube to within 0.1% of normal air pressure.

Julius Plucker (a colleague of Geissler’s) sealed a wire in each end of a glass tube and connected it to a high voltage power supply. He then steadily removed the air from inside using Geissler’s pump. To their surprise, they found that at reduced pressures, air (and all other gases) conduct electricity!

Plucker showed that as the pressure is reduced in the discharge tube (as it is now known), a series of changes progressively take place. We will examine these in the following first hand investigation:

ACTIVITIES

• Experiment 20A: Discharge tubes

As the pressure of the gas inside the tube was reduced, both the anode and cathode were surrounded by a luminous glow. As the pressure was reduced further, the positive glow extended about halfway along the tube (between the positive glow and the negative glow is an area called the Faraday dark space). At even lower pressure, the positive glow broke up into columns called striations. Lower still, an area called the Crooke’s dark space filled the entire tube and a green glow appeared in the glass at the end of the discharge tube opposite the cathode.

Faraday’s dark space

Crooke’s dark space

AnodeCathode

- +

Negative glow

Positive striations

Discharge Tube Sample observations:

The discharge coming from the cathode had by now been named cathode rays.

By 1875 Sir William Crookes had made further discoveries. He built and experimented with a variety of different tubes (which he called Crookes tubes - variations of the tubes used by Geissler and Plucker).

The Crookes tubes had structures built into or around them to allow the cathode rays to be manipulated. For example, electrodes were built into the cathode ray tube to create an electric field to attempt to change the path of the cathode rays. Magnetic fields were applied to the cathode rays through the glass from outside the tube, and solid objects were placed inside the tube to block the path of the rays.

Crookes Tubes

ACTIVITIES

• Prepare a Risk Assessment for the following experiment

• Experiment 20B: Properties of Cathode Rays

Sample observations:

A fluorescent screen shows that cathode rays can cause fluorescence. This demonstrates that cathode rays have energy. A fluorescent screen can also be used to trace the path of cathode rays being manipulated by other means.

A Maltese cross placed in the path of the cathode rays causes a clearly defined shadow at the end of the tube. This effect is used to infer that cathode rays travel in straight lines and are blocked by solid objects.

Pairs of electric plates cause the cathode rays to bend towards the positive plate. This shows that cathode rays have negative charges.

Charged plates

Note that Crookes believed that cathode rays could be deflected by an electric field but never succeeded in demonstrating this experimentally.

first

A lightweight glass paddle wheel, able to rotate freely, is placed in the path of the cathode rays. The cathode rays cause the wheel to spin and move away from the cathode. This demonstrates that the cathode rays have momentum, and therefore mass, and that they are emitted from the cathode.

A cathode ray in the presence of a magnetic field will deflect (bend). As we already know, moving charges experience a force in a magnetic field (RHPR). This shows that cathode rays carry a negative electrical charge.

Use the diagrams to show that the cathode rays are negatively charged

• always have the same properties regardless of the metal in the cathode

• travel in straight lines

• carry energy

• have mass

• cause a green luminescence when they strike glass

• change the colour of some silver salts (i.e. expose photographic film)

• pass straight through thin metal foil without damaging it

• travel considerably more slowly than light

• are deflected by magnetic fields

• are deflected by electric fields (we’ll come back to this one!!)

These (and other) experiments showed that cathode rays:

The cathode ray debate – waves or particles?

The controversy as to whether cathode rays were streams of charged particles or electromagnetic waves is a great example of the nature of scientific development. This particular debate raged for years.

• they produced fluorescence• they travelled in straight lines• they pass straight through thin metal foil • they produced similar chemical reactions on

photographic film to those produced by light• they were not deflected by electric fields (or so it

seemed).

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 the nature of cathode rays.

Some of the properties of cathode rays suggested to physicists that cathode rays were a wave similar to light. For instance:

J.J. Thompson was able to make a cathode ray tube with sufficiently low pressure and using a very high voltage supply he was able to deflect the cathode rays with an electric field. This showed conclusively that cathode rays were beyond doubt streams of charged particles. We now call these charged particles electrons!

Before we look at J.J. Thompson’s experiment, we need to look at the effects of charged particles moving in electric and magnetic fields.

The reason the debate took so long to clear up was that initially the cathode rays could not be deflected by an electric field.

The debate was finally resolved in 1897 by J.J. Thompson.

ACTIVITIES

• Read 10.1

• Complete 1 – CRTs

• Complete 2 – Properties of Cathode Rays

• Complete Assignment 1

Electric fields

An electric field is said to exist in any region in which an electrically charged object experiences a force. An electric field has both strength and direction.

The strength of the electric field due to a point charge diminishes with distance from it. The direction of the field around a point charge:

• is directed radially away from a positive point charge; and

• is directed radially towards a negative point charge.

The number of lines drawn to represent a field at any point indicates the electric field strength at that point. The stronger the field, the more lines are drawn in a given space.

The electric field between two oppositely charged parallel plates is uniform in strength and direction. The field direction is at right angles to the plates and away from the positive plate.

Electric field between two parallel charged plates

It should be noted that the electric field is not uniform at the edges of the parallel plates:

The electric field due to charged parallel plates

Hence,

E = V/d

• proportional to the potential difference, V, between the plates;

• inversely proportional to the separation, d, between the plates;

Where: E is electric field strength (V/m)V is the potential difference between the plates (V) d is the distance between the plates (m)

The electric field strength, E, between two oppositely charged parallel plates is:

Note: the syllabus expects you to be able to solve problems using this equation

Practice Questions

Example:

In a glass tube from which air has been removed, electrons are accelerated by a uniform electric field between a pair of charged parallel plates, separated by 5 cm. If an electrical potential difference of 4 kV is applied across the plates, determine the electric field strength half way between the plates.

Solution:

This is a trick question. The field is UNIFORM, hence the field strength is the same in all areas between the plates:

E = V/d

E = 4000 / 0.05

E = 8 x 104 V/m (N/C)

A charged object placed in an electric field will experience a force. The magnitude of the force acting on this charged object is given by:

F = qE

Where: F is the force acting on the charged object (N)q is the magnitude of the charge of the object (C) E is the electric field strength (N/C or V/m)


Example:

A particle carries a charge of -3.2x10-19C. It is placed in a uniform electric field of strength 5000 V/m.

(a) Where might such a uniform field exist?

(b) Determine the electrostatic force on the particle.

Solution:(a) Between two oppositely charged parallel plates

(b) F = Eq

F = 5000 x (-3.2x10-19)

F = -1.6x10-15 N(the negative reminds us that the force is in the opposite direction to the electric field)

Moving charges in magnetic field experience a force

As we saw in the topic ‘Motors and Generators’, a magnetic field exerts a force on electric currents – that is, on moving charged particles.

The direction of the force can be determined using the right hand palm rule. Remember that current is in the opposite direction to the flow of electrons.

