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9.4 FROM IDEAS TO IMPLEMENTATION PREPARED NOTES
INTRODUCTION:By the beginning of the twentieth century, many of the pieces of the physics puzzle seemed to be falling into place. The wave model of light had successfully explained interference and diffraction, and wavelengths at the extremes of the visible spectrum had been estimated. The invention of a pump that could evacuate tubes to 10-4 of an atmosphere allowed the investigation of cathode rays. X-rays would soon be confirmed as electromagnetic radiation and patterns in the Periodic Table appeared to be nearly complete. The nature of cathode rays was resolved and the measurement of the charge on the electron was soon to follow. There were some experimental observations still unexplained but to many scientists the understanding of the world of the atom seemed almost complete. This belief was about to be challenged seriously. The exploration of the atom was well and truly inward bound by this time and as access to greater amounts of energy became available, physics moved further into the study of sub-atomic particles. Careful observation, analysis, imagination and creativity throughout the early part of the twentieth century developed a more complete picture of the nature of electromagnetic radiation and matter. The journey taken into the world of the atom has not remained isolated in laboratories. The phenomena discovered by physicists have been translated with increasing speed into technologies, such as computers, to which society has ever-increasing access. These technologies have often assisted physicists in their search for further knowledge and understanding of natural phenomena at the sub-atomic level. This module increases students’ understanding of the history, nature and practice of Physics and the applications and uses of Physics, the implications of Physics for society and the environment and the current issues, research and developments in Physics.
ELECTRIC FIELDS REVISITEDRecall from the “Electrical Energy in the Home” topic from the Preliminary Course, the nature of the electric field around single point charges and around positive and negative charges in proximity to one another. Remember that the magnitude of the electric field strength at a particular point in space is defined as the force per unit charge at that point.
where E = electric
field strength, q = size of the charge and F
= force experienced by q at the point
in question. The SI units of
electric field strength are NC-1. The direction of the electric field at any point is defined as the direction in which a positive test charge would move if placed in the field at that point. Clearly, since the electric field is strongest where the field lines are closest together, the strength of the field around isolated charges decreases with increasing distance from the charges. Recall also, that two oppositely charged parallel metallic plates separated by a distance, d, can be used to produce an electric field as shown below:
Note that the strength of the field is uniform between the plates but non-uniform towards the edges. The magnitude, E, of the electric field between the plates can be shown to be:
where V is the potential difference between the plates.
Moving Charges In A Magnetic Field RevisitedRecall from the “Motors & Generators” topic that a moving electric charge carries with it an associated magnetic field. Thus, an electric charge moving through a magnetic field experiences a force, due to the interaction of the two magnetic fields present. The size of this force is given by: F = q v B where q = size of charge, v = velocity of charge perpendicular to the field and B = magnetic flux density vector. If the charge enters the field at an angle q to the field direction, instead of perpendicular to it, we must use the component of v that is at right angles to the field direction. Thus the formula becomes: F = q v B sin q. The direction of the force on a charge in a magnetic field may be determined by using Fleming’s Left Hand Rule. Hold the thumb, first finger and second finger of the LEFT hand mutually at right angles. Point the first finger in the direction of the magnetic field. Point the second finger in the direction of conventional current flow (ie in the direction of flow of positive charge). The thumb then points in the direction of the force on the charged particle.
THE INVESTIGATION OF CATHODE RAYSIn 1855 the German inventor and glassblower Heinrich Geissler, invented a vacuum pump that could remove enough gas from a glass tube to reduce the pressure to 0.01% of normal air pressure at sea level. (normal air pressure at sea level = 1 atmosphere = 760 mm of Hg = 101 325 N/m2) This provided his friend, Julius Plucker, with the apparatus to experiment with electrical current through gases at low pressure. Plucker sealed electrodes into a glass tube and then evacuated the tube to very low pressure. When Plucker applied very high voltage to the electrodes, current flowed through the tube and he noticed that the glass tube itself glowed with a pale green glow, mainly in the vicinity of the anode (positive terminal). He concluded that rays of some form were emanating from the cathode (negative electrode) and that these rays caused the glass to glow. These rays were eventually named cathode rays, as they appeared to come from the cathode (negative electrode) of the tube. Plucker also showed that the rays were deflected by an external magnetic field. When we repeat Plucker’s investigations in the laboratory, we find that if air is in the tube and the air pressure is reduced to a few centimetres of mercury, then electrical discharge occurs. Flickering red streamers are observed. If the pressure is further reduced the discharge beams become steady and a pink glow fills the tube. On further reducing the pressure, the anode glows, Faraday’s dark spaces are observed and the glow becomes striated. The following diagram shows a cathode ray tube with the various glows and dark spaces labelled. The voltage applied between the cathode and anode is a high voltage and is usually supplied by an induction coil. The diagram is not to scale.
By 1875, William Crookes had designed new tubes for studying the glow produced when an electric current passes through an evacuated tube. When he used a bent tube, the most intense green glow appeared on the part of the tube opposite the cathode. This suggested that the green glow was caused by something that came out of the cathode and then travelled down the tube until it hit the glass. Eugen Goldstein suggested the name cathode rays.
Crookes also did other ingenious experiments with gas tubes. He placed a metallic Maltese cross in the path of the rays from the cathode. This produced a sharp shadow of the cross on the glass at the end of the tube. Crookes concluded that cathode rays travelled in straight lines and could not penetrate metal. See this Maltese Cross tube or this Maltese Cross tube. Crookes also used a magnet near the tube to produce a horizontal magnetic field for the rays to pass through. The path of the rays was made visible by placing a fluorescent screen lengthways down the tube and arranging a small aperture near the cathode to collimate the rays into a thin beam. He observed that the rays were deflected by the magnetic field as if they were negatively charged particles. Using a tube containing a paddle wheel supported by glass rails, Crookes showed that the cathode rays possessed energy and momentum. The rays striking the paddle wheel moved it along the rails. See these Old Tubes. These and many other experiments led Crookes to conclude that cathode rays:
Note that Crookes also believed that cathode rays could be deflected by an electric field but never succeeded in demonstrating this experimentally. Some of the properties above suggested to Physicists that cathode rays were a wave similar to light. For instance, they produced fluorescence, they travelled in straight lines, they produced similar chemical reactions to those produced by light and they were not deflected by electric fields. Yet cathode rays were deflected by a magnetic field as if they were negatively charged particles. This apparently inconsistent behaviour of cathode rays led to much controversy over whether the rays were a stream of negatively charged particles or a form of EM wave like light. By the end of the 19th Century, the argument in favour of cathode rays being charged particles had become much stronger. By then, it had been shown by Eugen Goldstein that the rays could be deflected by electric fields and by Jean Perrin that the charge on the rays was negative. The final piece of evidence was provided by Joseph John Thomson in a brilliant experiment conducted in 1897.
