Fundementals Of Nuclear Physics


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Fundementals Of Nuclear Physics

  1. 1. 核能发电基本常识 认识科学做一个人聪明的外行人
  2. 2. 核能发电基本常识 认识科学做一个人聪明的外行人
  3. 3. Atoms and Nuclei Each topic is subdivided into a number of episodes. An episode represents a coherent section of teaching – perhaps one or two lessons. Each episode contains links to a number of activities. Quantum physics Episode 500: Preparation for quantum physics topic Episode 501: Spectra and energy levels Episode 502: The photoelectric effect Lasers Episode 503: Preparation for lasers topic Episode 504: How lasers work Wave particle duality Episode 505: Preparation for wave-particle duality topic Episode 506: Particles as waves Episode 507: Standing waves
  4. 4. Radioactivity Episode 508: Preparation for radioactivity topic Episode 509: Radioactive background and detectors Episode 510: Properties of radiations Episode 511: Absorption experiments Episode 512: Nuclear equations Episode 513: Preparation for exponential decay topic Episode 514: Patterns of decay Episode 515: The radioactive decay formula Episode 516: Exponential and logarithmic equations Accelerators and detectors Episode 517: Preparation for accelerators and detectors topic Episode 518: Particle accelerators Episode 519: Particle detectors Rutherford’s experiment Episode 520: Preparation for Rutherford scattering Episode 521: Rutherford’s experiment Episode 522: The Size of the Nucleus Nuclear stability Episode 523: Preparation for nuclear stability topic. Episode 524: Stable nuclides Episode 525: Binding energy
  5. 5. Nuclear fission Episode 526: Preparation for nuclear fission topic Episode 527: Nuclear transmutation Episode 528: Controlling fission X-ray and neutron diffraction Episode 529: Preparation for X-ray and neutron diffraction topic Episode 530: X-ray diffraction Episode 531: Neutron diffraction Particles and antiparticles Episode 532: Preparation for particle physics topic Episode 533: The particle zoo Episode 534: Antiparticles and the lepton family Episode 535: Particle reactions Episode 536: Vector bosons and Feynman diagrams Quarks Episode 537: Preparation for deep scattering and quarks topic Episode 538: Electron scattering Episode 539: Deep inelastic scattering Episode 540: Quarks and the standard model 资料来源: Nuclei/index.html
  6. 6. 1 Episode 500: Preparation for the quantum physics topic It is most likely that this will be a topic that is completely unfamiliar to all students from pre-16 level courses. It is also one where the impact on everyday life is apparently very limited and where students think that they have no direct experience of its consequences. Nothing could be further from the truth: e.g. all modern electronics relies on quantum physics. However these very facts make it a most fascinating subject and one whose very novelty should attract the interest of your students. Episode 501: Spectra and energy levels Episode 502: The photoelectric effect Main aims Students will: 1. Know that atoms absorb and emit light as quanta (photons). 2. Explain how this is used to explain emission spectra. 3. Know how to calculate photon energies. 4. Describe the photoelectric effect, and explain it in terms of photons and electrons. 5. Describe an experiment to determine Planck’s constant using the photoelectric effect. Prior knowledge Students should be familiar with the nuclear model of the atom. They should know that metals contain ‘free’ (conduction) electrons. Where this leads These episodes (and work on lasers) lead on to general ideas about wave-particle duality. INDEX
  7. 7. 2 Episode 501: Spectra and energy levels Summary Demonstration: Looking at emission spectra. (20 minutes) Discussion: The meaning of quantisation. (20 minutes) Demonstration: Illustrating quantisation. (10 minutes) Discussion: Energy levels in a hydrogen atom. (10 minutes) Worked example + Student Questions: Calculating frequencies. (20 minutes) Discussion: Distinguishing quantisation and continuity. (5 minutes) Worked example: Photon flux. (10 minutes) Student calculations: Photon flux. (20 minutes) Student experiment: Relating photon energy to frequency. (30 minutes) Demonstration: Looking at emission spectra Show a white light and a set of standard discharge lamps: sodium, neon, hydrogen and helium. Allow students to look at the spectrum of each gas. They can do this using a direct vision spectroscope or a bench spectroscope, or simply by holding a diffraction grating up to their eye. What is the difference? (The white light shows a continuous spectrum; the gas discharge lamps show line spectra.) Emission and absorption spectra (Diagram: INDEX
  8. 8. 3 The spectrum of a gas gives a kind of 'finger print' of an atom. You could relate this to the simple flame tests that students will have used at pre-16 level. Astronomers examine the light of distant stars and galaxies to discover their composition (and a lot else). Discussion: The meaning of quantisation Relate the appearance of the spectra to the energy levels within the atoms of the gas. Students will already have a picture of the atom with negatively charged electrons in orbit round a central positively charged nucleus. Explain that, in the classical model, an orbiting electron would radiate energy and spiral in towards the nucleus, resulting in the catastrophic collapse of the atom. This must be replaced by the Bohr atomic structure – orbits are quantised. The electron’s energy levels are discrete. An electron can only move directly between such levels, emitting or absorbing individual photons as it does so. The ground state is the condition of lowest energy – most electrons are in this state. Think about a bookcase with adjustable shelves. The bookshelves are quantised – only certain positions are allowed. Different arrangement of the shelves represents different energy level structures for different atoms. The books represent the electrons, added to the lowest shelf first etc Demonstration: Illustrating quantisation Throw a handful of polystyrene balls round the lab and see where they settle. The different levels on which they end up – the floor, on a desk, on a shelf – gives a very simple idea of energy levels. Some useful clipart can be found below TAP 501-1: The emission of light from an atom Resourceful Physics >Teachers>OHT>Emission of Light An energy input raises the electrons to higher energy levels. This energy input can be by either electrical, heat, radiation or particle collision. When the electrons fall back to a lower level there is an energy output. This occurs by the emission of a quantum of radiation. Discussion: Energy levels in a hydrogen atom Show a scale diagram of energy levels. It is most important that this diagram is to scale to emphasise the large energy drops between certain levels. The students may well ask the question, “Why do the states have negative energy?” This is because the zero of energy is considered to be that of a free electron 'just outside' the atom. All INDEX