The magnitude of the force is a maximum when the charge moves perpendicular to the magnetic field:

X X X X X

X X X X X

X X X X X

X X X X X

X X X X X

B +I

F

A constant magnitude force, which is perpendicular to the velocity of a particle, results in the particle travelling in a circular path.

Can you explain why?

• proportional to the size of the charge, q;

• proportional to the velocity of the charge, v;

• proportional to the magnetic induction, B; and

The force, F, on a charge moving through a magnetic field is:

F = qvB sinq

F is the force on the charged object (N)q is the charge of the object (C) v is the velocity of the charged object (m s-1)B is the magnetic field flux density (T)

q is the angle between the velocity and the magnetic field.


• proportional to the sine of the angle, q between the velocity and the magnetic field lines (being a maximum when it is 90o, and zero when the velocity is parallel to the field).

Example 1:

A proton travelling at 5.0x103 m s-1 enters a magnetic field of strength 1.0 Tesla at 90o. Determine the magnitude of the force experienced by the proton.

Solution:

Example 2:

The path of a helium nucleus, travelling at 3.0x103 m s-1, makes an angle of 90o to a magnetic field. The electron experiences a force of 1.2x10-15 N while in the field. Calculate the strength of the field.

Solution:

Example 3:

A charge of +5.25 mC moving with a velocity of 300 m/s north east, enters a uniform magnetic field of 0.310 T directed from left to right across the page. Calculate the magnetic force acting on the charge.

Solution:

NF

F

qvBF

345.0

45sin310.0300)1025.5(

sin3

into the page

ACTIVITIES:

• Read 10.2 – 10.3


• Complete 4 – Electric Fields

• Complete 5 – Charges in Magnetic Fields 1

• Complete 7 – Charges in Magnetic Fields 3

J.J. Thompson’s charge to mass ratio experiment

With the knowledge of how charges are influenced by electric and magnetic fields, we can return to the cathode ray controversy.

Remember that it was J.J Thomson who finally established the true nature of cathode rays – they were negatively charged particles.

In order to do so he carried out an astonishing experiment. He subjected beams of cathode rays to deflection by electric and magnetic fields set at right angles to each other. By doing so, he was able to measure the charge to mass ratio of cathode rays.

In his experiment, cathode rays were passed through two narrow slits to make a thin parallel beam aimed at the centre of a fluorescent screen. Charged parallel plates were placed to create a uniform electric field that exerted a upwards force on the beam. An external electromagnet (called a Helmholtz coil) was placed to produce a uniform magnetic field that exerted a downward force on the beam.

Thomson manipulated the strengths of the two fields until the beam passed through both fields undeflected. This occurred when the two forces on the particles in the beam were equal and opposite. By equating the expressions for these two forces, Thomson calculated the velocity of the particles.

Mathematically:

FB = FE

therefore, qvB = qE

hence, v = E/B

Note: the syllabus does not expect you to be able to solve problems using these equations, but you can use them when you explain Thompson’s experiment.

Thomson then removed the electric field and calculated the radius of the circular path followed by the particles in the uniform magnetic field alone. By equating the force due to the magnetic field to the centripetal force, he was able to calculate that all cathode ray particles had the same charge to mass ratio of 1.76 x 1011 C kg-1 – this was 1800 times larger than the q/m value for a hydrogen ion (a proton).

Mathematically:

FB = FC

therefore, qvB = mv2/r

hence, q/m = v/Br

Note: the syllabus does not expect you to be able to solve problems using these equations, but you can use them when you explain Thompson’s experiment.

On the basis of all these results, Thomson suggested that the cathode ray particle was a fundamental constituent of the atom (i.e. a sub-atomic particle). Although he originally referred to the particles as ‘corpuscles’, the name electron slowly became accepted as the official name.

In other experiments, Thomson showed that the charge on the cathode ray particles was the same magnitude as the charge on a hydrogen ion (a proton). This combined with the fact that the q/m ratio for cathode rays was 1800 times larger than that for the hydrogen ion meant that the mass of the cathode ray particles had to be 1800 times smaller than that of the proton.

The cathode ray TUBE

A cathode ray tube (CRT) consists of three main components:

• A fluorescent screen

• An electron gun

• The deflection system

fluorescent screen

The Fluorescent Screen:

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.

electron beam

deflection plates

electron beam

deflection plates

The Electron Gun:

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 emitted due to 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 into a single beam.

The ‘grid’ is negatively charged, and its magnitude can be varied easily. What effect would it have on the brightness of the screen? Why?

The grid is placed between the cathode and anodes and constantly varies its negative charge. This enables the intensity of the electron beam to be controlled – the more negative the grid, the fewer electrons are permitted to leave the electron gun and ultimately the spot on the end of the tube is less bright.

This allows the electron beam to be deflected from the straight-line trajectory with which it leaves the electron gun.

The deflection system usually 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 through the vertical plates. Thus, by applying appropriate voltages to the deflection plates, the position of the spot on the end of the screen can be controlled.

The Deflection System:

Both sets of plates are uncharged, and the cathode ray passes through undeflected.

The horizontal plates are charged and the cathode ray is deflected vertically.

The vertical plates are now charged, the cathode ray is deflected horizontally.

Horizontal plates

Vertical plates

A cathode ray oscilloscope (CRO) uses cathode rays to form an image on a fluorescent screen of the waveform of a periodically varying voltage. This allows the waveform to be analysed for frequency, amplitude and irregularities, etc.

Cathode Ray Oscilloscope (CRO)

An electric field is used to make the beam sweep horizontally from left to right, then rapidly back to the start. The periodically varying voltage of the input signal makes the beam move up and down with the same frequency as the input signal. The glowing trace on the fluorescent screen forms a visual representation of the waveform of the input signal.

A television picture tube is a cathode ray tube in which the cathode rays (beams of electrons) are focused onto a fluorescent screen to form a moving picture. The picture is formed by combining and synchronising the actions of horizontal and vertical electric fields (or sometimes electromagnetic coils), in response to signals from the television signal.

Television – a household particle accelerator!

The horizontal field causes the beam to sweep uniformly across the screen from one side to the other, then rapidly back to the start. The vertical field moves the beam down slightly for each successive sweep, filling the screen with a series of horizontal lines, until it reaches the bottom, then returning rapidly to the top. This process is repeated 50 or 60 times a second.

The intensity of the electron beam is modulated by the input signal (via the grid) to cause lighter and darker spots along on the fluorescent screen, forming the detail of the picture. The picture is constantly refreshed, giving the appearance of smooth motion. A television picture tube

Looking at the electron gun

Close up, you can see the filament in the center of the gold colored electron gun.

