# Outline the methods used by the Braggs to determine crystal structure

Diffraction occurs when waves bend around obstructions, and interference patterns result when waves interfere. Diffraction can often result in interference patterns when the bent wave (acting as a point source) interferes with the original wave. A diffraction grating uses small obstructions with separations similar to the wavelength of the wave in question placed side by side to produce a predictable interference pattern that is directly linked to the spacing within the diffraction grating. The Braggs realised that the spacing between layers in a crystal lattice were similar to the wavelength of x-rays, and would therefore act as a diffraction grating. Further, they realised that from the interference pattern they obtained they could calculate the spacing between the lattice layers. The Braggs used an x-ray tube as their x-ray source, and the x-rays travelled through a hole in a shield which acted as a collimator to produce a tightly focussed beam of x-rays. The waves then reflected through a crystal target which acted as a diffraction grating, and then the x-rays travelled to a sensor to analyse the interference pattern. From this they could calculate lattice separation distance, which was of great importance to science and understanding crystal structures.

Remember- The Braggs used diffraction and interference patterns with x-rays to calculate the spacing between crystal lattice layers.

# Identify that metals possess a crystal lattice structure

Metals, like many other molecules, have a crystal lattice structure in their solid state. This means that they exist as a 3-dimensional grid of atoms arranged into layers. It is a repeating structure where each atom occupies a well-defined equilibrium distance from its neighbours. In the case of metals, free electrons exist in between lattice layers and conduct electricity.

# Describe conduction in metals as a free movement of electrons unimpeded by the lattice

A metal has free electrons that exist in the space between metal ions in the lattice. This means that they exist in a more-or-less empty space containing no lattice ions, leaving them free to travel without being impeded by the lattice. However, collisions between the electron and the lattice still occur, as do collisions between electrons and other electrons. When an electric field or potential is applied to a metal, the metal conducts because the electrons move freely between the lattice layers.

Remember- Conduction occurs when electrons travel through the metal lattice, thereby moving charge.

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

In order to conduct electricity, electrons must travel through the space between lattice layers. Resistance is low when the electrons are free to travel unimpeded, and resistance is high when the passage of electrons is obstructed. Impurities in a metal distort the lattice structure and electrons collide with the impurity, increasing resistance. Similarly, vibrations in the lattice (often caused by heating) destabilize the structure and make it harder for electrons to flow, increasing resistance.

Remember- Impurities and lattice vibrations increase resistance.

# Describe the occurrence in superconductors below their critical temperature of a population of electrons unaffected by electrical resistance

Phonons are a particular type of quantum particle. They represent quantised vibration states within a crystal structure. It is not necessary to know precisely what they are, only the role that they play in the formation of Cooper pairs.

Superconductors are materials that exhibit no resistance. They only occur at low temperatures because at higher temperatures electron pairs are not capable of forming. In a superconductor, lattice vibrations are eliminated due to the low temperature. As an electron travels through the lattice, it attracts lattice ions causing a lattice distortion- a small region of positive space that attracts another electron. The two electrons then exchange phonons and bind, forming a Cooper pair of electrons which behaves as a single particle. Because the two electrons are interacting with each other they interact less with the lattice, and so travel through it very easily with very little resistance. So below the critical temperature, when a material becomes a superconductor pairs of electrons form that are unaffected by electrical resistance.

Remember- Superconductivity occurs at low temperatures when electrons swap phonons to form Cooper pairs that interact far less with the lattice, resulting in superconductivity.

# Process information to identify some of the metals, metal alloys, and com- pounds that have been identified as exhibiting the property of superconductivity and their critical temperatures

You shouldn’t need to remember this list, since in a test they will most likely give you a table of data to use in an answer. However, it will be useful to remember one or two values from this table so you can add them to any answer to show depth of knowledge. Also make sure you remember that 138K is the maximum temperature for superconductivity as of 2009 (though it probably isn’t necessary to remember the exact material).

 Material Critical temperature (K) Zinc 0.85 Aluminium 1.175 Mercury 4.15 Lead 7.196 Tin 7.72 AuBa2Ca3Cu4O11 99 Ba2Ca2Cu3O8.33 138

# Discuss the BCS theory

If asked a question like this in an exam, ensure you describe the BCS theory before discussing it.

The BCS theory of superconductivity is simply the idea that lattice distortions at low temperatures lead to the formation of Cooper pairs. This theory is extremely successful at explaining supercon- ductivity in Type 1 superconductors (substances that have a critical temperature below 30K) as it is almost 50 years old now, and still used. It provided a concrete framework on which to model superconductivity that was vital to understanding how it works. However, it is unable to explain superconductivity in Type 2 superconductors- the ceramic variety that can be superconductors at far higher temperatures. This is because the model predicts 30K as being the maximum temperature at which Cooper pairs are able to form. So while it is extremely important to understanding Type 1 superconductors, it does little to explain Type 2 and so is an incomplete theory.

Remember- The BCS theory explains Type 1 superconductivity but cannot explain Type 2 semicon- ductors.