  9. 9. 4 energy states 'below' this – i.e. within the atom are therefore negative. Energy must be put into the atom to raise the electron to the 'surface' of the atom and allow it to escape. Worked example + student questions: Calculating frequencies Calculate the frequency and wavelength of the quantum of radiation (photon) emitted due to a transition between two energy levels. (Use two levels from the diagram for the hydrogen atom.) E2 – E1 = hf Point out that this equation links a particle property (energy) with a wave property (frequency). Ask your students to calculate the photon energy and frequency for one or two other transitions. Can they identify the colour or region of the spectrum of this light? Emphasise the need to work in SI units. The wavelength is expressed in metres, the frequency in hertz, and the energy difference in joules. You may wish to show how to convert between joules and electronvolts. Discussion: Distinguishing quantisation and continuity The difference between the quantum theory and the classical theory is similar to the difference between using bottles of water (quantum) or water from a tap (classical). The bottles represent the quantum idea and the continuous flow from the tap represents the classical theory. The quantisation of energy is also rather like the kangaroo motion of a car when you first learn to drive – it jumps from one energy state to another, there is no smooth acceleration. It is all a question of scale. We do not 'see' quantum effects generally in everyday life because of the very small value of Planck's constant. Think about a person and an ant walking across a gravelled path. The size of the individual pieces of gravel may seem small to us but they are giant boulders to the ant. We know that the photons emitted by a light bulb, for example, travel at the speed of light (3 × 108 m s-1 ) so why don’t we feel them as they hit us? (Although all energy is quantised we are not aware of this in everyday life because of the very small value of Planck’s constant.) Students may worry about the exact nature of photons. It may help if you give them this quotation from Einstein: ‘All the fifty years of conscious brooding have brought me no closer to the answer to the question, “What are light quanta?”. Of course, today every rascal thinks he knows the answer, but he is deluding himself.’ Worked example: Photon flux Calculate the number of quanta of radiation being emitted by a light source. (Illustrations: INDEX
  10. 10. 5 Consider a green 100 W light. For green light the wavelength is about 6 × 10-7 m and so: Energy of a photon = E = hf =hc / λ= 3.3 × 10-19 J The number of quanta emitted per second by the light N = 100 × λ / hc = 3 × 1020 s-1 . Student calculations: Photon flux TAP 501-2: Photons streaming from a lamp TAP 501-3: Quanta Student experiment: Relating photon energy to frequency TAP 501-4: Relating photon energy to frequency. Students can use LEDs of different colours to investigate the relationship between frequency and photon energy for light. INDEX
  11. 11. 6 TAP 501-1: The emission of light from an atom Electron in orbit round a nucleus in an atom Energy input. The electron is excited and rises to a higher energy level (shell). The electron falls back to its original energy level and energy is emitted in the form of radiation. The bigger the drop the greater the energy emitted and the shorter wavelength the radiation has (blue light). INDEX
  12. 12. 7 INDEX
  13. 13. 8 TAP 501-2: Photons streaming from a lamp What to do Complete the questions below on the sheet. Provide clear statements of what you are estimating; show what calculations you are performing and how these give the answers you quote. Try to show a clear line of thinking through each stage. Steps in the calculation 1. Estimate the power of a reading lamp in watts. 2. Estimate the average wavelength of a visible photon. 3. Calculate the energy transferred by each photon. 4. Calculate the number of photons emitted by the lamp in each second. INDEX
  14. 14. 9 Practical advice This question, or a substitute for it, needs to come early on in the discussion of photons to avert questions concerning our inability to be aware of single photons. However, single photon detectors are now used in astronomy etc. Alternative approaches This may be prefaced or supplemented by such a calculation performed in class. It is well done by linking to other such questions that yield large numbers. Social and human context Every time we meet a pervasive quantity like power it is useful to compare it to our place in the Universe (75 W or so as a useful power output over any length of time) and to compare developed and developing countries in this respect. Answers and worked solutions 1. P = 40 W 2. λ = 5 × 10–7 m 3. Calculate the frequency of the photons corresponding to this wavelength: .Hz106 m105 sm103 14 7 18 ×= × × = = − − λ c f Now calculate the energy of each photon: J.104 Hz106sJ106 19 14134 − −− ×= ×××= = hfE 4. Energy per second = 40 J s–1 Energy per photon = 4 × 10–19 J. .101 J104 sJ40 photonperenergy secondperenergy secondperphotons 20 19 1- ×= × = = − External reference INDEX
  15. 15. 10 This activity is taken from Advancing Physics chapter 7, question 20E INDEX
  16. 16. 11 TAP 501- 3: Quanta Speed of electromagnetic radiation in free space (c) = 3.00 x 108 m s-1 Planck’s constant (h) = 6.63 x 10-34 J s 1. Write down the equation for the quantum energy of a photon in terms of its frequency. 2. Calculate the energies of a quantum of electromagnetic radiation of the following wavelengths: (a) gamma rays wavelength 10-3 nm (b) X rays wavelength 0.1 nm (c) violet light wavelength 420 nm (d) yellow light wavelength 600 nm (e) red light wavelength 700 nm (f) microwaves wavelength 2.00 cm (g) radio waves wavelength 254 m 3. Calculate the wavelengths of quanta of electromagnetic radiation with the following energies: (a) 6.63 x 10-19 J (b) 9.47 x 10-25 J (c) 1.33 x 10-18 J INDEX
  17. 17. 12 (d) 3.98 x 10-20 J INDEX
  18. 18. 13 Practical advice Pupils may need to be reminded that a wavelength of 10-3 nm is 1 x 10-12 m and that some students could need help in using their calculators. Answers and worked solutions 1 E = hf 2 (a) f = c/λ E = hf so E = h c/λ E = (6.63 x 10-34 x 3 x 108) / (1 x 10-12 ) = 1.99 x 10-13 J (b) E = 1.99 x 10-15 J (c) E = 4.74 x 10-19 J (d) E = 3.01 x 10-19 J (e) E = 2.84 x 10-19 J (f) E = 9.95 x 10-24 J (g) E = 7.83 x 10-19 J 3 (a) λ = hc/E λ = (6.63 x 10-34 x 3 x 108) / 6.63 x 10-19 = 3 x 10-7 m (300 nm) (b) 0.21 m (c) 1.5 x 10-7 m (150 nm) (d) 5 x 10-6 m INDEX
  19. 19. 14 TAP 501- 4: Relating energy to frequency Photons have a characteristic energy Light of a particular colour is a stream of photons of a specific frequency. Light appears granular when seen at the finest scale. A bright light delivers lots of energy every second. If light is granular then the amount of energy must be related to the number of granules arriving each second. The intensity of the light will also depend on the energy delivered by each granule. This activity relates the energy of each photon to the frequency of that photon. You will need multiple LED array peering tube power supply, 5 V (smooth and regulated) multimeter five 4 mm leads Measuring energy The energy released by each electron as it travels through the LED is transferred to a photon. To measure the energy released by each electron measure the potential difference across the LED when it just glows. Then we multiply this figure by the charge on the electron (1.6 × 10–19 C). The quantity that characterises the photon is the frequency so we then seek to find a connection between this frequency and the energy. 1. Set up the circuit and check that each LED can be lit by altering the pd 2. Calculate the frequency of the LEDs. V 0 V +5 V to 5 V power supply Knob on pot Alter pd so that LED just lights select LEDs one at a time by flying lead select LED by flying lead 470 nm 502 nm 650 nm563 nm 585 nm 620 nm to voltmeter 100 Ω INDEX