ACTIVITIES

• Read 10.4 – 10.6

• Assignment 3

2. The reconceptu-alisation of the model of light led to an understanding of the photoelectric effect and black body radiation

• describe Hertz’s observation of the effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate

• outline qualitatively Hertz’s experiments in measuring the speed of radio waves and how they relate to light waves

• identify Planck’s hypothesis that radiation emitted and absorbed by the walls of a black body cavity is quantised

• identify Einstein’s contribution to quantum theory and its relation to black body radiation

• explain the particle model of light in terms of photons with particular energy and frequency

• identify the relationships between photon energy, frequency, speed of light and wavelength:

E hf

and

c f l

• perform an investigation to demonstrate the production and reception of radio waves

• identify data sources, gather, process and analyse information and use available evidence to assess Einstein’s contribution to quantum theory and its relation to black body radiation

• identify data sources gather, process and present information to summarise the use of the photoelectric effect in photocells

• solve problems and analyse information using:

E hf

and

c f l• process information to discuss Einstein and

Planck’s differing views about whether science research is removed from social and political forces


In 1865 James Maxwell predicted the existence of electromagnetic waves. He derived four highly complex mathematical equations that suggested that an accelerating charge would produce a changing electric field that would in turn produce a changing magnetic field.

By Faraday’s Law, this uniformly changing magnetic field would in turn produce a changing electric field and so on.

Background Information

These fields will propagate outwards from the source through space as a wave 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. But there was no way to prove it.

Induction coil

Spark gaps

Receiver

Brass sphere

Heinrich Hertz, a German physicist, achieved the first experimental evidence of the existence of electromagnetic waves in 1887. Hertz used an induction coil to produce oscillating electric sparks between two brass spheres separated by a small distance. He used a small loop of wire with a tiny gap in it as the receiver.

Hertz discovers Radio waves

As sparks jumped across the gap between the spheres, sparks were also observed jumping the gap in the receiver. Hertz reasoned that the spark discharge oscillating backwards and forwards between the brass spheres set up changing electric and magnetic fields that propagated as an electromagnetic wave, as postulated by Maxwell. When these waves arrived at the receiver loop, the changing electric field caused charges in the loop to oscillate, thus producing the spark across the gap in the receiver.

Induction coil

Spark gaps

Receiver

Brass sphereTransmitter

EXPERIMENT: Radio waves

AIM: To demonstrate the production and transmission of radio waves.

MATERIALS: Power pack, induction coil, radio, wires.

RISK ASSESSMENT: The spark across the gap of an induction coil generates all wavelengths of EMR – including X-rays and short wavelength UV. These are potentially dangerous.

METHOD: 1. Adjust the gap on the induction coil to about 5mm and set the power pack to 6V DC

2. Adjust the tuner on the radio so that it receives a signal from a radio station. Set the radio at the back of the

laboratory.

3. Record any observations when the induction coil is turned on then off.

• travel in straight lines

• can be reflected by a metal sheet

• can be refracted

• can be diffracted

• can be polarised

• travel at the speed of light (we will see how Hertz calculated the speed shortly)

Hertz conducted several experiments on his waves (he called them radio waves) and showed that they:

These properties as you may recall are the same as the properties of light – Hertz had shown that his radio waves and light waves are part of the same family – (we now call it the electromagnetic spectrum). It wasn’t long before the other EMR waves were discovered.

Hertz measures speed of Radio waves

Hertz was able to calculate the velocity of his radio waves by reflecting the generated waves off a metal sheet and measuring the wavelength of the standing wave set up by interference. He the substituted this wavelength and the frequency of the waves (i.e. the frequency of the induction coil) into the general wave equation, v = f λ. Hertz then calculated the wave speed at 3 x 108 ms-1 – the same as that estimated by Maxwell and measured by Fizeau!

Thus, Hertz’s experiment confirmed Maxwell’s prediction of the existence of EM waves and provided strong experimental support for the idea that light was a form of transverse EM wave.

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 tinkering, Hertz discovered that the sparks jumping the gap in the receiver were greater if ultraviolet light from the initial spark was shone onto the gap. Although this was a most amazing discovery, Hertz did not further investigate this phenomenon but confined his research to the production and study of EM waves.

Hertz and the Photoelectric effect

Other scientists including J.J. Thompson found that the UV light itself was causing electrons to be emitted from the surface of the receiver. This effect is known as the Photoelectric effect and we will examine it shortly, but first, we need to look at black body radiation…

These diagrams show some experiments carried out by Hertz.

Remember that he only had a passing interest in this effect, and never actually investigated it.

Can you describe what he would have seen?

ACTIVITIES

• Read 11.1 – 11.3

• Assignment 4

Black body radiation and the Ultraviolet Catastrophe

The dominant wavelength (colour) of a hot object is directly related to the temperature of the object.

To understand exactly how the wavelength of the radiation varies with temperature, experiments were carried out using a ‘black body’.

A black body is a perfect emitter and absorber of energy. An example is a completely sealed oven with a small hole drilled in one side. At a temperature of say 6000 degrees, the inside walls of the oven will emit all types of radiation (including visible light, UV, IR), but will peak in intensity at a particular frequency (e.g. red – it will therefore appear red to our eyes).

When objects are heated, they begin to give off light - first red, then yellow, and finally white.

All light that enters the hole will be absorbed by the walls of the oven, the oven will increase in temperature, and the walls will emit radiation that peaks at a shorter wavelength (higher frequency) e.g. blue. Some of the emitted radiation will escape through the hole and can be analysed using a spectroscope.

The diagram below shows the black body curves (obtained through experiment) of the radiation emitted at different temperatures:

This emitted radiation is called black body radiation, and when it is plotted on a graph we get a black body curve.

Intensity(energy radiated)

Note: all wavelengths are emitted, but intensity peaks at a certain wavelength that is dependent upon the temperature.

visible light (VIBGYOR)

Wavelength (x10-6m)

Classical ‘wave theory’ states that light is a wave. It predicted that as the black body became hotter, the wavelength of the peak emitted radiation would become shorter, and the intensity (amount) of this peak wavelength would increase (i.e. as the oven becomes hotter it will produce more blue light than the other wavelengths and therefore appear blue).

This in itself is not a problem (after all it explains what we actually see), but when the predicted curve is plotted we get the following:

The shape of the curves presented a problem for scientists trying to explain the intensity and wavelength variations.

Experimental results gave this curve

UV Visible Infra-red

Classical (wave) theory of light predicted this curve

What happens at the wavelength of UV to the amount of energy released (i.e. the intensity) by this object according to classical (wave) theory?

The classical curve shows that as the energy decreased in wavelength from the visible into the UV portion of the spectrum, the intensity of the radiation emitted from the hole in the black box would approach infinity! This increase in energy would violate the law of conservation of energy!! This was called the Ultraviolet catastrophe.