# Discuss the advantages of using superconductors and identify limitations to their use

There are many advantages to using superconductors. These are mainly that they operate with very little loss and so are extremely efficient, and also that they generate no waste heat because they are perfect conductors. They are capable of generating very strong magnetic fields per unit of weight, useful for MRI scanners, and could be used to make very efficient motors, generators and batteries. There are two key limitations to superconductors, however. Firstly, it is very difficult to cool superconductors to below their critical temperatures- they require a constant supply of liquid nitrogen at the moment (given the low temperatures currently needed to achieve superconductivity), and secondly it is very hard to shape ceramic superconductors as they are not ductile, making it difficult to turn superconductors into wires

Remember- Superconductors increase efficiency and can reduce size and weight, but are difficult to manufacture and require cooling.

# Analyse information to explain why a magnet is able to hover above a super- conducting material that has reached the temperature at which it is superconducting

A magnet is able to hover over a superconducting material for two reasons- firstly because magnetic fields are excluded from the superconductor, forcing the magnet to be repelled from the supercon- ductor thus causing it to rise up (this is the Meissner effect), and secondly due to the phenomenon of quantum pinning which stops the magnet from moving horizontally off the superconductor.

The Meissner effect is separate to the induction of eddy currents which would theoretically perfectly oppose the magnetic field of a magnet. This is shown to be true because if a magnet is placed on a superconductor as it is being cooled, it will jump into the air as the superconductor becomes superconducting- this shows it is not an induction phenomenon as change in magnetic flux is required to induce eddy currents. Therefore the levitation occurs due to the exclusion of magnetic fields from the superconductor.

Remember- A magnet can float above a superconductor due to the Meissner effect.

# Perform an investigation to demonstrate magnetic levitation

In this experiment, we had a ceramic superconducting disk in a Petri dish and a small magnetic cube. We poured liquid nitrogen onto the superconducting disk (and into the dish) to lower it below its critical temperature, making it superconductive. When we used insulated plastic tongs to place the magnet just above the disk, the magnet floated. Nudging it with the tongs caused it to rotate. Eventually, the magnet fell as the disk warmed up and lost its superconductivity. In our second trial, we left the magnet on the disk before pouring liquid nitrogen. As the disk cooled, the magnet suddenly floated upwards off the disk. This showed that the Meissner effect is due to the exclusion of magnetic fields from superconductors, rather than the formation of perfect eddy currents due to changes in flux (because for eddy currents to form there must be an initial change in flux to create them. In the experiment the magnet rose upwards by itself. In fact, the movement of the magnet upwards would have ordinarily induced eddy currents that would drag the magnet down. So this is compelling evidence that the levitation of the magnet is due to the exclusion of the field and not due to eddy currents).

Remember- The exclusion of the magnetic field from the superconductor caused the magnet to levitate.

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

Note that this dotpoint is not only about how superconductors are used in maglev trains, but also how superconductors make maglev trains possible. Often questions will require to you to examine the benefits of using superconductors for maglev trains, in addition to outlining how they are used.

A maglev train relies on superconductors for operation, because superconductors are extremely light, extremely strong magnets, making them well suited to levitate a heavy load such as the train. Superconductors are used in two areas- to levitate the maglev train, and to propel the train. The tracks and the train both have superconductors. Superconductors on the train consist of a looped superconductor on either side of the train. The superconductor is charged with electric current when it is made, and because it is looped (physically, with one end joined to the other), the current flows continuously. This sets up a strong, constant magnetic field. Superconducting electromagnets on the track, positioned above and below the train’s magnetic loops, repel the train from the bottom, and attract the train from the top, causing the train to float. The track magnets are mounted on the vertical sides of the track. Additional superconducting electromagnets on the track serve to propel the train. These electromagnets are situated all along the side of the track. Magnets in front of the train attract the train’s magnets, while magnets on the track behind the train repel the train. By constantly changing the polarity of the track magnets, the train is attracted and repelled in the same direction constantly, causing the maglev train to move rapidly along the track. Superconductors are vital to the development of maglev trains, because permanent magnets would be too heavy to generate the same field strength, and conventional electromagnets would lose too much energy as waste heat due to electrical resistance.

Remember- Superconductors are used in maglev trains because they are light and can produce the incredibly strong magnetic fields required to levitate and propel a train.

# Process information to discuss possible applications of superconductivity and the effects of those applications on computers, generators and motors, and trans- mission of electricity through power grids

Superconductors offer great potential in a variety of fields, offering increased performance and ef- ficiency compared to conventional conductors. However, there are still two major obstacles that impede the use of superconductors in virtually all their applications. Firstly, superconductors must be extremely cold, necessitating liquid nitrogen cooling. In some cases this is merely inconvenient, such as in a maglev train, but in applications such as computers, it is extremely difficult and unwieldy to use liquid nitrogen as a coolant, although it has been accomplished by some computer enthusiasts. Secondly, at present type-2 superconductors, (the only realistic option for real-world applications be- cause they only require liquid nitrogen cooling, as opposed to type-1 superconductors with lower critical temperatures), are ceramic compounds that are not ductile. This makes it extremely difficult to use in electrical circuits that rely on ductility to produce a long wire to transfer electricity. Because they are not ductile, they would also be difficult materials to use in computer processors.