MEASUREMENT OF CHARGE TO MASS RATIO OF CATHODE RAYS J.J Thomson subjected beams of cathode rays to deflection by known electric and magnetic fields set at right angles to each other (crossed fields) in order to measure the charge to mass ratio of the cathode rays. See this diagram of Thomson's tube or this one Thomson's tube or these photos & diagrams Thomson's tubes. The tube used by J.J. Thomson contained a cold cathode that produced cathode rays by using a strong electric field in the vicinity of the cathode to cause gas discharge. The cathode rays so formed were accelerated towards the anode by the potential difference between the anode and cathode. At the anode, some of the cathode rays were collimated into a thin beam by passing through a slit and then travelled with constant velocity to produce a bright spot on the phosphorescent screen. An electric field could be applied between the metallic plates and a magnetic field at right angles to the electric field was produced by two Helmholtz induction coils sitting on either side of the tube. The experimental procedure was to set E and B to zero and note the position on the screen where the undeflected beam of cathode rays struck. Then a known magnetic field was applied and the position of the deflected beam noted. Finally, an electric field E (=V/d) was applied and its value adjusted until the deflection of the beam returned to zero. Mathematically, for the particles curving in the B field: mv2/R = qvB which can be re-arranged to give: q/m = v/BR (equation 1). Note that q/m, the charge to mass ratio of the cathode rays, is the value we are after. The value of B was known from the arrangement of the Helmholtz coils. R, the radius of curvature of the particles in the magnetic field, was found geometrically from the displacement of the beam spot on the screen. To determine v, the velocity of the particles, Thomson applied the E and B fields simultaneously and adjusted the E field value until the deflection of the beam returned to zero. This meant that the magnetic force (qvB) on the particles was exactly balanced by the electric force (qE) on the particles: qE = qvB
So we have that: v = E/B (equation 2) The value of E was known from the arrangements of the charged plates (E = V/d, where V = voltage between plates & d = distance between plates). So combining equations 1 & 2 we have:
and all of the quantities on the RHS are known. Thomson determined q/m for cathode rays as 1.76 x 1011 C/kg regardless of the material used for the cathode. This determination effectively confirmed the particulate nature of cathode rays.In other experiments, Thomson showed that the charge on the cathode ray particles was the same size as the charge on the hydrogen ion. This combined with the fact that the q/m ratio for cathode rays was 1800 times larger than that for the hydrogen ion (determined in electrolysis experiments) meant that the mass of the cathode ray particles had to be 1800 times smaller than that of the hydrogen ion. On the basis of all these results, Thomson suggested that the cathode ray particle was a fundamental constituent of the atom. Although he originally referred to the particles as “corpuscles”, the name “electron” slowly became accepted as the official name. (As an aside, it is an interesting historical point that Sir Joseph John Thomson was awarded the 1906 Nobel Prize in Physics for proving that the electron is a particle and his son, Sir George Paget Thomson was awarded the 1937 Nobel Prize for Physics for showing that the electron is a wave.)
THE CATHODE RAY TUBEThe cathode ray tube (CRT) consists of three main components: · fluorescent screen · electron gun · deflection system
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. Phosphorescent material can be used in place of the fluorescent material.
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 produced by thermionic emission from the heated filament. These electrons are accelerated towards the anodes by the electric field set up between the cathode and anodes. The dual anode system helps to focus the electron beam. The grid is placed between the cathode and anodes and is made negative with respect to the cathode. This enables the intensity of the electron beam to be controlled – the more negative the grid, the fewer electrons are emitted from the electron gun and the less the brightness of the spot on the end of the tube.
The Deflection System:This allows the electron beam to be deflected from the straight-line trajectory with which it leaves the electron gun. The deflection system consists of two sets of parallel plates, one set in the horizontal plane, and the other in the vertical plane. When potential differences are applied between each set of plates, electric fields are set up between the plates. The electrons in the beam then experience forces vertically while passing between the horizontal plates and horizontally while passing between the vertical plates. Thus, applying appropriate voltages to the deflection plates can control the position of the spot on the end of the screen.
A good diagram & some explanatory notes are at the following link. Just page down a little for the diagram when you get there. http://www.tpub.com/neets/book16/71.htm
Since CRT’s allow the manipulation of a stream of charged particles they are very useful for a number of applications. We will now examine some of these.