Experimental results clearly show the radiation intensity curve corresponding to a particular temperature having a definite peak and then declining – take another look at the black body radiation curves:

Intensity(energy radiated)

Note: all wavelengths are emitted, but intensity peaks at a certain wavelength that is dependent upon the temperature.

visible light (VIBGYOR)

Planck suggested that all EMR 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

It was becoming apparent that light might not be a wave! Clearly, a new approach was needed. This came in 1900 when a German physicist, Max Planck, suggested a revolutionary idea.

led to the successful explanation of the shape of the black body radiation curves. The big problem was that this explanation was based purely on mathematical equations, and the only way it could work was if Planck introduced a ‘fudge’ constant, h, (6.626 x 10-34) into his calculations.

With time and the contributions of many physicists – most notably Albert Einstein (who was now on the threshold of obtaining the experimental evidence needed to support Planck’s quantum theory), Planck’s hypothesis that all EMR is quantised eventually was proven to be correct and ultimately led to the development of a whole new branch of Physics called Quantum Physics. But in order to see how this occurred, we need to return to the photoelectric effect…

Unfortunately, Planck had no real direct experimental evidence for his theory. So he put it aside and forgot about it!!

ACTIVITIES

• Read 11.4 – 11.5

• Read Black Body Radiation and Quanta handouts


• Complete 17 – Planck and Black Body Radiation

The Photoelectric effect

In 1900, Philip Lenard (Planck’s student) 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.

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 photoelectric effect.

EXPERIMENT: The photoelectric effect.

AIM: To determine whether altering the intensity and frequency of the incident light on a metal surface will have an effect on the number of electrons ejected and the kinetic energy of these ejected electrons

BACKGROUND: The photoelectric induced current is a measure of the number of electrons released. The applied voltage (stopping voltage) needed to stop the photoelectric induced current is a measure of the electrons Ek

MATERIALS: Photoelectric apparatus.

METHOD: …

- The number of electrons released (the photocurrent) is proportional to the light intensity.

- The emission of photoelectrons was virtually instantaneous (if it occurred at all).

- 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.

Our experiment showed that:

Refer to the following diagrams…

threshold frequency f0

frequency of light (Hz)

maxim

um

Ek o

f eje

cted e

lect

rons

(J)

j

The gradient of the line is a constant for all types of metals used as the cathode. This gradient is is equal to 6.626 x 10-34, and is exactly the same value hypothesised by Planck – it is called Planck’s constant, h.

The energy required to release an electron from the surface of the cathode is called the work function (j)

Classical theory for instance predicted that electrons in any surface that absorbed low intensity radiation of any frequency should accumulate this energy over time and eventually have sufficient energy to be ejected.

The stage had now well and truly been set for a radical overhaul in our thinking about the nature of light – classical theory had to go!

The photoelectric effect didn’t make sense!

The last three of our experimental results could not be explained by classical wave theory.

Einstein and the Photoelectric effect

The amount of energy in each packet is a quantum (a discrete amount) and represents the quantity of energy associated with particular frequency.

Einstein gave the name photon to a quantum of energy.

In order to explain the photoelectric effect, Albert Einstein proposed that light energy was transmitted in discrete packets of energy rather than as a wave (this is exactly what Planck had hypothesised when he tried to explain black body curves!!).

The energy of a photon can be calculated using the following equation:

E = hf

where: E = energy of the photon (J)

h = Planck’s constant (6.626 x 10-34 J/ s)

f = frequency (Hz)

Note that h is the gradient of the K.E./frequency graph for the photoelectric effect.

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 of its energy to a single electron.

Part of that energy (j) is used in causing the electron to pass through the metal surface.

It follows that if the photon energy (hf), exceeds the work function (j) , then the photoelectric effect occurs and the electron escapes with the ‘leftover’ KE.

KEmax= (hf - j)

where j is the work function of the metal surface and is the minimum energy required to remove an electron from the surface.

and since, j = hfo

where fo is the threshold frequency below which no

photoelectrons are emitted. Then, the equation above becomes:

This explanation is summarised in Einstein’s photoelectric equation:

KEmax = h (f - fo)

Note: the syllabus does not expect you to be able to solve problems using this equation, but you can use it when you explain Einstein’s particle model of light (quantum theory).

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. This is known as the wave-particle duality of light (and all EMR).

Einstein’s experimental evidence based on the photoelectric effect had now confirmed Planck’s hypothesis that the light emitted in the black body experiments was quantised. Remember that this was the only way that Planck could explain BBR curves.

Planck’s ‘fudge’ constant used in his mathematical explanation of BBR curves was validated by Einstein – after all, he obtained the same value experimentally in his explanation of the photoelectric effect!!

Planck’s Quantum Theory had now been established – all EMR was quantised, and not simple waves as classical theory had suggested.

For each photon, its energy is related to its frequency, and as we know, frequency is related to both the speed of light and wavelength. We can see the connection in the two equations below:

c = f l

and

E = h f

Thus, all EMR have both wave and particle characteristics – they are basically bundles or packets of wave – NOT a continuous wave as classical theory suggested. This is the basis of Quantum Theory.

Note: the syllabus expects you to be able to solve problems using these equations

Remember that h = Planck’s constant (6.626 x 10-34 J/ s)

Example 1:

What energy would be associated with a photon of red light of frequency 3.85x 1014 Hz?

Solution:

E = hf

E = (6.626 x 10-34) x (3.85x 1014)

E = 2.55 x 10-19 J

Example 2:

If a photon has an energy of 1.0 J, what will its frequency be?

Solution:

E = hf

f = E/h

f = 1.0 / (6.626 x 10-34)

f = 1.6 x 10-33 Hz

Example 3:

At what velocity would a 1.75 x 10-6 g particle have the same energy as light of wavelength 4.62 x 10-13 m?

Solution:

c = fl

f = c/l

f = (3.0 x 108) / (4.62 x 10-13)

f = 6.49 x 1020

KE = ½ mv2

v = 2.22 x 10-13 m/s

m

KEv

2

10 x 1.75

) 10 x 4.3(26-

-13v

Now,

E = hf

E = (6.626 x 10-34) x (6.49 x 1020)

E = 4.3 x 10-13 J

ACTIVITIES

• Watch the Photoelectric Effect DVD

• Read 11.5

• Read Black Body Radiation

• Read The Photoelectric Effect

• Complete 18 – The Photoelectric Effect

Uses of the Photoelectric effect

The electrons that initiate an electric current are produced by the photoelectric effect. They also contain semiconductor material discussed in the next section.

Photocells:

They are used as ‘electric eyes’ (to open doors automatically), radiation detectors and light meters. You have used them when you used photogates. They turn street lights on and off by detecting the amount of light.

Because photocells can detect the amount of light, they can also be used to measure the concentration of particles in liquids and gases, as these particles scatter light. The more particles, the more light is scattered. Therefore they can also be used as breathalysers, to measure the purity of drinks and to determine the level of pollution.