However, once these obstacles are overcome, using superconductors in place of standard conductors would bring tremendous benefits. In computers, a great deal of energy is wasted as heat. Further, heating makes it difficult for processors to operate properly, as it changes the properties of the silicon presently used. By using a superconductor, there will be little, if any, waste heat produced, resulting in a processor that can function at far faster speeds. Further, by replacing transistors with superconducting quantum switches (SQUID, or superconducting quantum interference device), the processor can operate faster still. In motors and generators, they can be used to operate at high currents with no losses and no heat production, resulting in extremely efficient motors and generators. According to V = IR, current output will be maximised when there is low resistance, showing that a superconductor will improve current output. Finally, in terms of transmission, a great deal of energy is wasted in the transmission of electricity through conversion to heat in wires. By using superconducting wires, energy loss through the electricity grid will be eliminated, resulting in greater efficiency, with possible impacts such as reduced cost of power, or a reduced need for additional electricity generation capacity. A superconducting electricity grid was successfully trialled in America 4 years ago, and is presently used in parts of the New York grid.

Remember- Superconductors can be used in generators, computer chips and electricity grids, al- though at present there are challenges that need to be resolved first.

# Identify that some electrons in solids are shared between atoms and move freely

In solids, electron shells are replaced by electron band structures (because the energy levels of neighbouring atoms shift according to Pauli’s exclusion principle, with the energy levels clustering into broad band structures). These consist of the conduction band and the valence band. The valence band can be thought of as the normal outer shell of an atom where electrons are chained to that particular atom, while the conduction band can be thought of as a level where electrons are free to move between other atoms in the solid structure. Only electrons in the conduction band are shared- those in the valence band are not and remain immobile.

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

Because electrons can only move between atoms and therefore conduct electricity in the conduction band, the relative positions of the conduction band and valence band play a large part in determining the conducting properties of a material. In conductors, the conduction and valence bands overlap- this means that electrons in their normal valence positions can, without gaining any energy, be in the conduction band and move freely between atoms. Because it is so easy for electrons to move into the conduction band, there is little resistance. With insulators, there is a very large energy gap between the valence and conduction bands- this is known as the forbidden energy gap. In order to conduct electricity, electrons in an insulator must gain enough energy to jump from their normal valence band positions over the forbidden energy gap and into the conduction band- because this process requires a great deal of energy input it is very difficult to cause insulators to be conductive, and so they have high electrical resistance. Intrinsic semiconductors (pure semiconductor crystals consisting of only one element) have band gaps smaller than for insulators but bigger than conductors- they lie in between, so are initially insulators but when heated moderately become conductive. Other moderate energy input will cause conductivity. Extrinsic semiconductors (semiconductor crystals with deliberate impurities consisting of small quantities of a group 3 or group 5 element) also contain an extra energy level inside the forbidden energy gap for electrons to exist, reducing the energy required to get an electron into the conduction band.

Remember- Conductivity depends on the gap between the valence band the conduction band. Insulators have a large gap, semiconductors have a small gap, and conductors have no gap.

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

In a crystal lattice of a pure (intrinsic) semiconductor, all the outer shells are (theoretically) filled and there are no electrons available to conduct electricity (since free electrons in the conduction band are required). When a Group 3 impurity exists, an impurity with one less electron than a Group 4 semiconductor such as silicon or germanium, there is a hole in the crystal lattice structure where there should have been a bond electron. This hole forms a positive region of space, and because it’s charged it is capable of moving charge. To move the hole, bonds within the lattice switch around and change so that the position of the hole in the lattice changes. In this way, holes are able to carry current, helping to make a semiconductor conductive, with holes effectively behaving as if they were positive point charges (although the reality is they are regions of empty space that are positive relative to the lattice). With the application of additional energy to move lattice electrons into the conduction band, electrons can also carry current through the lattice.

Remember- Holes are positive points in a crystal lattice that behave as point charges, and both holes and electrons can carry current.

# Compare qualitatively the number of free electrons that can drift from atom to atom in conductors, semiconductors and insulators

Under normal conditions, conductors have very many free electrons that can drift from atom to atom (on the order of the number of atoms in the lattice), whereas in semiconductors and insulators very few, if any electrons are free and able to drift from atom to atom. However, with semiconductors if energy is applied to the system in the form of heat or a strong electrical field, the number of free electrons increases greatly causing it to conduct (although not to the same extent as straight conductors).

Remember- Conductors have many free electrons, insulators have very few.

# 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

Make sure that you are able to clearly explain this experiment. Don’t forget to talk about how holes and electrons move in opposite directions.

We modelled a semiconductor using marbles in a Petri dish, with each marble representing an electron. Removing a marble from the dish represented the creation of a hole. As the dish is disturbed by moving it, simulating the application of an electric field, the position of the hole changed as marbles moved in to fill it, moving the hole elsewhere in the dish. The gap and the marble moved in opposite directions, as a new gap was created when a marble moved to fill the old gap.

Then we modelled semiconductors using marbles as atoms and a metal ball bearing as an extra free electron that was capable of moving around the dish as the dish moved. When we moved the dish, the ball bearing moved from marble to marble, showing the movement of free electrons.

Remember- Swirling marbles in a dish along with a ball bearing.

# Identify that the use of germanium in early transistors is related to lack of ability to produce other materials of sufficient purity

During early research with transistors and semiconductors, germanium was the semiconductor of choice. The main reason germanium was used was because of purification- in order to operate with predictable properties, the semiconductor crystal needed to be very pure. The only two semicon- ductors suitable for transistor use are germanium and silicon, being Group 4 semiconductors and somewhat easily available. Silicon was in fact the superior material, being more abundant and therefore cheaper, easier to dope, and having superior thermal properties (germanium became too conductive with only moderate heating making germanium chip performance highly dependant on temperature).

However, in the 1940’s at the start of semiconductor research, scientists were only able to purify germanium. The techniques that they used to purify germanium crystals could not be applied to silicon crystals. This meant that although silicon was the superior material, it could not be used because silicon crystals could not be manufactured pure enough to make reliable chips. Germanium was therefore used in early transistors until suitable purity silicon was developed.

Remember- Germanium was used in early transistors because scientists couldn’t purify silicon.

# Describe how “doping” a semiconductor can change its electrical properties

The process of doping a semiconductor involves adding a Group 3 or Group 5 element as an impurity into the crystal structure of the semiconductor to reduce the energy input required for the semicon- ductor to become conductive. Only tiny amounts of the impurities are added- too much, and the semiconductor’s conductive properties become unpredictable. If a Group 3 element is added, then because it has one less electron in its outer shell the lattice structure will be missing an electron- in this way a hole is produced, and this hole is capable of moving charge. Similarly, if a Group 5 element is added there will be an extra, free electron in the lattice structure which is free to move between atoms and carry charge.

Remember- Adding impurities to “dope” a semiconductor makes it more conductive.

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

P-type semiconductors have been doped with Group 3 elements whereas n-type semiconductors have been doped with Group 5 elements. This means that although they both are capable of carrying charge, the p-type semiconductor has positive holes to move charge whereas n-type semiconductors have extra electrons- negative charge carriers, to do the same. Holes and electrons flow in opposite directions in the crystal structure to conduct electricity, but they both enable the passage of current through the lattice.

Remember- “P-type” stands for “positive” and so uses Group 3 elements. “N-type” is for “negative” and so uses Group 5.

# Describe differences between solid state and thermionic devices and discuss why solid state devices replaced thermionic devices

This dotpoint is focussed on the differences between solid state and thermionic devices in terms of their performance and usage. See the Extra Content chapter for an overview of the physics behind their operation.

Although thermionic devices and solid state transistors perform exactly the same function (amplification of a signal or electrical switching), solid state devices almost completely replaced thermionic devices because of their vastly superior properties in terms of operation.

 Attribute Thermionic device Solid state device Cost Expensive Cheap Dimensions Bulky and heavy Small and lightweight Durability Fragile, easily broken Durable and reliable Lifespan Short lifespan Long lifespan Warm-up time Significant None Energy efficiency Large power requirements Very low power

Although some audio enthusiasts claim valves are still better devices for amplification, it is generally accepted that transistors are superior to valves in almost every way. This led to solid state devices replacing valves.

# Gather, process and present secondary information to discuss how shortcom- ings in available communication technology lead to an increased knowledge of the properties of materials with particular reference to the invention of the transistor

The biggest problem with communication technology in the early days of the radio was amplification- the received signal was extremely weak and could not produce a loud sound without being amplified. This meant researchers were always trying to improve amplification technology to address the short- comings with valves such as their high failure rate, high power consumption, their weight and their warm-up time. When they first determined some of the properties of semiconductors this need for better amplifiers fuelled heavy research into the properties of semiconductors and the ways in which they could be used as amplifiers in the form of transistors. So the shortcomings in available com- munications technology led to the rapid development of the transistor which would have otherwise taken many years longer.

Remember- The drive for transistors to replace valves was brought about not only by the limitations of valves but also because of the high demand for communications technology.

# 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

The invention of the transistor has dramatically changed society, largely through the use of micro- processors and microchips. They have enabled the building of small, efficient computers that now have widespread applications throughout society as well as in scientific research. It has allowed the automation of repetitive tasks which has led to higher quality of life, at the expense of jobs and a rise in unemployment. However, in terms of communication it has had a tremendous benefit enabling the internet which has drastically changed society for the better. So overall transistors have had an extremely positive impact on society.

# The photoelectric effect

This is an additional dotpoint providing an overview of the photoelectric effect.

The photoelectric effect occurs when electromagnetic radiation (such as UV light) is shone on the surface of a metal. Photons are absorbed by electrons in the metal, which causes the electrons to be physically ejected from the surface of the metal. The velocity with which the electrons are ejected is dependent on the frequency of the radiation, while the quantity of electrons ejected depends on the intensity of the light.

The frequency of light at which the photoelectric effect commences is called the ‘threshold frequency’. Below this frequency, no electrons are emitted from the metal. The threshold frequency depends on the particular metal involved. The energy of the photon with a frequency equal to the threshold frequency is the ‘work function’ i.e. the work function is the value of E for $E=hf_threshold$.

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

Make sure you can clearly describe how Hertz measured the speed of radio waves. It’s a popular exam question that people often find difficult to answer properly. It may help to read through dotpoint

• first, for a description of the apparatus Hertz

Hertz was able to conclude that the radiation he was dealing with was part of the electromagnetic spectrum by analysing its properties in comparison to light. He carried out experiments to show that

• It could be reflected by metal plates
• It could be refracted by pitch or asphalt blocks
• It could be diffracted around obstructions
• It could be polarised (when he rotated the receiving coil he found that the sparks were stronger at certain angles compared to others)

And most importantly, that it travelled at the speed of light. Hertz connected the two loops together with a wire, so that there was interference between the AC wave in the wire and the wave caused by EMR transmission. From this, he was able to calculate the wavelength of the radio waves, and knowing the frequency of his wave generator he was able to show that the radio waves travelled at the speed of light.

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

Hertz discovered in 1887 that radio waves are capable of inducing currents in a receiver. In his experiment, he had a spark gap with a parabolic reflector connected to an induction coil that was constantly producing high voltage AC power and so constantly causing the spark gap to spark. A wire ring with a gap similar or identical to the spark gap in the transmitter was capable of receiving the radio waves, converting them to a spark between the gap in the receiver. This was clear proof that transmission and reception were occurring because there was no other source of electricity to the receiver to cause the spark. So Hertz observed that radio waves could induce currents in a receiver.

When he tried to enclose the receiver in a dark box to see the spark more clearly, the spark greatly diminished in size. Hertz concluded this was because light or more specifically, EMR, was affecting the size of the induced spark, and by irradiating the receiver with different frequencies of EMR he found that UV light maximised this effect. This was because of the photoelectric effect knocking electrons from the surface of the wire making it easier for them to jump the gap, although Hertz did not investigate this.

Wilhelm Hallwachs subsequently carried out experiments in which he shone different frequencies of EMR onto gold-leaf electroscopes to investigate the effect. A negatively charged electroscope would discharge in the presence of UV light while a positively charged electroscope would not. This was further evidence for the photoelectric effect, although it did not provide an explanation.

Remember- Hertz used rings with spark gaps to demonstrate induction, and found the effect was amplified when UV light was shone on the receiving ring. However, he never investigated this effect.

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

Classical theory predicted that the radiation emitted by a black body should continuously increase in intensity as the wavelength became shorter, forming a continuous spectrum with intensities effectively corresponding to an exponential curve. This was not supported by experimental data which showed that the amount of energy radiated reaches a maximum at a wavelength that depends on the temperature of the black body, and then drops sharply for smaller wavelengths. Also, an exponential curve would violate conservation of energy since the total energy (the area under the graph) would be infinite. Planck resolved this problem with his hypothesis of quantised radiation which explained the experimental data, stating that radiation could only occur in small packets which he called “quanta”. The energy contained within a single quanta is dependent only on the frequency of the radiation according to the formula E = hf . Further, the vibration states of atoms in the black body cavity were also quantised, meaning that they could only have specific discrete frequency values. Since energy is only emitted when these atoms change vibrational states moving to a less energetic state, the energy released is also quantised.

Remember- Planck devised a theory to explain black body radiation, in which light was not considered a wave but as packets of energy that occurred only in multiples of a particular value.

# Identify Einstein’s contribution to quantum theory and its relation to black body radiation

Einstein’s contribution was twofold. Firstly, he used Planck’s formula to create a more detailed quantum theory of light (with light packets called “photons”), and secondly he created an explanation for the photoelectric effect. In terms of defining light, he set up a concrete explanation for the particle theory, explaining intensity and frequency in terms of energy of and quantity of photons. He also stated that photons were the smallest units of light possible. In terms of its relation to black body radiation, Einstein’s theories came about directly because of the work undertaken by Planck regarding black bodies. Einstein’s work led him to explain the photoelectric effect in terms of work function and threshold frequency, also providing an explanation for photoelectron kinetic energy that matched Lenard’s puzzling results. Further, Einstein brought quantum theory further into the mainstream where other scientists continued to build on it.

Remember- Einstein applied Planck’s theories to black body radiation to produce a comparatively more detailed model of light as a particle, which served to bring quantum theory closer to mainstream science.

# 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

The focus of this dotpoint is not so much on what the contribution was, but how valuable it was to science. As such, when answering this dotpoint bear in mind that you need to make a conclusion as to the value of Einstein’s contribution.

Einstein made a very significant contribution to quantum theory by taking Planck’s theories about black body radiation and applying them to solve a separate problem. Further, he expanded on the work of Planck and turned quantum theory into a set of ideas with concrete principles and modelling. Effectively, he took it seriously while Planck simply deemed it a mathematical trick. By using quantum theory to explain the photoelectric effect, solving a real problem with a concrete model for the solution that fully explained experimental observations, Einstein validated quantum theory, endorsed its solving of black body radiation, and opened the door for further research based on quantum ideas. Therefore Einstein made a significant contribution to quantum theory and its relation to black body radiation.

Remember- Einstein contributed significantly to quantum theory by applying Planck’s black body radiation theory to the photoelectric effect, thereby solving a real world problem.

# Explain the particle model of light in terms of photons with particular energy and frequency

The particle model of light considers light to be transmitted by small particles. These particles have mass that depends on their energy, with more energetic photons having greater mass (although their rest mass is 0). To increase the energy of a photon, the frequency, not the amplitude of the light is increased. To increase the amplitude the number of photons is increased. Photon energies can only occur in multiples of Planck’s constant.

Remember- Under the particle model, light exists as particles. More particles means greater intensity, and more energetic particles means higher frequency light.

# Identify the relationships between photon energy, frequency, speed of light and wavelength

According to E = hf and c = , the relationships between variables can be deduced. Since the speed of light is constant, if the frequency of the light increases then wavelength decreases and vice versa. With photon energy, h is constant, so when f is increased photon energy increases (E is directly proportional to f ). Therefore it is inversely proportional to the wavelength λ, as deduced from the relationship between wavelength and frequency.

# Identify data sources, gather, process and present information to summarise the use of the photoelectric effect in solar cells and photocells

Essentially, a solar cell consists of a junction between a P-type and N-type semiconductor that is exposed to light. Electrons are ejected from the N layer due to the photoelectric effect, and they then travel around a circuit to reach the P layer. This movement of electrons results in a potential difference that can be used to do work. In a photocell, the resistance of a circuit changes depending on how much light is falling on a semiconductor. Essentially, by monitoring voltage, current flow and resistance, a quantifiable measurement of light is possible because these properties change when a semiconductor experiences the photoelectric effect.

Remember- In solar cells the photoelectric effect is used to push electrons around a circuit, while in photocells it is used to measure light intensity.

# Process information to discuss Einstein and Planck’s differing views about whether science research is removed from social and political forces

Einstein and Planck initially held differing views as to the relationship between science and politics, but in the end they both came to realise the two were intrinsically linked.

Einstein at first refused to support the war or use science to help governments fight the war, believing that science was removed from social and political forces. However, in the end he came to the realisation that the two are in fact linked together, and he ended up helping with the Manhattan project which almost certainly contributed to the ending of the war.

Planck initially felt that science definitely had a role to play in terms of politics, but eventually he turned against the Nazi regime, criticising it, believing that science should be separate. However, he understood that there is an unavoidable link between science and politics. Even after Planck attempted to separate science from politics, research science for the military continued through other scientists.

In a way, both Planck and Einstein are representative of the wider debate in science that continues even today as to the role the government’s agenda should be in terms of scientific research, but they, like today’s scientists, realised that science and politics can never be separated, even if that is the ideal situation.

Remember- Both scientists eventually agreed that science and politics are inextricably linked. They also agreed that ideally they would be separate. Einstein initially believed they had to be kept separate but then realised they couldn’t. Planck initially believed they had to be kept together, but then realised they shouldn’t.

# Describe cathode rays and cathode ray tubes

This is an additional dotpoint included to provide a quick general overview of what cathode rays are.

Cathode rays were first observed by Faraday in 1838, who noticed light emission from within the vacuum tube he was experimenting with. This led to the ongoing research into cathode rays that forms the majority of this HSC topic. A cathode ray tube is simply a vacuum tube with electrodes at either end. The electrodes are simply pieces of conductive metal, and have contacts outside the tube. When a high potential difference is applied to the tube, by passing high voltage electricity through the tube (by connecting the electrodes to a circuit), electrons jump from one electrode to the other, crossing the tube. This cannot occur in normal air because the high density of air molecules prevents the electrons from travelling large distances. However, this is not an issue in a vacuum tube. From this description, it is clear that cathode rays are in fact negatively charged electrons. The emission of light occurs when the electrons collide with particles inside the tube, causing the particles to emit light as they absorb and then release the energy carried by the electron (which is transferred to the particle in the collision). The appearance of the light, such as its shape and colour, is dependent on both the chemical composition of the gas inside the tube and on the gas pressure.

Remember- Cathode rays are the stream of electrons produced between electrodes in a vacuum tube.

# Explain that cathode ray tubes allowed the manipulation of a stream of charged particles

Cathode ray tubes allowed the manipulation of a stream of charged particles in several ways. Firstly, and most importantly, cathode ray tubes are a source of a steady stream of charged particles, a prerequisite to their manipulation. The manipulation of charged particles can either be done remotely via electric and magnetic fields, or directly by obstructing the charged particles (examples include with thin metals, thick metals like the Maltese cross, and small paddlewheels). Cathode ray tubes enabled the manipulation of charged particles in both these ways. Obstructions could be placed inside the tube to block the cathode rays, and fields could operate within the tube by placing charged plates or field coils next to the tube. In this way, cathode ray tubes allowed the manipulation of a stream of charged particles.

Remember- Cathode ray tubes allowed the manipulation of charged particles because objects could be placed inside the tubes, and because fields could permeate the tubes.

# Explain why the apparent inconsistent behaviour of cathode rays cause debate as to whether they were charged particles or electromagnetic waves

Cathode rays had properties that could classify it as a wave or as a particle. As a wave, they

• Travelled in straight lines
• Produced a shadow when obstructed by objects
• Could pass through thin metal foils without damaging them As a particle, they
• Left the surface of the cathode at 90 degrees, not radiating like a wave
• Were deflected by magnetic fields
• Could turn a wheel in the path of the ray (i.e. they have momentum)
• Travelled far slower than light

The reason the debate ensued is because scientists wanted to determine the nature of cathode rays to the extent where they could classify it as a wave or particle, and the fact that cathode rays had conflicting properties made this very difficult. Crookes insisted it was a particle while Hertz maintained it was a wave. The debate was resolved when an electric field was used to deflect the rays by Thompson, which had been impossible up to that point because older vacuum pumps were not strong enough to remove enough air to make the effect visible, and because the electric fields that were used before were not strong enough. This evidence was strong because scientists knew it was impossible to deflect electromagnetic waves with an electric field, and since cathode rays were deflected this was taken as proof they were not electromagnetic waves, and were therefore particle streams.

Remember- Cathode rays had both wave and particle properties, and it wasn’t until Thompson showed that they could be deflected with electric fields that the debate was resolved.

# Perform an investigation to demonstrate and identify properties of cathode rays using discharge tubes containing a Maltese cross, electric plates, a fluorescent screen, a glass wheel, and analyse the information gathered to determine the sign of the charge of cathode rays

To perform this experiment we had several discharge tubes each with element from the list above.

The Maltese cross tube had an anode mounted on the base of the tube, underneath the Maltese cross which was situated between the end of the tube and the cathode. When cathode rays travelled from the cathode, they did so in a straight line, and were obstructed by the Maltese cross. This caused a shadow to be formed, showing that the cathode rays could be blocked relatively easily. Also, the shadow had a very sharp edge, indicating that diffraction was not occurring and that therefore cathode rays could be particles, not waves. The shadow also indicated that the cathode rays travelled in straight lines.

When electric plates were set up, the cathode ray beam was deflected. To perform this experiment, the tube had a curved screen set up inside it so that the horizontal path of the beam was visible. When we applied an electric field, we were able to bend the beam, showing the beam was electrically charged. As the beam deflected towards the positive plate, we determined the cathode rays to be negatively charged. We also deflected the beam with a magnetic field from a bar magnet.

Setting up a fluorescent screen in the path of the cathode ray beam caused it to light up as it was struck. This suggested that the cathode rays carried enough energy to produce the reaction in the screen necessary to produce light, a property exploited in many TVs and computer monitors. Lastly, when a glass paddlewheel was mounted inside the tube on runners so it was able to move, the cathode rays striking the wheel caused it to rotate and roll along the tube. The movement was away from the cathode, showing that the rays were emitted from the cathode. Through conservation of momentum, the fact that cathode rays could move a wheel by colliding with it strongly suggested that they had mass, and were therefore particles.

Remember- The negatively charged cathode rays were blocked by the Maltese cross, could spin a paddlewheel, caused a fluorescent screen to emit light, and were deflected by electric and magnetic fields.

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

Most resources simply say ‘less air’ and ‘still less air’ when referring to the middle two tubes. There- fore, 2% and 0.5% are arbitrary figures here. Of course, the best option is to check when you’re performing the experiment the pressure on the tubes (the pressures will depend on the exact tubes used, so there will probably be variation between schools etc.), but if you didn’t, just remember the figures here.

Striation patterns refer to light and dark areas inside a discharge tube. Electrons colliding with air particles release light dependant on the energy of the electrons, but also on the amount of gas inside the tube. As the pressure of the gas changes, so too do the striation patterns. In this experiment, we had 4 discharge tubes each with different air pressures- 5%, 2%, 0.5%, and 0.01% (measured as a percentage of standard atmospheric pressure). With 5% air, glowing purple/pink streamers formed, extending all the way from the cathode to the anode. At 2%, the pattern changed to a series of alternating light and dark bands running perpendicular to the length of the tube. At 0.5%, the dark gaps between the lines widened (i.e. There were fewer lines), with the pink-purple glow concentrated around the anode, and a blue glow forming at the cathode. At 0.01%, there were no striations. Instead, the glass around the anode glowed yellow-green. The exact nature of the striation patterns varies depending on what gas is used eg. Normal air, hydrogen etc.

Remember- The striation patterns formed in a vacuum tube depend both on the gas inside the tube and on the pressure

# Identify that moving charged particles in a magnetic field experience force

When a moving charged particle travels through a magnetic field, it experiences a force related to its velocity and its direction of travel relative to a field. If the particle is travelling along with or parallel to field lines, there is no applied force. Maximum force is applied if the particle is travelling at 90 degrees to the field lines.

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

For a point charge, the electric field strength depends entirely on the magnitude of charge the object has. The field extends outward in all directions and so obeys inverse square law, rapidly diminishing as distance from the charge increases. For a positive charge, the field lines radiate outwards, indicative of the direction in which a positive test charge would experience force. For a negative charge, the field is identical except the field lines run in the opposite direction, pointing inwards to the point charge, indicative of the fact that a positive charge would be attracted to the negative charge. Oppositely charged parallel plates have a uniform field (in both direction and strength) running between them from the positive plate to the negative plate. Unlike a point charge where the direction of the electric field changes depending on where the field is being examined, the electric field lines between parallel plates always run in the same direction. Also, unlike a point charge where the field exists all around the point charge, the electric field from parallel charged plates only exists in between the plates. The spacing of field lines between the plates indicates field strength.

Remember- The field lines point away from a positive charge, towards a negative charge, and run from positive to negative between charged plates.

# Identify that charged plates produce an electric field

See 3.1.9 for a mathematical description of the field between the plates.

Charged plates- that is, plates with a potential difference between them, produce an electric field running between them. The field lines run from the positive plate to the negative plate, are parallel, and the field strength is equal at all points between the plates. The field does not exist outside the space between the plates.

# Describe quantitatively the force acting on a charge moving through a magnetic field, using F = qvBsinθ (including ”Describe quantitatively the electric field due to oppositely charged parallel plates”)

When a charged particle moves through a magnetic field, it experiences a force that is equal to qvBsinθ. This shows that the force experienced by a charged particle depends on 4 things- its velocity, its charge, magnetic field strength, and the angle that it makes with the field. The right- hand palm rule is used to calculate the direction in which this force is applied. To make the force larger, all of these attributes can be increased, including the angle, making force directly proportional to all of them.

The field between the parallel plates depends on only two things- the potential difference between the plates and the distance between them. It is calculated according to $E = \frac {V}{d}$ , where E is the field strength, V is the potential difference and d is the distance separating the plates in metres. From this, E is proportional to V and inversely proportional to d. The field is at right angles to the plates in all directions and is uniform in strength.

# Outline Thompson’s experiment to measure the charge/mass ratio of an electron

An examination of the mathematics behind Thompson’s experiment is not vital to addressing this dotpoint, and hence has not been included here.

Thompson carried out vitally important work to determine the charge-to-mass ratio of an electron. He accomplished this using a modified cathode ray tube. The first part contained a thermionic cathode (a thermionic cathode is one which is heated by a separate heating circuit, in order to release more electrons) and an anode with a small hole through the centre to produce a thin stream of electrons travelling into space rather than between a potential difference. The second part was a velocity filter, consisting of charged plates above and below the beam set to deflect the electrons upward, and a Helmholtz coil mounted on either side of the tube producing a magnetic field to deflect the electrons downwards. Finally, at the end of the tube was a fluorescent screen which indicated how the electrons were being deflected, if at all. Thompson used both the fields simultaneously and balanced them so that the electrons travelled on the original path they took when the fields were off, as gauged by the fluorescence on the screen. This also had the effect of filtering electron velocities such that only electrons with a single particular velocity travelled through the system uninterrupted. By equating the two field strengths, a formula for the electron velocity was produced related to the strength of both fields. By equating the potential energy and kinetic energy of the electrons at the cathode and anode respectively, and substituting the potential difference across the tube and the velocity of the electrons, he was able to calculate the charge-to-mass ratio of the electron.

# Outline the role of electrodes in the electron gun, the deflection plates or coils and the fluorescent screen in the cathode ray tube of conventional TV displays and oscilloscopes

The cathode ray tube in a display uses 3 parts- the electron gun, deflection plates and fluorescent screen, to form an image. The electron gun is used to produce a fast-moving stream of electrons. The electrodes have two roles- firstly to emit electrons to form the stream (as performed by the heated thermionic cathode) and secondly to accelerate the electrons to very high speeds (accomplished by a very large potential difference between the anode and the cathode). The anode has a hole in it to allow the stream of electrons to leave the electron gun. The deflection plates or coils are used to change the direction of the electron beam. This is because to form an image on the fluorescent screen (as opposed to a dot), the electron beam must sweep over the screen rapidly. This is accomplished by the deflection plates that guide the electron beam to particular parts of the screen. Deflection coils are used in TVs because magnetic fields can deflect the beam through larger angles which is necessary when using a large screen. The fluorescent screen is coated with phosphors that emit light when struck by electrons, which makes the electron beam visible. This is vital to the formation of an image that is viewed on an oscilloscope or TV.

Remember- The cathode ray tube in TVs and oscilloscopes uses electrodes in an electron gun to produce a beam of electrons, deflection plates/coils to steer the beam, and a fluorescent screen to turn the beam into light.