APPLICATIONS OF CATHODE RAYSThe Cathode Ray Oscilloscope:The cathode ray oscilloscope (CRO) is used to measure potential differences that change too rapidly with time to be measured using a simple voltmeter. Since many physical and biological effects can be converted into an electrical signal, the CRO has become an extremely useful tool in physics, electronics, biology, medicine and many other fields. The CRO uses a CRT to produce a graph of how an input signal voltage varies with time. The electrodes in the CRT's electron gun produce a narrow beam of electrons, which produces a bright spot on the CRO's fluorescent screen. The screen has a centimetre grid painted on it. When the potential difference across the horizontal & vertical deflection plates is zero, the spot on the screen is at the origin of the set of axes. A sawtooth voltage from within the electronics of the CRO is applied across the horizontal deflection plates. This causes the spot to move horizontally, at a constant speed, from left to right across the screen as viewed by the user. The sawtooth voltage automatically switches the spot off when it reaches the right side of the screen and moves it back to the left side of the screen to repeat its motion. The time base control on the CRO enables the speed with which the spot moves horizontally to be accurately controlled. The voltage signal to be measured is applied to the vertical deflection plates. So, as the spot is scanned across the screen horizontally, the vertical position of the spot changes in response to the input signal voltage. The vertical grid scale on the CRO is calibrated to represent the voltage of the applied signal. A varying potential difference across the vertical deflection plates can be synchronised with the time base on the horizontal deflection plates, to produce an apparently motionless picture on the screen. Click here for a photograph of a cathode ray oscilloscope. An explanation of what an oscilloscope is and what it is used for can be found at: http://whatis.techtarget.com/definition/0,,sid9_gci214508,00.html
Television:To produce television images in Australia, the image formed by the optical lens system of the camera is scanned electronically as a sequence of 625 vertically displaced horizontal lines. This is called raster scanning. The varying light value along each line is converted into a fluctuating electrical signal. The voltage drops to a negative value at the start of each new line to indicate the start of the line scan. The whole scan is repeated 25 times every second, which is fast enough to trick the brain of the viewer into thinking she is seeing continuous motion without noticeable flicker. In television receivers, a CRT called a picture tube translates the television signal back into the picture we see on the screen. The electrodes in the electron gun produce a beam of electrons, which produces a bright spot on the fluorescent television screen. Magnetic fields are used to deflect the electron beam in this CRT, since the magnetic fields allow for a wider-angle beam than would be possible with electric fields from charged plates. Two pairs of magnetic field coils lie on either side of the neck of the picture tube. One pair of coils provides a magnetic field to produce horizontal deflection. The other pair produces deflection in the vertical direction. Both the horizontal and vertical deflection plates are supplied with a continuously increasing time base voltage. The horizontal time base moves the spot from left to right across the screen, while the vertical time base moves the spot down the screen at a much slower rate. At the end of each line of the image, the horizontal deflection plates force the spot to “fly back” to the start of the next line. Thus, the electron beam zigzags down the screen from the top left corner to the bottom right and then repeats its motion. The brightness of the image on the screen is controlled by the signal voltages applied to the grid in the electron gun of the picture tube. In black and white TV the brightness of the spot on the screen determines whether that pixel is white, grey or black. In colour TV there are three electron guns, each one able to activate only one of the primary colours (red, green or blue) on the screen. The coloured image is the result of the combination of coloured pixels of various intensities. See the "How TV Works" page: http://electronics.howstuffworks.com/tv.htm and follow the links from there to get the full story.
The Electron Microscope:This section of notes is no longer required by the Syllabus but has been left here as a matter of interest. The electron microscope uses a beam of electrons rather than light to study objects too small for conventional light microscopes. First constructed by Max Knoll and Ernst Ruska around 1930, the instrument now consists typically of an evacuated column of magnetic lenses with an electron gun at the top and a fluorescent screen or photographic plate at the bottom. It can thus be thought of as a kind of cathode ray tube. The various magnetic lenses (basically electromagnets) allow the operator to see details almost at the atomic level (0.2 nm resolution) at up to a million times magnification and to obtain diffraction patterns from very small areas. In the transmission electron microscope (TEM), electrons are transmitted through the sample and form an image on the fluorescent screen or photographic plate. In the scanning electron microscope (SEM), the beam is focussed to a point and scanned over the surface of the sample. Detectors collect the backscattered and secondary electrons coming from the surface and convert them into a signal that in turn is used to produce an image of the sample. NOTE: For excellent diagrams & information on both TEM’s & SEM’s see the links below. Electron microscopy: http://www.unl.edu/CMRAcfem/em.htm Scanning electron microscope: http://www.mse.iastate.edu/microscopy/highschool.html - this site provides information at various levels of complexity. The current link will give you the "High School" level. The more complex "College" level can be obtained by clicking on the tab at the bottom of the page.
MAXWELL’S WAVES DISCOVEREDIn 1865 James Clerk Maxwell predicted the existence of electromagnetic waves. He suggested that an accelerated charge would produce a non-uniformly changing electric field that would in turn produce a changing magnetic field. By Faraday’s Law, this non-uniformly changing magnetic field would in turn produce a changing electric field and so on. He showed mathematically that such fields would propagate through space as a wave motion with a speed of 3 x 108 m/s. This speed agreed so closely with values of the speed of light measured by Fizeau in 1849 and Foucault in 1862 that Maxwell became convinced that light was a form of electromagnetic wave. Heinrich Hertz, a German physicist, achieved the first experimental demonstration of electromagnetic waves in 1887. Hertz used an induction coil to produce oscillating electric sparks between two brass balls connected to two brass plates. The brass plates acted as an aerial system. He used a small loop of wire with a tiny gap in it as the receiver. See diagram below.
As sparks jumped across the gap between the balls, sparks were also observed jumping the gap in the receiver. Hertz reasoned that the spark discharge oscillating backwards and forwards between the brass balls set up changing electric and magnetic fields that propagated as an electromagnetic wave, as postulated by Maxwell. When these waves arrived at the receiver, the changing electric field component caused charges in the loop to oscillate, thus producing the spark across the gap in the receiver. Hertz carried out a thorough investigation of these waves and showed that they did indeed possess properties similar to light – reflection, refraction, interference, diffraction and polarisation. By setting up an experiment in which he allowed the waves to reflect from a metal sheet and interfere with themselves to produce standing waves, Hertz was able to determine their wavelength. He calculated the frequency of oscillation of the sparks in his transmitter from knowledge of the parameters of the circuit. Then using v = f l he calculated the speed of the waves as 3 x 108 m/s, as predicted by Maxwell. Thus, Hertz’s experiment confirmed Maxwell’s prediction of EM waves and provided strong experimental support for the idea that light was a form of transverse EM wave. The waves produced by Hertz eventually became known as radio waves and his research led to the development of radio communications. As Hertz suspected it was indeed oscillating charges that produced the EM waves. Today we know that radio waves are produced when an oscillating voltage applied to an antenna causes free electrons to oscillate along that antenna. This generates an EM wave that spreads out from the transmitter at 3 x 108 m/s. When the EM wave strikes a receiving antenna it forces charges in the antenna to oscillate at the frequency of the wave. This oscillating electrical signal is then converted into an audio-frequency signal by diodes in appropriately tuned electronic circuits. Applications of the production of EM waves by oscillating electric charges in radio antennae started with the demonstration of “wireless” telegraphy by Sir Oliver Lodge in 1894. Marconi accomplished the first trans-Atlantic transmission in 1901. The invention of the triode valve amplifier in 1906 enabled radio transmission of speech and music over long distances. The invention of the transistor in 1948 eventually resulted in further improvements in radio transmission and reception and decrease in size of transmitters and receivers. Today, radio communications networks, citizen-band radio, mobile phone networks and television image transmission are examples of applications of EM wave production. (This information in this last paragraph is no longer required by the Syllabus.)