  20. 20. 15 3. Measure the pd just sufficient to strike each LED. At this pd the energy supplied by the electrons is all transferred to photons. Use the peering tube to cut out room lighting. 4. Look for a pattern connecting energy to frequency (plot a graph!). You should be prepared to re-measure any points that do not fit and to check your results with those from other measurements. 5. See if you can quantify the relationship. By how much does the energy of the photon change for each hertz? Energy and frequency 1. The energy associated with a photon is related to its frequency. 2. This relationship introduces the important quantity, h, the Planck constant. Practical advice We suggest setting up several competing research groups, and actively encouraging students to form a consensus about the relationship between frequency and energy. An appropriate degree of collaboration gets the correct answer; inappropriate degrees yield a work of fiction or no consensus. Thus can physics progress. Students will know about the existence of an LED from previous work on electricity and will know that it conducts in one direction only. Thus electrons, simply introduced as what moves when electricity is conducted, can be presented as meeting an electrical barrier when the LED is reverse biased and falling down that barrier when forward biased. This simple model of the action of an LED is enough for this purpose. Connecting this electrical model to an energetic model requires the notion of potential difference to be reviewed as being likely to be the sensible way of determining the height of the barrier and the energy as being the potential difference times the charge on the electron. Analogies with the energy released in falling down a hill can reinforce this idea. So as to make sure that none of the electrical energy is dissipated we need to insist that we require the smallest pd across the photodiode. This energy, plotted against the frequency of emitted light (taken from the manufacturer's specifications), can then be used. Experience shows that the measurements made by the students may not be so accurate, and that encouragement to settle on a simple pattern, together with the consensual approach suggested above and the ability to make several measurements before deciding on the accurate answer, will be necessary. A class using a graph-plotting package may make this review and interaction more likely. Students should easily establish E = h f. A consensus on the value of h should give a value that is far from embarrassing. Students who are red/green or other forms of colour blindness will get different results. Often red/green colour blind students need a higher striking pd to see some light from the LED or may not be able to see particular wavelengths of light. INDEX
  21. 21. 16 Sample results: LED colour Wavelength / nm Frequency / 1014 Hz Striking pd / V Energy / J h / 10–34 J s Blue 470 6.38 2.38 0.381 6.0 Green 563 5.33 1.69 0.270 5.1 Yellow 585 5.12 1.63 0.261 5.1 Orange 620 4.83 1.48 0.237 4.9 Red 650 4.62 1.47 0.235 5.1 Technician’s information The array of LEDs is used to make the connection between the frequency at which a photon is emitted and the energy carried by that photon. Measurements are made of the minimum pd required to just turn an LED on and of the wavelength of light from it. The wavelength may be better taken directly from the manufacturer's specification. Each LED emits photons of one characteristic frequency, specified in many catalogues by the peak wavelength emitted by the LED. You need a wide range of wavelengths, fairly evenly spaced, so as to get a reasonable graph of pd against frequency or wavelength. You may find a wider range of LEDs available at lower cost than when this design was first produced, if so then exceeding the range suggested is fine; reducing that range does not yield a reliable graph. To measure the energy carried by each photon students will need to be able to measure the pd applied across each LED in turn. Students then plot energy / frequency. So it may be useful to mark the peak frequencies or wavelengths emitted by the LEDs on the apparatus. How to make it The requirement is to be able to apply a variable pd, 0 - 3 V, across a series of LEDs, one at a time in turn. 5 LEDs are sufficient. Increasing the range of frequencies is more important than adding more LEDs. We suggest that the LEDs be mounted in plastic ducting, a 150 mm length of 40 mm by 25 mm proved sufficient to mount all the components neatly. Here is a circuit diagram: INDEX
  22. 22. 17 Variations are, of course possible. You may choose not to have sockets (which enable the current through the LEDs to be measured), or perhaps to have only one return wire so that the LEDs come on one after another as the pd is increased. A suitable protective resistor (roughly equal in value to the resistance of the shortest wavelength LED) in series with the wiper arm of the potentiometer will prevent applying too much pd across the LEDs. Important features • Use as wide a range of wavelengths for the LEDs as are currently available. • The LEDs should all be mounted in clear plastic, not mounted in coloured plastic. • The LEDs should all have approximately the same power output. • Provide a narrow opaque tube, about the length of a pencil, through which to peer at each LED, excluding extraneous light, so as to detect when it just comes on, and obtain a good value for the pd needed. Black paper or card is usually sufficient for the tube. • The arrangement of the potential divider together with the protective resistor to protect the LEDs allows the apparatus to be driven from a 5 V supply whilst protecting the LEDs. Other arrangements might also work. Alternative approaches To establish the connection between the energy associated with each click as a Geiger counter detects a gamma ray photon we suggest measuring the energy required to release one photon of light in a light-emitting diode. This has the advantage that we can cheaply try out several frequencies and rapidly obtain a picture of how energy varies with frequency. It is, of course, not the only technique for establishing a link between frequency and energy. You may substitute others. The photoelectric effect has been used for this for many years, as has appeal to the evidence of spectra. Social and human context V 0 V +5 V to 5 V power supply Knob on pot Alter pd so that LED just lights select LEDs one at a time by flying lead select LED by flying lead 470 nm 502 nm 650 nm563 nm 585 nm 620 nm to voltmeter 100 Ω INDEX