Einstein vs Planck: The clash of values

Einstein and Planck were great friends – both were German and shared many of the same laboratories. They collaborated on many scientific works, yet they had very differing views regarding whether their work should be used for the pursuit of scientific knowledge or the evils of war.

ACTIVITIES

• Read 11.6

• Read Source 1 and Source 2


3. Limitations of past technologies and increased research into the structure of the atom resulted in the invention of transistors


• identify that some electrons in solids are shared between atoms and move freely

• describe the difference between conductors, insulators and semiconductors in terms of band structures and relative electrical resistance

• identify absences of electrons in a nearly full band as holes, and recognise that both electrons and holes help to carry current

• compare qualitatively the relative number of free electrons that can drift from atom to atom in conductors, semiconductors and insulators

• identify that the use of germanium in early transistors is related to lack of ability to produce other materials of suitable purity

• describe how ‘doping’ a semiconductor can change its electrical properties

• identify differences in p and n-type semiconductors in terms of the relative number of negative charge carriers and positive holes

• describe differences between solid state and thermionic devices and discuss why solid state devices replaced thermionic devices

• perform an investigation to model the behaviour of semiconductors, including the creation of a hole or positive charge on the atom that has lost the electron and the movement of electrons and holes in opposite directions when an electric field is applied across the semiconductor

• gather, process and present secondary information to discuss how shortcomings in available communication technology lead to an increased knowledge of the properties of materials with particular reference to the invention of the transistor

• identify data sources, gather, process, analyse information and use available evidence to assess the impact of the invention of transistors on society with particular reference to their use in microchips and microprocessors

• identify data sources, gather, process and present information to summarise the effect of light on semiconductors in solar cells

A new model of the atom

Einstein and Planck had challenged the way that we look at EMR. Previous models visualised light as waves. Physicists now described light (and all EMR) as photons. In doing so they pioneered a new way of describing both matter and energy. This is the wave-particle duality of matter and energy. This then, meant that the model of the atom had to be adjusted!

Neils Bohr presented a new particle model of the atom, where the electrons orbits were quantised:

Background information

Nucleus

lowest energy level (n=1)

n =2

diagram 1

The electrons were only allowed to occupy discrete energy levels (the orbits).

The lowest energy state of an atom is called the ground state. This is when the electrons fill up all of the energy levels as close to the nucleus as they can.


Wolfgang Pauli in his ‘Pauli exclusion principle’ worked out that only 2 electrons could exist in the lowest energy level and 8 electrons were permitted to exist in the second energy level at any one time.

Using Pauli’s work, Prince de Broglie came up with a new model of the atom. He suggested that:

- electrons certainly have mass, but should not be considered as tiny ball satellites orbiting the nucleus.

- electrons should be considered as standing waves with whole number wavelengths.


The waves (electrons) are therefore quantised, meaning that they are allowed to occupy only certain positions out from the nucleus.

de Broglie could now explain that when electrons jump down a single energy level, they emit a photon and lose one whole wavelength from their shape (therefore this photon has a particular frequency!!). If electrons absorb energy, they move out from the nucleus to the next quantised energy level.


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.

Conductors, Insulators and Semiconductors -Band Structures

Quantum theory shows that when two atoms are brought close enough together, each of the allowed electron energy levels within the atoms splits into two distinct but closely spaced energy levels as they ‘overlap’ to form the two-atom system.

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.

In a six-atom system for example, each allowed electron energy level is split into a set of six separate but closely spaced energy levels.

The spaces between these allowed bands are called forbidden energy gaps. These forbidden energy gaps correspond to the gaps between electron energy levels within the isolated atoms.

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 highest energy band that is occupied by electrons is called the valence band. The very next empty energy band is called the conduction band.

If an electron can get into the conduction band, it is called a free electron and can drift from atom to atom in the solid. In other words, some electrons are shared between atoms.

This means that the solid becomes a conductor of electricity.

The wider the forbidden energy gap between the valence and conduction bands, the more likely the solid is to be an insulator.

The concept of overlapping energy levels (bands) and forbidden energy gaps in solids can best be described with a diagram:

In an insulator, there is a substantial gap between the valence band and the conduction band. You need to supply a lot of energy to an insulator in order to get electrons to jump up to the conduction band. Since there are no free electrons in the conduction band, the solid, as expected, acts as an insulator – it has a high electrical resistance.

Valence Band

Conduction Band

BIG energy gap

This is empty

A lower band This is full

This is at least partially full

In a conductor (eg a metal), the valence band and the conduction band actually overlap. This means that there are many free electrons in the conduction band. The valence band is also the conduction band!! It has a low electrical resistance.

Valence Band

Conduction Band

A lower band

The valence band is full, and the next energy level (the conduction band) is partly full. This is because the valence band and the conduction band overlap.

This is full

The band diagram for a semiconductor is similar to that of an insulator, except that there is a smaller forbidden energy gap between the valence band and the conduction band than with an insulator. They are therefore insulators, but not quite as insulating as insulators. They only need a bit of energy to excite the electrons up to the conducting band, but once they are there, they are free to move around. They have electrical resistance between those of conductors and insulators.

Conduction Band

Smallish energy gap

This is empty

Valence Band

A lower band

This is full

This is full

Here is another band diagram showing all the solids together.

This means that a‘hole’ has been created in the valence band where an electron has left.

Since this hole represents the absence of an electron, it can be treated as a positive charge.

A nearby electron then moves into the hole, creating a new hole at the position from which it moved, and so on.

Semiconductors can have HOLES!

At low temperatures, all electrons in a semiconductor fill the valence band and it is therefore an insulator. But, as the temperature increases, thermal energy allows some electrons to jump the small gap into the conduction band. This leaves the valence band unfilled.

As such, current flow is now possible in both the valence band (as a flow of positive holes) and in the conduction band (as a flow of electrons).

In essence, these holes act as a positive flow of current, moving in the opposite direction to the electron current flow.

Who cares !?!?

You should! Semiconductors have led to the invention of an incredibly important piece of technology – the transistor. With its development, unprecedented progress has taken place – particularly in the field of computers. Enter the silicon chip! We’ll look at this stuff shortly.

But first… a very very silly experiment…

In a pure semiconductor the number of holes in the valence band is exactly equal to the number of electrons in the conduction band. The conduction of a piece of pure silicon (a semiconductor) is very low compared with copper, because there are relatively few free electrons.

EXPERIMENT: Modeling the behaviour of semiconductors.

AIM: To model the behaviour of semiconductors, including the creation of a hole and the movement of holes and electrons in opposite directions when an electric field is applied across the semiconductor

MATERIALS: 20 tennis balls, 10 students.

METHOD: …

ACTITIVES

• Read 12.1 – 12.3

Germanium,Silicon and Transistors

Early devices made of semiconductor materials included diodes and transistors. Diodes are rectifiers – they block the backward and forward movement of electric current in a circuit (i.e. they act as a one way traffic cop – consider their effect on AC current!). Transistors are manufactured to act as switches and amplifiers in integrated circuits.

The most widely used semiconductor materials are made from crystals of elements of Group IV of the periodic table.

In order to see how this can happen, we will look at the example of Germanium (symbol Ge) – a Group IV element.

Ge is very rare on Earth and is quite brittle. It only became economically significant after 1945 when its semiconducting properties were first recognised as being useful in electronics. The first transistor was made of germanium.

Group IV atoms have 4 electrons in their outer (i.e. valence) energy level. This means that they have a half complete valence shell. This is a great source of atomic unhappiness and they desperately want another 4 electrons in order to fill it.

Each of these atoms contributes an electron to the partnership, forming a pair of electrons which act to bond the atoms together – this is a covalent bond.

This occurs over and over with many individual atoms – eventually forming a crystal of Germanium.

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

In order to fill its valence shell, a Ge atom shares a valence electron with each of four adjacent Ge atoms.

Here we can see the regular arrangement of atoms – this is called a crystal lattice.

Despite its rarity and fragile nature, Ge was the semiconductor of choice – for one simple reason – no other Group 4 element was capable of being produced at a suitable purity.

Silicon (Si) is also a group IV element and is the second most abundant element (by weight) in the Earth’s crust. Single crystals are grown slowly from molten silicon. This is a difficult process, and it was not until the late 1950’s that silicon crystals of suitable purity could be produced.

Ge crystals could be grown with tremendous purity. Purity is important as contaminants as little as one part per billion will upset the electrical properties.

Germanium use was surpassed by silicon in the 1960’s, when it became the new semiconductor of choice for use in solid state devices.

Both Ge and Si do not conduct electricity at room temperature. In fact they are unable to conduct electricity unless the bonds are broken by the application of heat. This is undesirable, as the crystal lattice would break up!

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Ge

Enter the dope…

Doping semiconductors

We can dope Si by melting a part of the crystal and adding small quantities of either group III atoms, or group V atoms. It can also be done using transmutation in a nuclear reactor.

A group III element has only 3 electrons in it valence shell e.g. boron, aluminium, gallium and indium.

A group V element has 5 electrons in it valence shell e.g. nitrogen, phosphorous, arsenic and antimony.

By doping a semiconductor we can radically change its electrical properties!

Adding an impurity to the crystal lattice of a semi-conductor can actually be a good thing – only if done properly!! Adding an impurity is called doping.

When a dope group III atom replaces a silicon atom, an electron is missing from the crystal lattice. There is an empty quantum position in the valence band. This is a positive hole!! This is called a p-type semiconductor.

p-type semiconductors have positive holes.

Si

Si

Si

Si

In

Si

Si

Si

Si

In

Si

Si

Si

Si

Si

diagram 7

Indium has 3 valence electrons NOT 4

Positive holes in crystal structure where an electron is missing

p-Type Semiconductor

p-type Semiconductors

The diagram below shows how p-type semiconductors conduct electricity readily under the application of an external voltage:

Such p-type materials are inclined to grab electrons from outside to repair the defect holes. It is important to note that the overall charge of the semiconductor is neutral, because the number of protons in the crystal exactly balance the number of electrons, so they often become negative when brought in contact with other materials.

p-type semiconductors conduct electricity by the migration of positive holes.

n-type Semiconductors

The electrons sit in energy levels above the valence band (i.e they are in the conduction band).

They are called n-type because negative charges move.

To make an n-type, you have to melt the silicon (or Ge) and add small amounts of group V elements.

An n-type semiconductor is shown below:

n-type semiconductors conduct electricity by the migration of electrons, which are surplus to the crystal structure.

Si

Si

Si

Si

As

Si

Si

Si

Si

As

Si

Si

Si

Si

SiElectrons surplus to crystal structure

Arsenic has 5 valence electrons NOT 4

The following diagram shows how n-type semiconductors conduct electricity readily under the application of an external voltage:

n-type obviously have a large number of negative charge carriers (i.e. free electrons) because they have been doped with Group V elements.

p-type have a large number of positive holes because they have been doped with Group III elements.

In comparison, undoped semiconductors have no free electrons or positive holes (unless they are heated up).

p-type and n-type semiconductors differ in terms of the relative number of negative charge carriers (electrons) and positive holes.

Thermionic devices

Thermionic emission is the spontaneous emission of electrons from solids (and liquids) when they are heated to high temperatures. (Remember the filament inside the electron gun in TV tubes??)

The first application of semiconductors was in radio technology - they replaced the old valve radios.

These valve wirelesses were the first amplifying radios capable of driving a speaker. The valve was a thermionic device called a triode.

In order for a radio to work, the very faint radio wave has to be made not so faint!

You will recall that radio waves set up a current in an antennae (remember Hertz’s experiment) – but this current is very very small. It has to be boosted (amplified) somehow. A triode could do this very effectively. The diagram below shows how a triode works:

The grid becomes negatively charged because it is connected directly to the antennae, and it varies in charge constantly. This causes the electrons that are trying to pass through the grid from the cathode to slow down or even stop. This has the effect of constantly varying the current that arrives at the speaker – sometimes lots of current (a loud sound) and sometimes no current (no sound).

A cathode is heated by connecting it to a high voltage circuit, it then emits electrons thermionically and a current flows towards the anode. This current is used to make the speaker work. In between the two electrodes is a third (hence the name triode) electrode called the grid.

In this way the current produced by the radio wave is amplified!

EXPERIMENT: Thermionic devices.

AIM: To examine a triode in order to identify the cathode, anode and grid, and to determine how this device can act as an amplifier of radio waves.

MATERIALS: Triode.

METHOD: …

first

Solid State devices replace Thermionic devices

The race was on to build better valves for higher frequency RADAR’s that could detect smaller targets. Eventually, the scientists realised that there was a frequency limit above which thermionic valve devices could not detect.

This current technology had shortcomings! Research into an alternative technology to replace thermionic devices began.

Thermionic devices dominated the war years, and the allies secret weapon was RADAR.

It soon became apparent that semiconductors could easily, efficiently and cheaply replace valves. All electronic devices made of semiconductors are called ‘solid-state’ devices.

The first solid-state device was called the transistor. Transistors replaced valves, since they did the same job – only better.

The search for a replacement technology lead to an increased knowledge about the properties of many materials – especially elements that were known as semiconductors.

• solid state devices are much smaller than valves. Huge numbers of transistors can be printed onto microchips.

The advantages of solid state devices over thermionic devices are:

• the huge power use caused valves to burn out quickly, like light bulbs.

• because of the low current use in solid state devices, other circuit components could be miniaturised.

• solid state devices require tiny voltages and current to operate. Valves used the entire mains voltages, took time to warm up, and wasted huge amounts of energy as heat.