DISCOVERY OF PHOTOELECTRIC EFFECTWhile conducting his initial experiments, Hertz often placed the receiver in a darkened box to make it easier to see the tiny sparks in the gap. He noticed that the sparks across the gap in the receiver were distinctly weaker when the receiver was in the box. After much effort Hertz discovered that the sparks jumping the gap in the receiver were more vigorous when the receiver was exposed to the ultraviolet light coming from the sparks in the gap of the transmitter. Although this was a most amazing discovery, Hertz did not further investigate the phenomenon but confined his research to the production and study of EM waves. What Hertz had discovered in fact was the photoelectric effect. We will examine this effect shortly.
PLANCK AND BLACK BODY RADIATIONAs we saw in the Cosmic Engine topic physicists use black body cavity radiators to approximate perfect absorbers and emitters of radiation. A “black body” by definition is a body whose surfaces absorb all the thermal radiation incident upon them and allow none to be reflected. All black bodies at the same temperature emit thermal radiation with the same spectrum, independent of their composition. The intensities of the colours in the spectrum depend only on the temperature. The energy density of black body radiation inside a cavity radiator at various temperatures as a function of wavelength is shown on the Cosmic Engine page. Note that the intensity versus wavelength plot for the radiation emitted from the hole connecting the cavity to the outside has the same shape. The radiation inside a cavity whose walls are at temperature T has the same character as the radiation emitted by the surface of a blackbody at temperature T. The shape of these energy density curves was determined experimentally as early as 1899. Theoretical physicists, however, could not satisfactorily explain the shape of these curves using classical electromagnetic theory. In fact, two physicists, Rayleigh and Jeans derived an equation for black body radiation that suggested that at low wavelengths (high frequencies) the energy density approaches infinity. Historically, the grossly unrealistic prediction at high (ultraviolet) frequencies became known as the “ultraviolet catastrophe”. Clearly, a new approach was needed. This came in 1900 when a German physicist, Max Planck, suggested a revolutionary idea. Planck suggested that radiation was emitted or absorbed by a black body in discrete quanta (packets of energy) rather than continuously, as suggested by classical physics. This daring hypothesis led to the successful explanation of the shape of the energy density curves for black body radiation. With time and the contributions of many physicists, Planck’s hypothesis led to the development of a whole new branch of Physics called Quantum Physics. Mathematically, Planck expressed the quantisation of energy emitted from a black body as:E = n h n where E = the energy of the radiation emitted, h = a constant, now called Planck’s constant with a value of 6.626 x 10-34 Js, n = the frequency of the radiation emitted and n = 0, 1, 2, 3, ….. to represent the different multiples of allowed energy coming from the black body at a particular temperature. Conversely, the energy inside a black body cavity is quantised, the allowed energy states are called quantum states and the integer n is called the quantum number. (As an aside, the formula that Planck obtained for the energy density in the black body spectrum is:
Cute, eh? This can be expressed in terms of l by using c = n l. This is how the plots of energy density shown above were drawn.) [Top]
EINSTEIN AND THE PHOTOELECTRIC EFFECTAs 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. In 1900, Philipp Lenard showed that the photoelectric effect is actually
the emission of electrons from the surface of material when the material is
illuminated by light of high frequency. In a series of experiments Lenard found that: u The number of electrons released (the photocurrent) is proportional to the light intensity. u The emission of photoelectrons was virtually instantaneous (if it occurred). u Emission was frequency dependent. There is a certain threshold frequency below which no photoelectrons were emitted. u As the intensity of the light increased, the maximum kinetic energy of emitted electrons remained constant. The maximum kinetic energy of emitted electrons was found to depend on the frequency of the light used and the type of surface.
The last three of these experimental results could not be explained by the classical wave theory of electromagnetism. Classical theory for instance predicted that electrons in a surface absorbing low intensity radiation of any frequency should accumulate energy for several seconds and then have sufficient energy to be ejected. Electrons absorbing higher intensity radiation should be ejected more quickly. Experimental results showed, however, that emission was almost immediate for all frequencies above the threshold frequency and was independent of intensity. Inspired by the work of Planck, Albert Einstein proposed the radical idea that light energy is transmitted in discrete packets of energy rather than as a spreading wave. The amount of energy in each packet is a quantum and represents the smallest quantity of light energy of a particular frequency. Einstein gave the name photon to a quantum of radiant energy and expressed the energy, E, of this photon as: E = h f where h = Planck’s constant = 6.626 x 10-34 Js & f = the frequency of the radiation emitted. This model of light is referred to as the particle model. Einstein used his particle model of light to explain the photoelectric effect in the following way: Light striking a surface consists of photons. Each photon carries an energy hf into the surface. Each photon gives up all its energy to a single electron. Part of that energy (f) is used in causing the electron to pass through the metal surface. The rest of the energy (hf - f) is given to the electron as kinetic energy. This is the kinetic energy the electron will have outside the surface if it does not suffer any internal collisions on the way out. In other words, (hf - f) is the maximum kinetic energy, Kmax, of the photoelectron. This explanation is summarised in Einstein’s photoelectric equation: (hf - f) = Kmax where f is called the work function for the surface and is the minimum energy required to remove an electron from the surface. Thus, f = hf0 where f0 is the threshold frequency below which no photoelectrons are emitted. So, the equation above becomes: h (f - f0) = Kmax Robert Millikan, an American physicist, experimentally verified Einstein’s explanation of the photoelectric effect in 1916. Einstein received the 1921 Nobel Prize in Physics for his work on this effect. Today, we view light as having a dual character. Light behaves like a wave under some circumstances and like a particle, or photon, under others. When we consider the propagation of light or its interaction with other EM radiation we usually find it convenient to consider light as a wave motion. When we deal with the interaction of light with matter we usually find it convenient to think of light as a stream of particles. On some occasions we need to consider the wavelength and frequency properties of light, on others we need to consider the energy or momentum aspects. The energy is related to the frequency, the frequency is related to the speed of light. c = f l and E = h f Clearly, these equations can be rearranged as needed. Note also that the Syllabus requires you to summarize the use of the photoelectric effect in both photocells and solar cells. We will look at this a little later, after we have dealt with thermionic and solid state devices.