  23. 23. 18 Studying engineering barriers of different heights to release different amounts of energy takes us into the structures of semiconductor materials and engineering band gaps, which, whilst fascinating, does not contribute to the central understanding sought here. It is, however, central to quantum engineering. This can be used to start a discussion linking the potential barrier to an energetic understanding of the situation. External reference This activity is taken from Advancing Physics chapter 7, activity 10E INDEX
  24. 24. 19 Episode 502: The photoelectric effect This episode introduces an important phenomenon. Light releases electrons from metal surfaces. Summary Demonstration: The basic phenomenon. (15 minutes) Discussion: Summarising the phenomenon. (10 minutes) Discussion: An analogy. (5 minutes) Student questions: Using the photoelectric equation. The Millikan experiment: to verify Einstein’s photo-electric relationship (30 minutes) Student experiment: Measuring Planck’s constant. (30 minutes) Demonstration: The basic phenomenon Introduce the topic by demonstrating the electroscope and zinc plate experiment. TAP 502-1: Simple photoelectric effect demonstration Point out to the students that the photoelectric effect is apparently instantaneous. However, the light must be energetic enough, which for zinc is in the ultraviolet region of the spectrum. If light were waves, we would expect the free electrons to steadily absorb energy until they escape from the surface. This would be the case in the classical theory, in which light is considered as waves. We could wait all day and still the red light would not liberate electrons from the zinc plate. So what is going on? We picture the light as quanta of radiation (photons). A single electron captures the energy of a single photon. The emission of an electron is instantaneous as long as the energy of each incoming quantum is big enough. If an individual photon has insufficient energy, the electron will not be able to escape from the metal. Discussion: Summarising the phenomenon Summarise the important points about the photoelectric effect. Ultra violet light Negatively charged zinc plate Gold leaf falls immediately the zinc plate is illuminated with ultra violet light (Diagram: INDEX
  25. 25. 20 Potential well high energy violet quantum Electron leaves metal Quantum energy Electron energy Work function (Diagram: There is a threshold frequency (i.e. energy), below which no electrons are released. The electrons are released at a rate proportional to the intensity of the light (i.e. more photons per second means more electrons released per second). The energy of the emitted electrons is independent of the intensity of the incident radiation. They have a maximum KE. Discussion: An analogy Try this analogy, which involves ping-pong balls, a bullet and a coconut shy. A small boy tries to dislodge a coconut by throwing a ping-pong ball at it – no luck, the ping-pong ball has too little energy! He then tries a whole bowl of ping-pong balls but the coconut still stays put! Along comes a physicist with a pistol (and an understanding of the photoelectric effect), who fires one bullet at the coconut – it is instantaneously knocked off its support. Ask how this is an analogy for the zinc plate experiment. (The analogy simulates the effect of infrared and ultra violet radiation on a metal surface. The ping-pong balls represent low energy infrared, while the bullet takes the place of high-energy ultra violet.) Now you can define the work function. Use the potential well model to show an electron at the bottom of the well. It has to absorb the energy in one go to escape from the well and be liberated from the surface of the material. Units The electronvolt is introduced because it is a convenient small unit. You might need to point out that it can be used for any (small) amount of energy, and is not confined to situations involving electrically accelerated electrons. Potential well It is useful to compare the electron with a person in the bottom of a well with totally smooth sides. The person can only get out of the well by one jump, they can't jump half way up and then jump again. In the same way an electron at the bottom of a potential well must be given enough energy to escape in one 'jump'. It is this energy that is the work function for the material. Now you can present the equation for photoelectric emission: INDEX
  26. 26. 21 Energy of photon E = hf Picture a photon being absorbed by one of the electrons which is least tightly bound in the metal. The energy of the photon does two things. Some of it is needed to overcome the work function φ. The rest remains as KE of the electron. hf = φ + (1/2) mv2 A voltage can be applied to bind the electrons more tightly to the metal. The stopping potential Vs is just enough to prevent any from escaping: hf = φ + eVs Student questions: Using the photoelectric equation Set the students some problems using these equations. TAP.502-2: Photoelectric effect questions TAP 502-4: Student Question. The Millikan experiment The Millikan experiment question may best come after TAP 502-3: Student experiment: Measuring threshold frequency. Student experiment: Measuring Planck’s constant TAP502-3: Measuring threshold frequency Students can measure Planck’s constant using a photocell. (Some useful clipart is given here below) to oscilloscope coloured filter INDEX
  27. 27. 22 TAP 502-1: Simple photoelectric effect demonstration Resources needed Gold leaf electroscope or coulomb meter Zinc plate attachment (sand-papered clean to remove oxidation) Laser (class 2) Mains lamp (a desk lamp is ideal) Ultra violet lamp with clear quartz envelope Safety A class 2 laser requires a warning: Do not stare down the beam. A short-wave UV lamp must be shielded so that the UV emerges through a hole. The hole is always directed away from eyes. The presence of UV can be demonstrated by showing fluorescence of paper. Technique Attach the zinc plate to the top of the electroscope. (A coulomb meter can be used instead of the electroscope.) Charge the plate negatively. o No effect No effect With U.V. leaf falls immediately (Diagrams: INDEX
  28. 28. 23 Shine red laser light onto the cleaned zinc plate – no effect. Use a mains light bulb emitting white light – no effect. Use an ultra violet lamp – the leaf falls immediately. INDEX
  29. 29. 24 TAP 502-2: Photoelectric effect questions hf = φ + (1/2) mv2 and hf = φ + eVs e = 1.60 x 10-19 C, h = 6.63 x 10-34 J s, mass of electron = 9.11 x 10-31 kg 1 The work function for lithium is 4.6 x 10-19 J. (a) Calculate the lowest frequency of light that will cause photoelectric emission. (b) What is the maximum energy of the electrons emitted when light of 7.3 x 1014 Hz is used? 2 Complete the table. Metal Work Function /eV Work Function /J Frequency used /Hz Maximum KE of Ejected electrons /J Sodium 2.28 6 x 1014 Potassium 3.68 x 10-19 0.32 x 10-19 Lithium 2.9 1 x 1015 Aluminium 4.1 0.35 x 10-19 Zinc 4.3 1.12 x 10-19 Copper 7.36 x 10-19 1 x 1015 3 The stopping potential when a frequency of 1.61 x 1015 Hz is shone on a metal is 3 V. (a) What is energy transferred by each photon? (b) Calculate the work function of the metal. (c) What is the maximum speed of the ejected electrons? 4 Selenium has a work function of 5.11 eV. What frequency of light would just eject electrons? (The threshold frequency is when the max KE of the ejected electrons is zero) 5 A frequency of 2.4 x 1015 Hz is used on magnesium with work function of 3.7 eV. (a) What is energy transferred by each photon? (b) Calculate the maximum KE of the ejected electrons. (c) The maximum speed of the electrons. (d) The stopping potential for the electrons. INDEX
  30. 30. 25 Answers and worked solutions 1(a) hf = φ hf = 4.60 x 10-19 f = 4.60 x 10-19 / 6.63 x 10-34 = 6.94 x 1014 Hz (b) hf = φ + (1/2) mv2 . (6.63 x 10-34 x 7.30 x 1014 ) = 4.60 x 10-19 + (1/2) mv2 4.84 x 10-19 - 4.60 x 10-19 = (1/2) mv2 = 0.24 x 10-19 J 2 Metal Work Function / eV Work Function / J Frequency used / Hz Maximum KE of ejected electrons / J Sodium 2.28 3.65 x 10-19 6 x 1014 0.35 x 10-19 Potassium 2.30 3.68 x 10-19 6 x 1014 0.32 x 10-19 Lithium 2.90 4.64 x 10-19 1. x 1015 1.99 x 10-19 Aluminium 4.10 6.56 x 10-19 1.04 x 1015 0.35 x 10-19 Zinc 4.30 6.88 x 10-19 1.2 x 1015 1.12 x 10-19 Copper 4.60 7.36 x 10-19 1 x 1015 0 For copper 1 x 1015 Hz is below the threshold frequency so no electrons are ejected. 3 (a) 1.07 x 10-18 J (b) hf = φ + eVs, so φ = hf - eVs, so φ = 1.07 x 10-18 – (1.6 x 10-19 x 3) = 5.9 x 10-19 J (c) eVs = (1/2) mv2 so (1.60 x 10-19 x 3) = 0.5 x 9.11 x 10-31 x v2 so v2 =1.04 x 1012 and v = 1.02 x 106 m s-1 4 1.2 x 1015 Hz 5 (a) 1.6 x 10-18 J (b) (1/2) mv2 = 1.x 10-18 J (c) v2 = 1.1 x 1012 so v = 1.1 x 106 m s-1 (d) eVs = (1/2) mv2 so eVs = 1.00 x 10-18 and Vs = 0.63 V INDEX
  31. 31. 26 TAP502- 3: Measuring threshold frequency Use a white light source and a set of coloured filters to find the threshold frequency, and hence the work function, of the photosensitive material in a photocell. This may well be a standard piece of kit in your school or college. Use a spreadsheet to plot and analyse a graph of your results. This experiment uses a photocell to investigate the photoelectric effect. Light of various frequencies is incident on the cell and photoelectrons are emitted and then form an electric current. A white light source is shone through various coloured filters to produce a series of different frequencies of light falling on the photocell. The current of photoelectrons produced in the cell maybe amplified internally and is measurable on the ammeter. Otherwise an amplifying picoammeter is needed. The potential divider provides an adjustable voltage. The incident frequency, threshold frequency, and stopping potential are related by the following equation: hf =eV + hfo Procedure For each coloured filter, adjust the potential divider until the stopping potential has been reached. Record the stopping potential and the wavelength of light transmitted by the filter. Select the middle of the range as the transmitted frequency. NB: the filter might have written on it the range of wavelengths it transmits measured in Enter your results of frequency and stopping potential on a spreadsheet and plot a graph of frequency f versus stopping potential V. Use your graph to determine the value of the threshold frequency f and hence calculate the work function φ. Express your result in J and in eV. Estimate the uncertainties in your measurements of V and in the values of f that you have used. Use these estimates to add error bars to your graph and hence estimate the uncertainty in your values of f0 and φ. Decide how you could use your graph to determine the value of Planck's constant if you knew only the value of e and not h. INDEX
  32. 32. 27 Data Planck constant h = 6.60 x 10-34 J s electron charge e = 1.67 x 10-19 C speed of light c = 3.00 x 108 m s-1 1eV = 1.67 x 10-19 J Practical advice This section revisits ideas about charge, energy and potential difference and introduces the idea of a stopping potential in order to measure the kinetic energy of photoelectrons. Students need to realise that, if a charged particle is accelerated by a pd, energy is transferred to it, whereas if it moves the other way, it loses kinetic energy, and that the two situations are the exact reverse of each other. Students should appreciate that the work function represents the minimum amount of work that an electron must do in order to get free and that the expression for kinetic energy represents the maximum possible kinetic energy of the photoelectron. This energy is only attainable if the energy transfer from photon to electron is 100% efficient and there is no energy dissipation, e.g. due to heating. This is quite a demanding activity, as it involves a relatively complicated and unfamiliar set-up. Make sure students appreciate the use of the potential divider, (as in Episode 118 The Potential Divider). In analysing their results, students need to plot a graph and determine the y-intercept. Students will have met graphs of the type y = mx + c before but still might not be very confident in using them, this might need some discussion. We recommend using a spreadsheet graphing package here. Students should also take account of experimental uncertainties; the most significant is likely to be in the frequency, as the filters available do not have a very definite cut-off wavelength. There might also be some uncertainty in deciding exactly the pd at which the photocell current drops to zero. Einstein's ideas Albert Einstein explained the photoelectric effect in a paper published in 1905. It was the second of five ground-breaking papers he wrote that year. In the first paper, Einstein explained the mysterious Brownian motion of particles contained in pollen grains as due to the random impact of much smaller particles. This work led to the acceptance of the molecular or atomic nature of matter, which until then had been quite speculative. Einstein's third paper that year is now his most famous. Here Einstein introduced his Special Theory of Relativity which, in a later paper, led to probably the most famous equation in science: E=mc2 , which describes the equivalence of mass and energy. But it was Einstein's second paper, that contained his work on the photoelectric effect, that at the time was the most revolutionary of the three, and it was for this work that Einstein was eventually awarded the Nobel Prize, in 1922. (The Nobel Committee works somewhat more slowly than the speed of light!) In this paper Einstein broke away from the idea that light (electromagnetic radiation) is continuous in nature and introduced us to the idea of the quantum (plural quanta) or photon as a `packet' of light. (The term quantum is used for any packet of energy, while a photon is a quantum associated with electromagnetic radiation.) The wave model of light had been fairly conclusively established a century earlier, mainly due to the work of Thomas Young, who demonstrated and explained interference patterns. But the wave model cannot explain the photoelectric effect; INDEX
  33. 33. 28 Einstein realised this and took the bold step of putting forward a completely different model in order to explain the following experimental results: • for any given metal, with radiation below a certain threshold frequency no electrons are released even if the radiation is very intense; • provided the frequency is above the threshold, some electrons are released instantaneously, even if the radiation is very weak; • the more intense the radiation, the more electrons are released; • the kinetic energy of the individual photoelectrons depends only on the frequency of the radiation and not on its intensity. Einstein was the first to use the equation E = hf to explain the photoelectric effect. It is known as the Planck equation, and h is called Planck's constant, because Max Planck had already proposed that when electromagnetic radiation was absorbed or emitted, energy was transferred in packets. That work earned Planck the 1918 Nobel Prize. External references This activity is taken from Salters Horners Advanced Physics, section DIG, activity 30 and the Einstein notes above from Salters Horners Advanced Physics, section DIG additional sheet 11 INDEX
  34. 34. 29 TAP 502- 4: The Millikan experiment to verify Einstein’s photo-electric relationship. The photoelectric effect was – well known by the end of the 19th century. Its explanation was one of Einstein’s first applications of his photon model for light. He devised an equation relating the energy of the photoelectrons to the frequency of the light and the work function of the metal used. In 1916, American physicist Robert Millikan completed some experiments that tested Einstein's equation. Though Millikan had been firmly against quantum theory, the results convinced him that Einstein was right. In Millikan's photoelectric apparatus, monochromatic light was incident on each of the newly-cleaned metal plates in turn. The resulting photoelectrons were collected by electrode C and flowed, via the variable resistor and microammeter, back to the plate assembly. By adjusting the potentiometer, Millikan found the potential difference that was just large enough to stop the electrons moving round the circuit. For each metal, he used radiation of several different frequencies, noting the `stopping voltage' for each. This graph shows some of his results for sodium. (a) Use the graph to find the threshold frequency for sodium. (b) Calculate the work function for sodium using your answer to (a). h = 6.63 x 10-34 J s. (c) Use your answer to (b) to find the maximum kinetic energy of photoelectrons emitted from sodium when the frequency of the incident light is 10 x 1015 Hz. Give your answer in joules and in electronvolts. e = 1.6 x 10-19 C INDEX
  35. 35. 30 INDEX
  36. 36. 31 External reference This activity is taken from Salters Horners Advanced Physics, section DIG, additional sheet 13 Answers and worked solutions External reference Answers and worked solutions are taken from Salters Horners Advanced Physics, section DIG, additional sheet 14 INDEX
  37. 37. 32 Episode 503: Preparation for lasers topic It is likely that all pupils will have experienced laser technology in their homes or at school but may well not familiar with the range of uses of lasers, their operation and safety. Section TAP 504-2 gives details of the safety measures required. Lasers form rather more of a 'tool' and so demonstration experiments are relatively few. However some ideas and an explanation of the workings and other details of a laser are given. Episode 504: How lasers work Main aims As regards post-16 examinations, the formal requirements laid down are modest, or non-existent, so that the level of treatment here is not detailed. Students will: 1. Outline the principles of operation of a laser. 2. State some uses of high and low energy lasers. Prior knowledge Students should know about the wave nature of light, including interference. They should also know how light is emitted by electron transitions within atoms. ruby rod (Diagram: INDEX
  38. 38. 33 Episode 504: How lasers work This episode considers uses of lasers, and the underlying theory of how they work. Safety: Ensure that you are familiar with safety regulations and advice before embarking on any demonstrations (see TAP 504-2). Summary Demonstration: Seeing a laser beam. (10 minutes) Discussion: Uses of lasers. (15 minutes) Discussion: Safety with lasers. (10 minutes) Discussion: How lasers work. (20 minutes) Worked examples: Power density. (10 minutes) Student calculations: (10 minutes) Demonstration: Seeing a laser beam A laser beam can be made visible by blowing smoke or making dust in its path. Its path through a tank of water can be shown by adding a little milk. Show laser light passing through a smoke filled box or across the lab and compare this with a projector beam or a focussed beam of light from a tungsten filament light bulb. Show the principle of optical fibre communication by directing a laser beam down a flexible plastic tube containing water to which a little milk has been added. Show a comparison between the interference pattern produced by a tungsten filament lamp (with a 'monochromatic' filter) and that produced by a laser. Discussion: Uses of lasers Talk about where lasers are used – ask for suggestions from the class. As far as possible this should be an illustrated discussion with a CD player, a laser pointer, a set of bar codes, a bar code reader and the school’s laser with a hologram available for demonstration. TAP 504-1: Uses of lasers Show the list of uses. Invite students to consider the uses shown in the list. Can they say why lasers are good for these? The reasons might be: • A laser beam can be intense. INDEX
  39. 39. 34 • A laser beam is almost monochromatic. • A laser beam diverges very little. • Laser light is coherent. Discussion: Safety with lasers Lasers must be used with care. Use the text as the basis of a discussion of the precautions which must be taken. TAP 504-2: Lasers and safety Discussion: How lasers work If students are familiar with energy level diagrams for atoms, and of the mechanisms of absorption and emission of photons, you can present the science behind laser action. Point out the difference between: (a) excitation – an input of energy raises an electron to a higher energy level (b) emission - the electron falls back to a lower energy level emitting radiation and (c) stimulated emission – the electron is stimulated to fall back to a lower energy level by the interaction of a photon of the same energy Define population inversion: Usually the lower energy levels contain more electrons than the higher ones (a). In order for lasing action to take place there must be a population inversion. This means that more electrons exist in higher energy levels than is normal (b). For the lasing action to work the electrons must stay in the excited (metastable) state for a reasonable length of time. If they 'fell' to lower levels too soon there would not be time for the stimulating photon to cause stimulated emission to take place. ‘Laser’ stands for Light Amplification by Stimulated Emission of Radiation. The diagrams in TAP 503 shows the ruby laser and the snowball effect of photons passing down a laser tube, and the diagram above shows the three level laser action. The electrons are first ‘pumped’ up to the higher energy level using photons. They then drop down and accumulate in a relatively stable energy level, where they are stimulated to all drop back together to the ground state by a photon whose energy is exactly the energy difference to the ground state. (a) (b) (Diagram: INDEX
  40. 40. 35 Discuss coherent and non-coherent light. Coherent light is light in which the photons are all in 'step' – in other words the change of phase within the beam occurs for all the photons at the same time. There are no abrupt phase changes within the beam. Light produced by lasers is both coherent and monochromatic (of one 'colour'). Incoherent sources emit light with frequent and random changes of phase between the photons. (Tungsten filament lamps and 'ordinary' fluorescent tubes emit incoherent light) Worked examples: Power density The laser beam also shows very little divergence and so the power density (power per unit area) diminishes only slowly with distance. It can be very high. For example consider a light bulb capable of emitting a 100 W of actual light energy. At a distance of 2 m the power density is 100 / 4πr2 = 2 W m-2 . The beam from a helium-neon gas laser diverges very little. The beam is about 2 mm in diameter 'close' to the laser spreading out to a diameter of about 1.6 km when shone from the Earth onto the Moon! At a distance of 2 m from a 1 mW laser the power density in the beam would be 0.001 / (π × 0.0012 ) = 320 W m-2 ! This is why you must never look directly at a laser beam or its specular reflection. Student calculations Ask the class to calculate the power densities for a 100 W lamp and a 1 mW laser at the Moon. (Distance to Moon = 400 000 km; diameter of laser beam at Moon = 1.6 km) INDEX
  41. 41. 36 TAP 504-1: Uses of lasers • repairing damaged retinas • bar code reader • communication via modulated laser light in optical fibres • neurosurgery - cutting and sealing nerves sterilization – key hole surgery (microsurgery) • laser video and audio discs (CD and DVD) • cutting metal and cloth • laser pointer • laser printer • holography - three-dimensional images • surveying - checking ground levels • production of very high temperatures in fusion reactors • laser light shows • making holes in the teats of babies' bottles • cutting microelectronic circuits • physiotherapy - using laser energy to raise the temperature of localised areas of tissue e.g. removing tonsure tumours • laser lances for unblocking heart valves; removal of tattoos or birth marks • laser guidance systems for weapons • laser defence systems ('Star Wars') • a modification of the Michelson-Morley experiment to check the existence of the ether • distance measurement • laser altimeters INDEX
  42. 42. 37 TAP 504-2: Lasers and safety The following is an extract from the CLEAPSS Science Publications Handbook Section 12.12: 12.12 Lasers A low-power, continuous-wave, helium-neon laser is useful for teaching wave optics because it produces a beam of light that is: • highly monochromatic (very narrow spread of wavelengths) and coherent (the same phase) both across the beam and with time; • of high intensity; • of small divergence (typically 1 mm in diameter when it leaves the laser, 5 mm in diameter 4 m away). Because of its intensity, care must be taken to prevent a beam from a laser falling on the eye directly or by reflection, as it could damage the retina. In fact, it is now known that eyes could be damaged by the beam from the low power Class II lasers used in schools only if a deliberate attempt were made to stare at the laser along the beam or to concentrate the beam from a IIIa laser with an instrument; the normal avoidance mechanism of the body would prevent damage in other cases. Nevertheless, it is good practice to take precautions to avoid a beam falling on the eye. Lasers should be positioned so that beams cannot fall on the eyes of those present, i.e., are directed away from spectators. Ancillary optical equipment must be arranged so that reflected beams cannot reach eyes. Ten years ago, the lasers affordable by schools would work for only a few years and then only if run periodically. Those currently available have longer lives and do not require this. DES Administrative memorandum 7/70 This advises on the use of lasers in schools and FE colleges. It confines use at school level to teacher demonstration. Safety rules include the avoidance of direct viewing; screening pupils who should be at least 1 m away; keeping background illumination as high as possible (so that eye pupils are as small as possible); displaying warning notices; keeping lasers secure from unauthorised use or theft; use of goggles by the demonstrator. Because of the more recent realisation that the lasers used in schools and colleges will not harm an eye by a beam accidentally falling on it, these rules are not strictly necessary but following them is good training. However, goggles are expensive, impractical and do not reduce hazard as they make it harder for the demonstrator to see the beam, stray reflections etc. INDEX
  43. 43. 38 Episode 505: Preparation for wave-particle duality topic In the first quarter of the twentieth century physicists began to realise that particles did not always behave like particles – they could behave like waves. They called this wave-particle duality. This theory suggests that there is no basic distinction between a particle and a wave. The differences that we observe arise simply from the particular experiment that we are doing at the time. As with quantum theory, this is a section of the course that candidates will find completely new. They are unlikely to have already met the wave nature of particles or the wave nature of electrons bound within atoms. Episode 506: Particles as waves Episode 507: Standing waves Main aims Students will: 1. Understand that electron diffraction is evidence for wave-like behaviour. 2. Use the de Broglie equation. 3. Identify situations in which a wave model is appropriate, and in which a particle model is appropriate, for explaining phenomena involving light and electrons. 4. Use a standing wave model for electrons in an atom. Prior knowledge Students should have an understanding of wave phenomena, including diffraction and interference. They should know how to calculate momentum. This work follows on from a study of the photoelectric effect. Where this leads These episodes merely skim the surface of quantum physics. For students who wish to learn a little more, here is some suggested reading: The new quantum universe; Tony Hey and Patrick Walters; CUP Quantum physics: An introduction; J Manners; IoPP You can extend the idea of electrons-as-waves further, to the realm of the atom. INDEX
  44. 44. 39 Episode 506: Particles as waves This episode introduces an important phenomenon: wave - particle duality. In studying the photoelectric effect, students have learned that light, which we think of as waves, can sometimes behave as particles. Here they learn that electrons, which we think of as particles, can sometimes behave as waves. Summary Demonstration: Diffraction of electrons. (30 minutes) Discussion: de Broglie equation. (15 minutes) Worked examples: Using the equation. (15 minutes) Student questions: Using the equation. (30 minutes) Discussion: Summing up. (10 minutes) Student questions: Practice calculations. (30 minutes) Demonstration: Diffraction of electrons The diffraction of electrons was first shown by Davisson and Germer in the USA and G P Thomson in the UK, in 1927 and it can now be observed easily in schools with the correct apparatus. Show electron diffraction. It will help if students have previously seen an electron-beam tube in use (e.g. the fine beam tube, or e/m tube). TAP 506-1: Diffraction of electrons ……… Electrons show particle properties Electrons show wave properties Thin graphite screen Electron gun Evacuated tube Diffraction rings (Diagram: INDEX
  45. 45. 40 Before giving an explanation, ask them to contemplate what they are seeing. It is not obvious that this is diffraction/interference, since students may not have seen diffraction through a polycrystalline material. (Note that the rigorous theory of crystal diffraction is not trivial - waves scattered off successive planes of atoms in the graphite give constructive interference if the path difference is a multiple of a wavelength, according to the Bragg equation. The scattered waves then appear to form a wave that appears to “reflect” off the planes of atoms, with the angle of incidence being equal to the angle of reflection. In the following we adopt a simplification to a 2D case - see TAP 506-1) Qualitatively it can help to show a laser beam diffracted by two ‘crossed’ diffraction gratings. Rotate the grating, and the pattern rotates. If you could rotate it fast enough, so that all orientations are present, you would see the array of spots trace out rings. TAP506-2: Diffraction of light From their knowledge of diffraction, what can they say about the wavelength of the electrons? (It must be comparable to the separation of the carbon atoms in the graphite.) How does wavelength change as the accelerating voltage is increased? (The rings get bigger; wavelength must be getting smaller as the electrons move faster.) Discussion: de Broglie equation In 1923 Louis de Broglie proposed that a particle of momentum p would have a wavelength λ given by the equation: wavelength of particle λ = h/p where h is the Planck constant, or λ = h/mv for a particle of momentum mv. The formula allows us to calculate the wavelength associated with a moving particle. Worked examples: Using the equation 1. Find the wavelength of an electron of mass 9.00 × 10-31 kg moving at 3.00 × 107 m s-1 . λ = h/p = [6.63 × 10-34 ] / [9.00 × 10-31 × 3.00 × 107 ] = 6.63 × 10-34 / 2.70×10-23 = 2.46×10-11 m = 0.025 nm This is comparable to atomic spacing, and explains why electrons can be diffracted by graphite. 2. Find the wavelength of a cricket ball of mass 0.15 kg moving at 30 m s-1 . λ = h/p = [6.63 × 10-34 ] / [0.15 × 30] = 1.47×10-34 m = 1.5 10-34 J s (to 2 s.f.) This is a very small number, and explains why a cricket ball is not diffracted as it passes near to the stumps. INDEX
  46. 46. 41 3. It is also desirable to be able to calculate the wavelength associated with an electron when the accelerating voltage is known. There are 3 steps in the calculation. Calculate the wavelength of an electron accelerated through a potential difference of 10 kV. Step 1: Kinetic energy Ek = eV = 1.6 × 10-19 × 10000 = 1.6 × 10-15 J Step 2: EK = ½ mv2 = ½m (mv) 2 = p2 / 2m, so momentum p = √2mEk = √2 × 9.1 × 10-31 × 1.6 × 10-15 = 5.4 × 10-23 kg m s-1 Step 3: Wavelength λ = h / p = 6.63 × 10-34 / 5.4 × 10-23 = 1.2 × 10-11 m = 0.012 nm. Student questions: Using the equations A useful set of questions can be found at Resourceful Physics on the web This can also be accessed from and is available to subscribers. Discussion: Summing up You may come across a number of ways of trying to resolve the wave-particle dilemma. For example, some authors talk of ‘wavicles’. This is not very helpful. Summarise by saying that particles and waves are phenomena that we observe in our macroscopic world. We cannot assume that they are appropriate at other scales. Sometimes light behaves as waves (diffraction, interference effects), sometimes as particles (absorption and emission by atoms, photoelectric effect). Sometimes electrons (and other matter) behave as particles (beta radiation etc), and sometimes as waves (electron diffraction). It’s a matter of learning which description gives the right answer in a given situation. The two situations are mutually exclusive. The wave model is use for ‘radiation’ (i.e. anything transporting energy and momentum, e.g. a beam of light, a beam of electrons) getting from emission to absorption. The particle (or quantum) model is used to describe the actual processes of emission or absorption. Student question: Interpreting electron diffraction patterns TAP 506-3: Interpreting electron diffraction patterns TAP 506-4: Electron diffraction question INDEX
  47. 47. 42 TAP 506- 1: Diffraction of electrons Start by setting up the electron diffraction demonstration tube according to the manufacturer’s instructions. Check the connections before switching on as it is easy to burn out the graphite grid unless manufacturer’s instructions are correctly followed. Wire carefully, no bare conductor above 40 V School EHT supplied are limited to a maximum output current of less than 5 mA so they are safe, but can still make the user jump. The lead connecting the supply to the anode should have a female connector so that no metal is exposed. You will need two supply voltages: a low-voltage supply to provide the current to heat the cathode; a high-voltage supply to provide the potential difference between the cathode and the anode, to accelerate the electrons. These are both usually supplied by the EHT unit. Qualitative experiments Check that you can identify the following: • the electron gun, which includes the cathode and the anode; INDEX
  48. 48. 43 • the graphite target; • the fluorescent screen, which will glow when the electrons strike it. When the cathode has heated up (you will see it glowing), increase the accelerating voltage V. An invisible beam of electrons emerges from the electron gun and passes through the graphite film. To show that there is an electron beam present, bring up a bar magnet close to the tube and observe the pattern shifting. Magnetic fields deflect moving electrons. So this qualitative demo shows both the wave aspects (the diffraction pattern) and the particle aspects (deflection by a magnetic field) in the same equipment. Look for a diffraction pattern on the screen at the end of the tube. What shape is the pattern? Where can you see constructive interference? And destructive interference? Now predict: If you increase the accelerating voltage, how will the energy and speed of the electrons change? How will this affect the diffraction pattern? Test your ideas. Quantitative experiments Choose a feature of the diffraction pattern that is easy to measure. It might be the diameter of the first bright ring, or of the first dark ring. We will call this chosen quantity d. Investigate how d depends on V. Make several measurements. Determine the mathematical relationship between d and V. If the relationship is of the form d proportional to Vn , you can find the value of n by plotting a log-log graph. The gradient of the graph is equal to the value of n. What other information would you need if you were to use this experiment to determine the atomic spacing in graphite? INDEX
  49. 49. 44 Practical advice It is difficult to present a convincing discussion of wave–particle duality in a few lines. We have adopted the approach that it is an observed phenomenon, witness the diffraction of electrons. The de Broglie equation wavelength = h/p simply allows us to translate between the wave and particle pictures. