[wpsm_accordion][wpsm_accordion_section title=”Notes for From Ideas to Implementation”]Below are the dot points of From Ideas to Implementation. Click on the dot point to expand relvant information. These notes were written by; Steven Zhang Click here to donate him[/wpsm_accordion_section][wpsm_accordion_section title=”Cathode Rays”]
Explain that cathode ray tubes allowed the manipulation of a stream of charged particles
- Investigation of vacuum tubes could not occur until good vacuum pumps had been invented. A vacuum tube is a glass tube fitted with an electrode at either end, and almost all of the air sucked out.
- The positive electrode is the “anode”; The negative electrode is the “cathode”. When a high voltage is connected between the electrodes, an invisible ray travels from the cathode to the anode. They were called “cathode rays”. Cathode rays cause glass to glow green.
- A discharge tube is a cathode ray tube with a vacuum pump fitted, so that the air pressure inside the tube can be varied. At different air pressures, different bright effects appear in the tubes e.g. bands, striations and dark spaces. These are caused by cathode rays striking atoms in the air inside the tube. The atoms become excited then release photons of visible light
- A beam of electrons travels from the cathode to the anode and can be deflected by electrical and/or magnetic fields.
Explain why the apparent inconsistent behaviour of cathode rays caused debate as to whether they were charged particles or electromagnetic waves
In 1892 Hertz demonstrated that cathode rays could penetrate thin metal foils. This he believed supported a wave nature.
In 1895 Jean-Baptise Perrin showed that cathode rays deposited negative charges on impact with an object, suggesting a particle nature.
There was controversy over the nature of cathode rays – waves or particles.
If metal plates are separated by a distance and are attached to a power source, an electric field will be produced between them. E = V/d
Describe quantitatively the force acting on a charge moving through a magnetic field
Recall that the force (F) acting on a charge (q) moving with a velocity (v) at an angle to a magnetic field (B), is given by:
FB = qvB
Where FB = magnetic force
( N) q = charge (C)
v = velocity of charge (ms-1 ) B
= magnetic field strength (T)
Discuss qualitatively the electric field strength due to a point charge, positive and negative charges and oppositely charged parallel plates.
If a positive charge is placed near another positive charge, it will experience a force of repulsion. A positive charge placed in a field will experience a force in the direction of the arrow. A negative charge placed in a field will experience a force opposite to the direction of the arrow.
Describe quantitatively the electric field due to oppositely charged parallel plates
FE = qE
Where FE = electric force
(N) q = charge (C)
E = electric field strength (NC-1)
Thomson adjusted the strength of the fields so that the particles were not deflected. By carefully measuring the strength of the fields, Thomson could calculate v.
J. J. Thomson’s Experiment
- By fitting plates to his CRT, he could subject the cathode rays to an electric field. The rays deflected, proving that they were charged particles, not electromagnetic waves
- He noticed that the rays deflected toward the positive plate, proving that they were negatively charged particles.
- By crossing electric and magnetic fields, Thomson was able to deduce the velocity of the cathode rays.
- By turning off the E field, the particles followed a circular arc caused by the B field. The magnetic force was acting like a centripetal force.
- Thomson had already measured B and worked out v. By measuring the radius of curvature r,he could then calculate q/m, i.e. the charge/mass ratio of an electron.
- q/m for these particles was 1800 times greater than for a hydrogen ion, the simplest known atomic ion.
- Thomson quickly compared the charges and found them to be about the same (though opposite in sign)
- Therefore mass for cathode ray particles was 1800 times smaller than hydrogen
- Therefore cathode ray particles were subatomic particles!
- This was the first discovery of subatomic particles
- They were later called electrons.
Outline the role in a cathode ray tube of:
Electrodes in the electrode gun
The electric field
The fluorescent screen
The Cathode Ray Tube
Each CRT has a vacuum tube/chamber, a cathode, an anode, and a target.
Electrodes in the Electrodes in the electron gun
The electron gun produces a narrow beam of electrons. It consists of a filament, a cathode and two open-cylinder anodes. The anodes help to accelerate and focus the electrons. The electric field A ring shaped electrode – the grid – between the cathode and anodes controls the brightness of the spot by controlling the number of electrons emitted by the gun. By making the grid negative with The fluorescent respect to the cathode the number of electrons, and hence the brightness is reduced.