THE DE BROGLIE MODEL OF THE ATOM:This brief section on the de Broglie model of the atom is no longer required by the From Ideas To Implementation Syllabus but is useful background to the Band Theory of Solids and so has been left in this topic. Most physics students at senior high school level picture the atom as consisting of electrons in planetary-like orbits around a tiny central nucleus that contains protons and neutrons. Roughly speaking, this is the model of the atom as described by Niels Bohr. One of the assumptions Bohr made in creating his model was that electrons could rotate in what he called “stationary states” around the nucleus without losing energy. This assumption was necessary to explain why the electrons undergoing circular motion around the nucleus did not radiate energy as predicted by Maxwell’s Theory of Electromagnetism. Exactly how the stationary states enabled the electrons to orbit without losing energy was not explained. In 1924, Louis de Broglie, a French physicist, explained how this could be so. He suggested that the wave-particle dualism that applies to EM radiation also applies to electrons and other atomic particles. In other words, electrons can be thought of as either particles or waves. De Broglie reasoned that the electrons in an atom existed as matter waves in standing wave orbits around the nucleus. No energy would be lost from such an orbit. De Broglie showed mathematically that for such orbits to exist the angular momentum of the electron could only have certain values. We say that the angular momentum of the electron is quantized. In other words, there are only certain discrete energy levels that an electron can occupy within the atom.
CLASSICAL MECHANICS VERSUS QUANTUM MECHANICS:This section is non-examinable but may be of interest to you. Ever wondered what the basic difference is between classical physics and quantum mechanics? Well, take a detour for a minute and investigate the paradox of Schrodinger's Cat. This link takes you to the Brainteasers page of this site & to the description of the Schrodinger's Cat paradox that resides there. After reading the paradox, follow the links to the discussion of the paradox and then, if you are still interested, to a description of the domain of quantum mechanics itself. Use the back button of your browser to get back here. Go to Schrodinger's Cat.
BAND THEORY OF SOLIDS:The de Broglie model of the atom was the stimulus for further research that eventually led to the wave and matrix formulations of Quantum Mechanics, proposed by Erwin Schrodinger and Werner Heisenberg respectively in 1925. According to modern quantum theory, only certain discrete energy levels or energy states are permissible in a given atom and an electron must therefore absorb or emit discrete amounts of energy, or quanta, in passing from one level to another. A normal atom at absolute zero temperature has an electron occupying every one of the lower energy levels, starting outward from the nucleus and continuing until all electrons have been placed. Quantum theory shows that when two atoms are brought close enough together to interact, each of the allowed electron energy levels within the atoms splits into two distinct but closely spaced energy levels as the atoms combine to form the two-atom system. In a six-atom system, each allowed electron energy level is split into a set of six separate but closely spaced energy levels. Clearly then, as we pack more and more atoms closely together each set of split energy levels contains more and more levels spread over the same energy range allowed at that particular radius from the nuclei. So, in a crystalline solid, such as a metal or a diamond, where billions upon billions* of atoms are packed closely together, the energy levels within each set become so closely spaced in energy that they form a practically continuous energy band. (*6.023 x 1023 atoms /mole of substance, to be precise.) In solids, the bands of permissible energy levels are called the allowed bands. These may either be filled with electrons or empty depending on whether they correspond to filled or empty energy levels in the isolated atoms. The energy bands between these allowed bands are called forbidden bands. These bands correspond to the gaps between electron energy levels within the isolated atoms. The highest energy band that is occupied by electrons is the valence band. A higher energy band called the conduction band lies above the valence band. See the diagram below.
Energy band theory can be used
to describe the difference between conductors, insulators and semiconductors.
If an electric field is applied to a solid, electrons in the valence and
conduction bands can be accelerated by the field and gain energy.
However, this can only happen if the electrons can move from their own
energy level within the band to an unoccupied level of higher energy. Metallic solids are composed of
atoms that have some weakly bound valence electrons. As these atoms come together to form the crystal lattice,
some of the weakly bound electrons are freed from their atoms by the energy
released in binding. In good
conductors such as copper, aluminium and silver, all the atoms are fully ionised,
one electron becoming detached from each nucleus in the lattice. These delocalised valence electrons are shared between all
the atoms in the lattice and are free to move from atom to atom. In conductors such as metallic solids the valence band is only partially filled and the valence and conduction bands overlap as shown in diagram (a) below. Thus, valence electrons are free to move in both the valence and conduction bands. Hence conductors have low electrical resistance and allow current to flow when a potential difference is applied across them. In insulators the valence band is completely filled and the energy gap between it and the conduction band is very large as shown in diagram (c) below. Thus, electrons cannot move under the influence of an applied potential difference. Insulators therefore have very high electrical resistance and do not conduct electric current. Note that if an appropriately large amount of energy was supplied to electrons in the valence band to enable them to reach the conduction band, conduction would then occur. This is what happens when an insulator “breaks down”. Also note that in reality some electrons in insulators are free to move but their numbers are extremely small compared with those of metallic conductors.
In semiconductors there is a small forbidden gap between the valence band and the conduction band as shown in diagram (b) above. At absolute zero the valence band is completely full with electrons and the material acts as an insulator. As the temperature increases some electrons gain sufficient thermal energy to escape from the valence band and cross the forbidden gap into the conduction band. Once sufficient electrons have crossed the gap conduction of electric current becomes possible and conductivity increases with temperature. Semiconductors have electrical resistances between those of conductors and insulators.
SEMICONDUCTORS:At room temperature the valence band of a semiconductor is almost completely full. Very few electrons have gained enough thermal energy to move to the conduction band. When an electron does move from the valence band to the conduction band it leaves behind a vacancy or hole. Since this hole represents the absence of an electron from the valence band, it can be treated as a positive charge. A nearby electron can move into the hole, creating a new hole at the position from which it moved. In a sense the hole has moved within the valence band. Thus, both electrons and holes are responsible for carrying current in a semiconductor. In a semiconductor, under the influence of an external electric field, holes move within the valence band in the direction of the electric field, while electrons move within the conduction band in the opposite direction. See the diagram below.
In a pure semiconductor the number of holes in the valence band is exactly equal to the number of electrons in the conduction band. Despite the duplication in the number of charge carriers, the conduction of a piece of pure silicon (semiconductor) is very low compared with copper, since so few charge carriers are actually available. When conduction happens in a pure semiconductor, the material is called an intrinsic semiconductor.
DOPING SEMICONDUCTORS:The introduction of small amounts of certain “impurities” into germanium or silicon can markedly increase their conductivity. The process is known as doping. When conduction occurs in a doped semiconductor, the material is called an extrinsic semiconductor. Both germanium and silicon atoms have four electrons in their valence shell. When these atoms combine with others of their species, each atom shares one valence electron with each of its four neighbours. The introduction of atoms that have five electrons in their valence shell means that where such atoms replace the germanium or silicon in the crystal lattice, there is a surplus electron that is not used for bonding. This surplus electron thus becomes available for conduction. Semiconductors doped in this way contain more electrons than holes and are called n-type semiconductors, since conduction takes place mainly by electrons – negative charges. Group V elements from the Periodic Table, such as phosphorus (P), arsenic (As) and antimony (Sb) are used to dope germanium or silicon and produce n-type material. The pentavalent element used is called a donor atom because it donates an electron. Where an atom that has only three electrons in its valence shell replaces a germanium or silicon atom in the crystal lattice, there is a shortage of one electron to complete the bonding. Effectively a hole has been added to the lattice. This hole thus becomes available for conduction. Semiconductors doped in this way contain more holes than electrons and are called p-type semiconductors, since conduction takes place mainly by holes – positive charges. Group III elements from the Periodic Table, such as boron (B), aluminium (Al), gallium (Ga) and indium (In) are used to dope germanium or silicon and produce p-type material. The trivalent element used is called an acceptor atom because it accepts an electron. The fact that we can control
the number and type of charge carriers in semiconductor material by adding
impurity atoms makes semiconductors extremely useful in electronics.
The other exciting feature of semiconductors is that when a crystal is
produced consisting of p-type and n-type material in contact, the resulting p-n
junction has the following useful properties: u Current can flow in one direction only. The p-n junction can therefore be used as a semiconductor diode, an extremely useful electronic device. u
Exposure to light produces electron-hole pairs that migrate to
opposite sides of the junction. The
resulting potential difference across the junction is proportional to the
intensity of the light. This has
obvious applications in solar cells.
SILICON VERSUS GERMANIUM:Historically, semiconductors were discovered in the 1930’s. Semiconductor crystals were used as rectifiers in radio and radar receivers. These rectifiers took the high frequency alternating signal of the radio wave and extracted the low frequencies necessary for the headphones. In 1942-43, during World War II, Seymour Benzer, a graduate student at Purdue University accidentally discovered that a crystal of germanium (Ge) could withstand higher voltage than any rectifier that was then in use. Benzer went on to discover that mixing trace elements of tin into the germanium could produce rectifiers that were ten times more resistant to damage than was standard at the time. Germanium became the experimental physicists’ choice of material for research into semiconductor properties and devices. The production of semiconductor devices requires semiconductor material with almost perfect crystalline structure. Due to the interest in germanium at that time, techniques for its purification were developed and improved throughout the 1940’s. Although silicon (Si) was also known to be a semiconductor at that time, techniques for its purification were not developed until the 1950’s. For this reason germanium was the first semiconductor material used to produce semiconductor devices. Most notably germanium was used to produce the first transistors in 1948. Today, silicon is the most commonly used semiconductor material in the world. Other semiconductors used for particular applications include germanium, selenium, gallium arsenide, zinc selenide, lead telluride and indium antimonide. Silicon is the preferred material for manufacturing solid-state devices such as transistors, integrated circuits, solid-state memories and so on because: u
It is more abundant than germanium, being the second most
abundant element in the earth’s crust; u
It continues working as a semiconductor at higher temperatures
than does germanium. When they are
heated up, germanium transistors produce too many free electrons. u It develops a glassy, insulating oxide layer when heated to high temperatures in an oxygen-rich atmosphere. This is part of the manufacturing process of integrated circuits. This last section in blue (on why silicon is the preferred semiconductor material for transistors) is no longer examinable.
SOLID-STATE VERSUS THERMIONIC DEVICES:When a metal or carbon filament is heated to high temperatures electrons are emitted from the filament. This process is called thermionic emission. Thermionic devices consist of an evacuated tube (vacuum tube) containing a cathode and at least one other electrode. Vacuum tubes called diode valves are the simplest thermionic device, containing a cathode and only one other electrode. In the simplest diode valve, thermionic emission from the cathode releases electrons that are then attracted to the anode, producing a flow of current through the tube. If an alternating potential difference is applied across a diode a current only occurs when the potential difference is such that the anode is positive with respect to the cathode. The diode is said to rectify alternating current. Triode valves contain three electrodes, a cathode, an anode and a control grid that lies between them. Because the grid is between the cathode and anode, all electrons have to pass through it in their paths to the anode. Small changes in the potential difference between the grid and the cathode produce changes in the current between the cathode and the anode that would have required much larger changes in the anode-cathode potential difference. The triode therefore amplifies small potential differences. In a radio receiver for instance, the signal voltage applied to the grid of the triode valve modulates the tube current passing from the cathode to the anode. A small change in the signal voltage produces a much larger change in the tube current and hence in the circuitry connected to the anode. Prior to 1948 vacuum tubes were the state of the art amplifiers used in radio equipment to increase signal voltages to levels that could drive loudspeakers. Triodes and more complex vacuum tubes such as tetrodes (4 electrodes) and pentodes (5 electrodes) were widely used in amplifying circuits even up until the 1960’s. A solid-state device is an electronic component or device that is composed chiefly or exclusively of solid materials, usually semiconducting, and that depends for its operation on the movement of charge carriers within it. The development of simple solid-state devices such as semiconductor diodes in the 1930’s eventually led to the development of the point contact transistor by Walter Brattain and John Bardeen in 1948. In the same year William Shockley proposed the idea of the junction (sandwich) transistor and by 1950 had turned the idea into reality. Shockley’s transistor turned out to be the more useful of the two. It consisted of a sandwich structure in which two n-type semiconductor layers were separated by a p-type semiconductor layer, as shown below.
The two n-type layers are known as the emitter and collector. The p-type layer is called the base. Transistors can be connected in a number of different ways in circuits. In a typical connection small variations in the base current result in much larger changes in the collector current for a constant potential difference between the collector and emitter. In other words, the transistor can be used as an amplifier. From the 1960’s onwards
solid-state devices such as transistors, and later integrated circuits
and microprocessors, replaced thermionic devices for the following
reasons: u Thermionic devices are much bigger physically than solid-state devices and therefore equipment built from them is unnecessarily large. u Vacuum tubes require a warm up period before they become operational, whereas solid-state devices do not. u Vacuum tubes are fragile and can suffer a decrease in operational effectiveness due to leaking (air in) and burning and pitting of the electrodes. u Vacuum tubes consume much more electrical energy than solid-state devices and produce much more heat energy. u Vacuum tubes operate more slowly than solid-state devices. Modern day transistors are usually either bipolar junction transistors or field-effect transistors (FET’s). They are used worldwide in a huge range of electronics applications – computers, medical equipment, telecommunications, industrial equipment, household devices such as stereos and so on.
USE OF PHOTOELECTRIC EFFECT IN PHOTOCELLSSyllabus point 9.4.2 Column 3 Dot Point 3 requires students to gather, process and present information to summarize the use of the photoelectric effect in photocells. In essence the summary of the
use of the photoelectric effect in photocells should contain information similar
to the following. Photocells consist of a cathode and anode in an evacuated
glass tube. The photoelectric
effect is used in photocells to free electrons from the cathode, thus enabling a
current of electrons to flow from the cathode to the anode. The cathode is usually coated with a photosensitive compound
that emits electrons when light falls upon it. If a photon of light with frequency above the threshold frequency for the photosensitive compound strikes an atom of the compound it will be absorbed and will cause the atom to emit an electron. This electron leaves the cathode and moves towards the positive potential of the anode. In this same way a continuous beam of light shining on the cathode produces sufficient electrons via the photoelectric effect to enable a continuous current of electrons to flow between the cathode and anode. The size of this photocurrent is proportional to the intensity of the light incident on the cathode.
EFFECT OF LIGHT ON SEMICONDUCTORS IN SOLAR CELLSSyllabus point 9.4.3 Column 3 Dot Point 4 requires students to gather, process and present information to summarize the effect of light on semiconductors in solar cells. In essence the summary of the effect of light on semiconductors in solar cells should contain information similar to that in the following example. Solar cells are photovoltaic devices composed of
semiconductor material such as silicon. Usually
a p-n junction is used. This is a
junction formed between a piece of n-type silicon and a piece of p-type silicon.
An electric field is set up at the junction and this forms a potential
barrier that forces any free electrons in the silicon to move to the n-type
silicon and any holes to move to the p-type silicon.
Light shining on the semiconductor material
frees electrons from
the valence band to the conduction band of the semiconductor material, thus
producing electron-hole pairs in the semiconductor.
A photon of light with energy greater than the band gap energy between
the valence and conduction bands but less than the work function energy for the
semiconductor strikes an electron and is absorbed.
This gives the electron sufficient energy to jump the forbidden energy
gap from the valence to the conduction band. Once the electron is free it is forced by the barrier potential to move to the n-type material, while the hole left behind is forced to move to the p-type material. If an external circuit is supplied, the electron will move out of the n-type material, around the external circuit through a load and back into the p-type material to recombine with the hole. Clearly, as many electrons undergo the same process, an electric current has been produced by the solar cell. The size of the current produced is proportional to the light intensity incident on the solar cell. Overall, light energy has been transformed into electrical energy.
DIFFERENCES BETWEEN PHOTOCELLS AND SOLAR CELLSBy way of general information, solar cells are actually one type of photocell. The few basic differences that exist between the two can be stated as follows:
X-RAY DIFFRACTION:Crystalline solids consist of a regular, three-dimensional arrangement of atoms in a periodic pattern called a crystal lattice. The internal structure of such solids can be determined using a technique called X-ray diffraction. As you will recall from the Preliminary Course, diffraction is the name given to the phenomenon in which a wave spreads out as it passes through a small aperture or around an obstacle. Diffraction patterns are most intense when the size of the aperture or obstacle is comparable to the size of the wavelength of the wave. Since the wavelength of X-rays is of the order of 10-10m and since the interatomic spacing in solids is of the same order, X-rays produce strong diffraction patterns from crystals. (Note that both neutrons and electrons can be used in place of X-rays.) The British physicists William and Lawrence Bragg (father & son) applied X-ray diffraction to the study of crystals from about 1912 onwards. A beam of X-rays with a wide range of wavelengths was collimated and directed onto the single crystal specimen under study. A flat film behind the specimen received the diffracted beams. The diffraction pattern consisted of a series of spots of light that indicated the symmetry of the crystal. William Bragg presented a simple explanation of the diffracted beams from a crystal. He suggested that the X-ray waves incident on parallel planes of atoms in the crystal are reflected, with each plane reflecting only a very small fraction of the radiation. The diffracted beams are formed when the reflections from parallel planes of atoms interfere constructively, as in the diagram below.