• there was a frequency limit beyond which valve devices would not operate – this limited their use in such things as RADAR and long distance phone calls.

• solid state devices can be made robotically and cheaply from simple raw materials like sand. Valves were difficult to manufacture.

Solid State devices change the world

They are particularly useful in computers because they act as ‘gates’ in microchips, where they control the flow of charge. The gates are either open or closed (1 or 0). Other transistors acts as amplifiers when information is being retrieved. Miniature transistors pack modern integrated circuits (microprocessors).

Transistors are solid state devices that allow the current in one circuit to vary the current in a second circuit, just like the old valves (triodes) used to do).

How solid state devices work

These consists of a piece of n-type material in contact with p-type material:

e.g.1 The semiconductor diode:

When the voltage is connected as shown in the diagram, electrons on the n-side and holes on the p-side migrate towards the junction and current flows in the circuit (i.e. it is a conductor). If you reverse the voltage, the electrons and holes migrate away from the junction so that current flow stops. The diode is now an insulator.

The diode therefore prevents backward motion in AC currents.

A pnp transistor has 3 slices: the base, collector and emitter. It performs exactly the same function as the old triode valves. It takes a small AC current from the antennae and ‘imprints’ it onto the mains current. This varies the amount of current fed into the speaker of the radio – in this sense, the current coming from the antennae has been ‘amplified’. Examine the following diagram:

e.g.2 The pnp transistor:

These amplify the AC current that is induced in radio antennae. They transfer the AC current from the antennae to a mains (high voltage) circuit (they were originally called ‘transfer resistors’ – hence ‘transistor’).

P (collector)

P (emitter)

N (base)

Mains voltage Antennae

voltage

Arrows show electron flow

+

-

+

-

speaker

Solar cells

Solar cells, or photovoltaic cells, are used to power lights, telephones, radio beacons, calculators and other household devices .

Solar cells are made up of a number of layers. The anti-reflective coating reduces reflection losses and the glass cover provides protection from the weather while allowing light through.

n and p semiconductors are layered together and are electrically neutral. Electrons from the n-layer migrate into the p-layer until an equilibrium is formed, with the p-layer negatively charged and the n-layer positively charged. This is called a depletion layer, which is an electric field.

Light photons provide energy for electrons to move from the valence band to the conduction band and so move freely. Under the influence of the electric field (depletion layer) the electrons will move to the n-layer. The electrons are collected by a metal contact on the n-layer side and moved around a circuit (where they do work) back to the p-layer side.

ACTIVITIES

• Read 12.4 – 12.9

• Research task - Assess the impact of the invention of transistors on society with particular reference to their use in microchips and microprocessors

• Read Microchip and The Impact of Transistors


4. Investigations into the electrical properties of particular metals at different temperatures led to the identification of superconductivity and the exploration of possible applications

• outline the methods used by the Braggs to determine crystal structure

• identify that metals possess a crystal lattice structure

• describe conduction in metals as a free movement of electrons unimpeded by the lattice

• identify that resistance in metals is increased by the presence of impurities and scattering of electrons by lattice vibrations

• describe the occurrence in superconductors below their critical temperature of a population of electron pairs unaffected by electrical resistance

• discuss the BCS theory

• discuss the advantages of using superconductors and identify limitations to their use

• process information to identify some of the metals, metal alloys and compounds that have been identified as exhibiting the property of superconductivity and their critical temperatures

• perform an investigation to demonstrate magnetic levitation

• analyse information to explain why a magnet is able to hover above a superconducting material that has reached the temperature at which it is superconducting

• gather and process information to describe how superconductors and the effects of magnetic fields have been applied to develop a maglev train

• process information to discuss possible applications of superconductivity and the effects of those applications on computers, generators and motors and transmission of electricity through power grids


Diffraction

Diffraction occurs when waves pass through an opening. If the width of the opening is of a similar dimension to the wavelength, maximum diffraction occurs:


Why is it that person A, standing beside an open doorway, can be heard inside the room by person B but cannot be seen by her?


With two openings, the diffracted waves interfere (either constructively or destructively) with each other, and we get an interference pattern:

1. What type of interference is occurring at A?

2. What type of interference is occurring at B?

3. If the waves were red light waves, draw what you would see on a screen held along the line X-Y.


William Henry Bragg (1862–1942) and his son, William Lawrence Bragg (1890–1971), used the principle of diffraction to study crystals – in particular to measure the spacing between atoms in crystals. They used X-rays because their wavelength (10-10) is similar to the separation between the atoms. In 1915 they won the Nobel Prize in physics for their work. They were Australian.

The Braggs – Crystal structure

The X-rays were reflected from layers within the crystal. The reflected X-rays produced an interference pattern, and the pattern was recorded on photographic film.

Subsequent mathematical analysis of the diffraction pattern permitted the crystal structure to be deduced.

The diagram shows X-rays being reflected from adjacent atomic planes (i.e. rows in the crystal lattice). The reflected X-rays then interfered constructively and destructively producing the familiar interference pattern on the photographic plate.

Incoming X-rays of wavelength l

Reflected X-rays

q

d

ions in crystal lattice

By measuring the angles, the distance to the screen and the separation between the bright and dark patches on the interference pattern, the spacing of atoms (d) and their arrangement within the crystal was calculated.

They showed that metal crystals are composed of an orderly arrangement of atoms. This is called a crystal lattice.

A typical x-ray crystallography diffraction interference pattern

Knowledge of the lattice structure of metals led to the development of models to explain why metals are such good conductors.

This eventually resulted in theoretical suggestions that superconductors should exist and finally led the discovery of superconductors themselves!

But before we can look at superconductors, we must first examine the conduction of electricity in metals…

As we already know from the study of band structures, metals are good conductors because their valence band overlaps with their conduction band, resulting in the presence of many free electrons in the conduction band.

Conduction in metals

Once there are free electrons, they can move around from atom to atom in the crystal lattice. (Recall that the movement of electrons is defined as a current).

Notice that there is no net movement of electrons in any one direction.

–

–

–

–

+

+

+

+

Under the influence of an applied potential difference however, the electrons drift in a net direction. This is called an electric current.

The instantaneous speed of the electrons is approximately 1.6x106 m/s, but the average drift velocity is only 1.0x10-5 m/s.

Suggest a reason for this!

Answer:

Since the electrons are moving enormously fast, they undergo random collisions with other electrons, with impurities in the lattice and imperfections in the crystal lattice.

Although drift velocity is small, the speed at which the influence of the current moves is close to the speed of light. Can you explain why? Background information

As we saw earlier, conduction electrons undergo collisions with the atoms in the lattice – this causes the electrons to scatter. The collisions cause the atoms in the lattice to vibrate, and the conductor becomes hotter. As the temperature increases, the atoms in the lattice vibrate more, increasing the chance of collision (and scattering) and so resistance increases further…

Metals have resistance

Temperature

Resistance

The resistance of metals is also increased by the presence of impurities in the lattice.

These impurities are usually other atoms that ‘corrupt’ the crystal lattice. This then increases the chance of collision between the free electrons and the lattice, hence the resistance increases.

It follows that if a temperature increase causes an increase in resistance, then if a metal conductor is cooled, there would be less vibration and fewer collisions. This would cause the resistance to decrease.

Think carefully about this!!

…if the resistance of a conductor decreases as temperature decreases…

…and if you could reduce the temperature of the conductor low enough…

…then theoretically you should reach a stage where it has zero resistance…

…and a conductor like that would be SUPER!

Superconductors

Superconductors are materials which, below a particular temperature called the critical temperature allow electrons to move through the crystal lattice unimpeded.

This means that these materials have lost all resistance to the flow of electricity.

The first superconducting material was discovered by Heike Onnes, in 1911. His results are shown on the next page:

Temperature (oC)

-273 -271 -269 -267

0.04

0.08

0.12

0.16

Resistance curve for Mercury

Examples of Superconductors

Since Onnes discovered the superconducting property of mercury, many more materials have been shown to have the ability to superconduct.

You can see that the critical temperature at which the transition to the superconducting state occurs is different for different materials.

Some alloys have higher critical temperatures than the constituent elements.

Ceramic materials and other compounds have been made with even higher critical temperatures than the metal alloys - these are called high-temperature superconductors.

Why do you think there is a special interest in high-temperature superconductors?

BCS theory

Realising that it was the interaction of electrons with the vibrations of the crystal lattice that produced superconductivity, they proposed that forcing electrons to pair up into ‘Cooper pairs’ would result in them being able to bypass the obstacles in the crystal lattice which were responsible for electrical resistance.

Here is what they proposed…

In 1957, Bardeen (B), Cooper (C) and Schrieffer (S) developed a theory (known as BCS theory) to explain how superconductors work. Their theory described the formation of pairs of electrons in materials when they are below their critical temperature. These pairs of electrons were called ‘Cooper pairs’.

1. An electron moves through the lattice. As it moves it causes the lattice to distort (because it attracts the

positively charged lattice ions). This sets up a disturbance (called a phonon) in the lattice:

2. There is now an increased positive charge density (caused by the lattice distortion) directly behind the electron. This causes a second electron to be attracted to the first in what is called a phonon-mediated attraction, and travel through the crystal as a pair. This pair of electrons is called a ‘Cooper pair’.

3. All of the Cooper pairs represent a highly ordered system and when an external electric field is applied, the pairs move through the lattice with each pair’s motion synchronised to that of every other pair so that none are involved in the random scattering within the lattice (which would otherwise give rise to electrical resistance).

+

+

+

+

++

Cooper pair

Obviously superconductivity only occurs if the material is cooled to the correct critical temperature. If the temperature rises above the critical temperature, the lattice vibrations increase and break up the Cooper pairs. Superconductivity is lost.

Advantages and applications of Superconductors

APPLICATION ADVANTAGES

Computers The speed and further miniaturisation of computer chips is limited by heat generation. Super-conductive film can be used. Switching devices (Josephson junctions) are being tested for use in high-speed computers, they are around 10 times faster than the semiconductor switches currently used.

APPLICATION ADVANTAGES

Generators Superconducting magnets would not need an iron core – therefore they would be much smaller and lighter. Higher efficiency in generation results in less energy wasted, so less fossil fuels would be burnt - BIG positives for the environment.

Motors Increased efficiency results in less demand for electricity (see above).

Electricity Transmission

No electrical loss therefore thin wires could carry very large currents.

• Superconductors have a critical temperature, above which it returns to a normal conductor. Metal super-conductors require temperatures a few degrees above absolute zero!! It is incredibly difficult to do this on a large scale, and prohibitively expensive to cool them.

• Modern ceramic superconductors operate at higher temperatures, but they are brittle – they lack the flexibility of metals. Also it is very difficult to make them into wires.

• Some superconducting compounds are chemically unstable – this limits their application.

Limitations of Superconductors

Magnetic levitation – the Meissner effect

In 1933, W. Meissner discovered that a superconductor does not allow an external magnetic field to penetrate its interior. The exclusion of a magnetic field is called the Meissner effect. A consequence of this is that a superconductor in its superconducting state can cause an external magnet to levitate above it!!

When a superconducting material in its normal state is placed in a magnetic field, the magnetic field strength inside the material is almost the same as outside. This is true of all metals.

But, when the material is cooled so that it is in its super-conducting state, electric currents begin to flow through it, and as we know, these currents will produce their own magnetic field.

This is how it works:

These induced magnetic fields cancel out the applied magnetic field inside the super-conductor. That is, the magnetic field inside the superconductor is zero.

The magnetic field caused by the flowing currents not only cancels out the external magnetic field but also extends outside the superconductor itself.

If a magnet is bought close to a superconducting superconductor, the currents set up magnetic fields with poles in such a direction that cause repulsion between the magnet and the superconductor (remember Lenz’s Law??).

This is the cause of magnetic levitation.

N S

NCurrents produced in superconductor extending outside.

Superconductor

Magnet

EXPERIMENT: Magnetic levitation.

AIM: To observe the Meissner effect – the levitation of a magnet above a superconductor.

MATERIALS: Superconductor, small neodymium magnet, liquid nitrogen, petri dish, styrofoam cup, plastic tweezers, insulated gloves

METHOD: 1. Carefully fill the styrofoam cup with liquid nitrogen. Place the petri dish on top of the cup, and pour in

enough liquid nitrogen until it is about 1cm deep. Wait until the boiling subsides.

2. Using the tweezers, carefully place the superconductor in the petri dish. Again wait until the boiling subsides.

3. Using the tweezers, carefully place the small magnet about 2 mm above the centre of the superconductor. Release the magnet.

4. While the magnet is levitating, gently rotatethe magnet using the tweezers. first

If this is not possible refer to the next page…

Maglev Trains

In Japan, levitation is achieved by using helium cooled super-conducting magnets on the train, which interact with the coils in the ‘guideway’ (or track) in such a way that repulsion between the ‘like poles’ causes the train to levitate. Another set of coils along the sides of the guideway propel the suspended train forwards.

The magnetic levitation described above suspends an object so that it is free of contact with any surface – this provides a frictionless surface – particularly appropriate for high-speed trains.

Floating

The onboard superconductors interact with the the coil in the walls of the guideway. This raises the train and keeps it centred.

Propulsion

In addition to the levitation coils, there are also propulsion coils. These push the suspended train forward.

The advantages of Maglev trains are very high speed, reliability, safety, minimum maintenance and low environmental impact.

The main obstacle to higher speeds is air resistance. Maximum speeds of around 520 km/h have been achieved.

ACTIVITIES

• Read Chapter 13


THE END!