The electric field
Acts as a deflection system. It consists of two sets of parallel plates connected to a parallel plates connected to a potential difference. This produces an electric field between the plates. The Y-plates control the vertical deflection and the X-plates the horizontal deflection
The fluorescent screen
The inside glass of the end of the tube is coated with a fluorescent material for example, zinc sulphide. When an electron beam hits the screen, the coating fluoresces and a spot of light is seen on the screen. The screen acts as a detector of cathode rays.
Outline applications of cathode rays in oscilloscopes, electron microscopes and television sets
The Cathode Ray Oscilloscope (CRO)
Is an electronics diagnostics device because it can show a graph of how voltages vary over time.
Deflection of the electron beam is achieved by two sets of plates.
Horizontal plates cause vertical deflection while vertical plates cause horizontal deflection.
An electron gun again produces the electron beam. Coils are used instead of plates, however. Electric current through the coils produce magnetic fields that can deflect the beams quickly from side to side, and more slowly from bottom to top. In this way the beam scans the entire screen. By varying the intensity of the beam, a picture is built up. The picture is refreshed 50 times / second, which is too fast to be noticed by the human eye.
The Electron Microscope
Uses electrons instead of light. Their wavelength is 100,000 times smaller than visible light,
therefore their resolving power is 100,000 times greater.
- A “sample” is placed inside the chamber (which is really the CRT)
- The air is then sucked out
- An electron gun produces the electron beam
- Coils produce magnetic fields to focus the beam (“magnetic lenses”)
- The beam scans over the surface of the sample
- Detectors pick up the reflected and scattered electron beam, and from this information a 3 dimensional image is constructed
Discuss the impact of increased understandings of cathode rays and the development of the oscilloscope on experimental physics
The introduction of electronic control systems into all forms of science and industry has seen the cathode ray oscilloscope (CRO) become one of the most widely utilised test instruments. Because of its ability to make ‘voltages’ visible, the cathode ray oscilloscope is a powerful diagnostic and development tool.[/wpsm_accordion_section][wpsm_accordion_section title=”Quantum Theory”]
Explain qualitatively Hertz’s experiments in measuring the speed of radio waves and how they relate to light waves
Recall: Maxwell’s theory of electromagnetic waves
In 1864 Maxwell, through a set of four brilliant equations, predicted a range of invisible waves made up of an electric and magnetic wave that regenerate each other. The speed of these waves was calculated to be 3 x 108 ms-1 and probably included light.
Heinrich Hertz’s Experiment: (proving Maxwell’s theory)
Performed in 1886, Hertz built equipment to generate and transmit EM waves with λ ≈ 1m. He also had a separate receiver (a loop of wire) located about 20m away. Spark gaps were included to show when high voltage AC was present in the transmitter or receiver. The receiver spark only appeared when the transmitter spark was present. Hertz hypothesised that the sparks set up changing electric and magnetic fields that propagated as an electromagnetic wave, as postulated by Maxwell. He showed that these were waves being transmitted because he could reflect, refract and polarise them. By measuring the frequency, he calculated v (v = f λ) and it came out as 3 x 108 ms-1. These properties proved Maxwell’s theory and as they are also exhibited by light, Hertz was able to provide experimental evidence that light is a form of transverse electromagnetic wave.
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 observed that the transmitter spark was producing something else to assist the production of the receiver spark. Thinking it to be light, he performed a dispersion experiment and discovered that UV light from the transmitter spark was causing extra electrons to join the receiver spark, making it stronger. He did not investigate this further, but did report his observations
Outline applications of the production of electromagnetic waves by oscillating electric charges in radio antennae
Electromagnetic waves are produced by accelerating charges such as electrons oscillating in a wire. Consider a charge oscillating with simple harmonic motion. The field lines ‘produce’ a sine curve where the amplitude of the wave represents the electric field intensity at that point. This changing E produces a changing B; the result is an electromagnetic wave.
Simple radio aerials use an alternating electric current in the antenna, which continually accelerates electrons back and forth, hence producing electromagnetic radiation that has the same frequency as the alternating current operating in the antenna.
Philipp Lenard’s Experiment
Lenard added a reverse voltage (“stopping voltage”, Vstop) to measure the energy of the electrons. Cathode ray tubes became specialised for this investigation and gained some new names.
Lenard wanted to investigate the relationship between the energy of the photoelectron and the intensity of the light. His results were surprising!
He used a reverse current to stop the photoelectron’s motion. This “stopping” voltage was a measure of their kinetic energy Ek He used a carbon arc lamp that could be turned up or down to vary the light intensity. He went further and placed colour filters in front of the lamp to investigate how the frequency of light affected the photoelectrons.
Classical physics could explain why the photoelectrons were produced – the incident light gave energy to the surface electrons until they had enough energy to escape the surface. Further, classical physics predicted that:
- As light intensity increased, the energy of the photoelectrons would increase.
- The frequency of the light should have no effect on the energy of the photoelectrons.
- Increasing the light intensity did not increase the energy of the photoelectrons, although it did produce more photoelectrons.
- Increasing the frequency of the light (making it bluer) did increase the Ek of the photoelectrons.
- There is a threshold frequency f0 (which depends on the metal used) below which no photoelectric effect occurs, no matter how intense the light.
- Above f0, the photoelectric effect occurs no matter how dim the light.
Classical physics could not explain these results!
Identify Plank’s hypothesis that radiation emitted and absorbed by the walls of a black body cavity is quantised
Max Planck and Black Body Radiation – The Quantum Theory
A “black body” is a theoretical concept – an object that perfectly absorbs all radiation falling on it until it is warmer than its surroundings, and then becomes a perfect emitter. The radiation it emits is spread across the EM spectrum and has a peak that depends on the nature of the black body.
Classical physics could not explain the shape of the black body radiation curve. Max Planck provided a complex explanation that did work but had to assume that the energy radiated in lumps he called “quanta”. The energy of each quantum was given by: E = hf
E = energy of quantum, in J
f = frequency of radiation, in Hz
h = Planck’s constant = 6.63 x 10-34 Js
Identify Einstein’s contribution to the quanta and its relation to black body radiation
Einstein’s Explanation of the Photoelectric Effect
Einstein used Planck’s idea and said that the incident light was quantised. He named a quantum of light a “photon”. The energy of a photon depended on its frequency, according to E = hf. Further, Einstein stated that a certain amount of energy was required by an electron to escape the metal surface. He called this the work function, φ (where φ = hf0).
When a photon of light strikes an electron in the metal, it gives all of its energy to the electron.
Explain the particle model of light in terms of photons with particular energy and frequency
Light exists as photons, each with an energy represented as E = hf. Light intensity depends on the number of photons.
Photons with the highest energy correspond to light of the highest frequency.
The energy of a light photon of any known wavelength of light can be determined as they all travel with the same velocity (speed of light).
Describe the de Broglie model of electrons in orbits around atoms
Bohr’s Model of the Atom
- Positive nucleus
- Electrons orbit nucleus in certain allowable orbits, each orbit represents a certain energy level with outer orbits having higher energies
- Electrons can jump up or down by absorbing or releasing an appropriate amount of energy (quanta)
However, Bohr did not know why these certain orbits were stable because his model suggests a natural instability.
De Broglie’s Explanation
- Electrons move in waves with calculated wavelength
- He proposed that the circumference of each allowable orbit must be a whole number of electron wavelengths
- The allowable orbits then became standing-wave patterns of vibration (∴ stable) due to constructive interference
- Other orbits break down due to destructive interference
Identify that some electrons in solids are shared between atoms and move freely
In a solid the atoms are linked together into a network or lattice by bonds. The bonds are either covalent (electron-sharing) or ionic (electron-swapping). As the outer electrons are used in this way they become common property to the lattice. Similarly, the energy levels or bonds which they occupy become common property of the lattice. That is, the outer energy levels are restricted to the atoms but extend across the lattice.
- The outermost energy level normally occupied by electrons is called the valence band
- The next band up (normally not occupied) is called the conduction band
- In order to conduct electricity, an electron must gain sufficient energy to jump up to the conduction band. This means the electron is no longer restricted to its atom and is free
Describe the difference between conductors, insulators and semiconductors in terms of band structures and relative electrical resistance
Compare qualitatively the relative number of free electrons that can drift from atom to atom in conductors, semiconductors and insulators
Identify absences of electrons in a nearly full band as holes, and recognise that both electrons and holes help to carry current
The Creation of Charge Carriers in Semiconductors
Within the crystal lattice of semiconductor, atoms are (usually) bonded to 4 other atoms, using covalent bonds. Here and there will be imperfectly formed bonds – “electron holes”. Electrons in the bonds require only a small amount of energy to jump out of the bond, travel a short distance and then jump into one of the available holes. In doing so it has left behind another hole. As the electrons jump in one general direction, the holes appear to move in an opposite
direction, as if they were positive charge carriers. Hence, the provision of a small amount of energy to a semiconductor creates two types of charge carriers: negatively charged electrons and positively charged electron holes. Normally there are as many electrons as holes, and this is referred to as an intrinsic semiconductor.
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
Melting down a semiconductor then adding a small amount of impurity before recrystallising can alter the conducting properties of the semiconductor. This process is called “doping” and the material it forms is an “extrinsic semiconductor”.
- n-type semiconductors:If the impurity is from group 5 of the periodic table (eg Arsenic As, Phosphorous P) then it will have 5 outer electrons. Four will be used in covalent bonds, leaving one extra electron. Only one atom of impurity per 200,000 atoms of semiconductor is added. This material will have more negative charge carriers (electrons) than positives (holes).
- p-type semiconductors:If the impurity is from group 3 (eg Boron B, Gallium Ge) then it will only have 3 outer electrons and can only form 3 covalent bonds. This will leave one empty spot (a hole) where there would otherwise have been an electron. This material will have more positive charge carriers (holes) than negatives (electrons).
Photovoltaic cells: a layer of n-type over a layer of p-type. Light shines on the n-type layer. This energy causes more conducting electrons to become available in the n-type, which produces a voltage between the layers. This allows it to be used like a battery.
A transistor is like an electronic tap – a small voltage placed on the “base” can control a large current through the collector to the emitter.
Integrated Circuits: are thousands or millions of transistors (in circuits!) etched onto a single silicon chip. These have grown and developed into computer chips eg. Pentium 4 etc.
Identify that the use of germanium in early transistors is related to lack of ability to produce other materials of suitable purity
Germanium Vs Silicon
Transistors were invented in 1947, announced in 1948 and in production by 1950. These early transistors were made of germanium, as it was the only semiconductor available in pure form germanium was used in war-time military radio, so much research had already gone into how to grow it in pure form). However germanium has only a small energy gap between its valence and conduction bands. This made germanium transistors unreliable as the heat of normal operating conditions caused more conduction electrons to be created than expected. This made them behave erratically.
Explain why silicon became the preferred raw material for transistors
Silicon’s energy gap is slightly greater, so once it was learned how to grow pure silicon, it was immediately used to make transistors (this was done in the early 1950’s by Texas Instruments). Silicon transistors proved much more reliable.
Silicon is also more abundant than germanium, being very common in the Earth’s crust.
Discuss differences between solid state and thermionic devices and discuss why solid state devices replaced thermionic devices
Transistors Vs Thermionic Valves
Thermionic valves were used during the first half of the twentieth century as an electronic switch or amplifier. They were essentially a small cathode ray tube with an extra controlling electrode, called a “grid”. The problem was that these valves were power hungry, and often unreliable.
Bell Labs (part of AT&T) developed the semiconductor replacement – the transistor. Transistors required much less power to run and were (eventually) cheaper to produce. They were also much smaller. Within a few years they had replaced valves almost completely.[/wpsm_accordion_section][wpsm_accordion_section title=”Superconductivity”]
Superposition – if two waves act in the same place at the same time they add up to give a
Interference – the superposition of waves.
Interference pattern – interference in two or three dimensions can produce an interference pattern.
Eg. Interference with light transmitted through a “diffraction grating”. By measuring the geometry of the interference pattern it is possible to deduce the spacing of the lines on the diffraction grating.
The Braggs (father Sir William Henry Bragg and son Sir William Laurence Bragg) adapted this technique to investigating the crystal structure of many solids (in particular, metals). Their general technique is known as “X-ray crystallography”.
An X-ray tube emits X-rays onto a sample. The reflected interfering X-rays hit a photographic film, allowing the interference pattern to be seen.
X-rays needed to be used because the incident wavelength must be approximately equal to the atomic spacing.
Applications of this technique yielded much information about the crystal structure of many solids, especially metals.
Bragg’s Law is the formula used by the Braggs in their X-ray crystallography: d sinθ = nλ
Note this same formula can be applied to the laser/diffraction grating experiment described earlier, however in that case d = line spacing on the grating.
Analysis of the interference pattern as well as the angles involved therefore allows the calculation of the crystal layer spacing d.
Explain that metals possess a crystal lattice structure
The Crystal Lattice Structure of Metals
The Braggs established that metals have a crystal lattice structure. We know that metals, in general, have only one, two or three electrons in their outer energy shells. These electrons are only loosely bound to the positive ions, causing a lattice of positive ions to be surrounded by a ‘sea’ of electrons.
Identify that the conducting properties of metals are related to the large number of electrons able to drift through their crystal lattice structure
Free electrons in metals travel at approximately 0.01c in random motion, colliding with:
- Each other
- Imperfections in the lattice
- Impurities in the lattice
The formula for drift velocity is:
Discuss the relationship between drift velocity and:
The density of electrons
The cross sectional
area of wire
The electronic charge
If I is kept constant, the drift velocity is:
- Inversely proportional to the density of free electrons n;
- Inversely proportional to the cross-sectional area A;
- Inversely proportional to the electric charge e, which is a constant.
Discuss how the lattice impedes the paths of electrons causing heat to be generated
The collisions of the electrons cause a loss of energy as heat is generated. The collisions are the source of resistance of a wire (they don’t collide with normal ions; they ‘know where they are’). If a lattice has thermal energy (temp > 0 K) then it vibrates, which contributes to the collisions and the resistance of the lattice. If its temperature is reduced, then the vibrations also reduce, lowering the resistance. The resistance of a pure metal drops to zero at 0 K.
Identify that superconductors, while still having lattices, allow the electrons to pass through unimpeded with no energy loss at particular temperatures
Some materials, called “superconductors”, achieve zero resistance suddenly at some nonzero temperature, called the “critical temperature” or “transition temperature” (Tc).
Explain current theory that suggests that superconductors are conducting materials that, at specific temperatures, force electrons to pair and, through interactions with the crystal lattice, are ultimately able to form an unimpeded orderly stream
The BCS Theory of Superconductivity
This is the Nobel Prize winning theory to explain (type 1) superconductivity from Bardeen, Cooper and Shrieffer.
The theory states that superconductivity is the result of the interaction between electron pairs (called ‘Cooper’ pairs) and vibrations of the crystal lattice:
- A first electron travelling through the lattice attracts the positive ions and this distorts the lattice.
- The distortion creates a concentration of positive charge that attracts a second electron.
- The second electron ‘rides the wave’ behind the first electron.
- The sonic frequency vibration of the lattice forms energy units called ‘phonons’. The exchange of phonon energy from the first to the second electron keeps the cooper pair together for some time.
- Discuss the advantages of using superconductors and identify current limitations to their use
Application of Superconductors
One of the biggest problems with current power transmission systems is ‘joule heating’. The resistance of the cable causes the cable to be heated. This represents a loss of energy. Since P = I^2R, the joule heating is proportional to I2. Hence transformers are used to lower current as much as possible prior to transmission, and this necessitates the use of AC electricity.
If superconductors could be used for transmission cables then their zero resistance means that no energy would be lost (i.e. no joule heating).
- Cable of same size could carry 3 to 5 times as much current
- DC is the more logical choice because
- Don’t need to lower current
- Don’t need transformers; and
- AC involves a slight energy loss
- No joule heating, hence energy savings
- This would lower demand for new power stations
- Greater efficiency means less wastage and less demand for fuel, and therefore less environmental impact
- The cables would need to be kept very cold
- Installation costs would be high
- All appliances would need to be redesigned to work on DC
- Current high temperature superconductors are ceramic and therefore too brittle to be made into wires
The huge dynamos in a power station can also be made more efficient with superconductors because these use electromagnets to produce the necessary magnetic field. If superconductors were used to make the electromagnets then they would be more efficient, making the whole device more efficient.
This is something that is very difficult to do with current technology, and means that power stations must adjust their output to the demand at the time. With superconductors, a long loop can function as a storage device. Current introduced into the loop will continue to flow around the loop indefinitely, and can be retrieved when required. A power storage device connected to a power station would allow the station to run continuously at peak efficiency, regardless of fluctuations in demand.
Most electronics would also become more efficient if built using superconductors. Consider a computer CPU. This is a 70W device, which means that heat generation is a problem and a limitation to how fast it can be run. If built using superconductors, this heat problem would be eliminated, allowing the CPU to be run at faster speeds. But how could we replace the semiconductor transistor? In 1962, Brian Josephson invented a superconductor switch that performs the same task as a transistor switch but is much faster. This device is called a “Josephson Junction”. CPUs built of those would be very much faster than current CPUs.
An MRI machine maps the water molecules inside a person’s body to build up a 3D computer image of the person’s organs. It does this by having a large superconducting coil that produces an intense magnetic field (4T). The person lies inside the coil. Radio frequency radiation is directed to the patient’s body and these conditions cause the H atoms to vibrate. The device picks up the signals produced by the H atoms, works out their locations and maps them.[/wpsm_accordion_section][/wpsm_accordion]