Bragg derived the following formula, now called the Bragg Law, which enables the determination of the interatomic spacing, d, of the atoms in the specimen or the wavelength, l, of the X-rays (depending on what is known):
where q = the angle of reflection at which constructive interference occurs and n = the order of diffraction (n = 1, 2 , 3, ….. corresponding to occasions when the path difference between the two reflected rays in the diagram is an integral number, n, of wavelengths, allowing constructive interference to occur). The Braggs’ contribution to our understanding of crystal structure has had a lasting beneficial impact in many areas of science and engineering. They were pioneers in a field which has allowed us to greatly increase our knowledge and understanding of materials and which has assisted tremendously in the development of new materials. The Braggs received the 1915 Nobel Prize for Physics in recognition of their important contribution to science.
STRUCTURE OF METALS:Metals possess a crystal lattice structure. As mentioned previously, metals are composed of atoms that have some weakly bound valence electrons. As these atoms come together to form the crystal lattice, some of the weakly bound electrons are freed from their atoms by the energy released in binding. In very good conductors such as copper, aluminium and silver, all the atoms are fully ionised, one electron becoming detached from each nucleus in the lattice. These delocalised valence electrons are free to move from atom to atom and are thus shared by all atoms in the lattice. In this sense, they behave like a gas, an “electron gas”. Thus, there are many valence electrons available for conduction in metallic solids. Conduction in metals can be considered as a free movement of electrons, relatively unimpeded by the crystal lattice.
Drift Velocity in Metals - Not Examinable:In the absence of an electric field, thermal energy causes electrons in a metal to move randomly throughout the crystal lattice at speeds of up to 106 m/s. When an electric field is applied across a metallic conductor, the electrons experience a net force in a direction opposite to the applied field direction. This results in a net drift of electrons towards the high potential end of the field. This drift motion is superimposed on the random motion of the electron and produces a net drift velocity of around 10-4 m/s. The net drift of electrons in one particular direction constitutes a current. The size, I, of this current can be shown to be:
where n = electron density (number of electrons per unit volume of conductor), e = charge on the electron, v = drift velocity of electrons, and A = cross-sectional area of the conductor.
Causes of Electrical Resistance:Electrons can move freely through a regular crystalline lattice, but any disruptions in the regularity of the lattice will obstruct their flow and cause resistance. There are two main sources of this electrical resistance. The first is imperfections in the crystal lattice, such as those caused by impurity atoms or by vacancies, where an atom is missing from a site in the lattice. Each time an electron collides with an imperfection, it loses kinetic energy. This energy is added to the vibrational energy of the lattice, which, in turn, is measured as a rise in temperature of the conductor. Secondly, every atom in a lattice vibrates. The thermal energy emitted or absorbed by these lattice vibrations is quantized and the quanta are called phonons. Every lattice contains rapidly moving phonons. When electrons collide with phonons, they are scattered and lose kinetic energy, which is again added to the vibrational energy of the lattice and produces a rise in the temperature of the conductor. Note that collisions between electrons and phonons account for most of the electrical resistance of a conductor. The higher the temperature of the conductor, the more energetic the vibrations of ions in the lattice and the more phonons there are present in the lattice. So, as the temperature rises so too does the electrical resistance of the metallic conductor. Hence, the electrical resistance of a metallic conductor should decrease to a low but non-zero value as the temperature decreases towards absolute zero. We would still expect a residual resistance even near absolute zero due to crystal lattice imperfections. The fact is, however, the electrical resistance of some metals disappears completely at sufficiently low temperatures.
SUPERCONDUCTIVITY:In 1911, the Dutch physicist Heike Kamerlingh-Onnes found that the electrical resistance of solid mercury drops to an immeasurably small value when cooled to a temperature of 4.15 K (-269oC). This phenomenon in which a conductor loses all of its electrical resistance at a certain critical temperature Tc, is called superconductivity. Mercury goes from a normal state to a superconducting state as the temperature drops below 4.15 K. Many other elements, and many compounds and alloys have since been found to exhibit similar behaviour. Up until 1986 the highest value of Tc discovered was about 23 K. In 1986, Georg Bednorz and Alex Muller discovered certain ceramic materials that became superconducting at 30 K and since then other ceramics have been produced with Tc values as high as 134 K. These new ceramic materials are known as high temperature superconductors. The German physicists Walther Meissner and Robert Ochsenfeld discovered another exciting property of superconductors in 1933. They found that when a superconducting material is cooled below its critical temperature in the presence of an applied magnetic field, it expels all magnetic flux from its interior. If the field is applied after the material has been cooled below Tc the magnetic flux is excluded from the superconductor. This effect is now called the Meissner Effect and lends itself to a startling demonstration of superconductivity. A magnet can be made to float above a piece of superconducting material, as shown in the diagram below. Supercurrents induced by the magnet flow through the superconductor and produce a magnetic field that exactly cancels out the magnet’s own field.
THE BCS THEORY OF SUPERCONDUCTIVITY:In 1957, John Bardeen, Leon Cooper and John Schrieffer of the USA proposed a detailed quantum mechanical theory, now known as BCS Theory, to explain superconductivity. The predictions of this theory are in excellent agreement with experimental results for low temperature superconductors. Some adjustments or perhaps even a new theory are necessary in order to fully explain high temperature superconductivity. BCS Theory suggests that superconductors have zero electrical resistance below their critical temperatures because at such temperatures the electrons pass unimpeded through the crystal lattice and therefore lose no energy. The theory states that the supercurrent in a superconductor is carried by many millions of bound electron pairs, called Cooper pairs. These pairs form when one electron passing between adjacent positive ions in the lattice attracts the ions, causing them to move slightly inwards and to create a region of increased positive charge density. Due to the elastic properties of the lattice, this region of increased positive charge density propagates through the lattice as a wave. A second electron passing through the lattice is attracted into this moving region of increased positive charge density and is effectively swept along by the lattice wave created by the first electron. Thus, by pairing off two by two, the electrons pass more smoothly through the lattice. See diagram below.
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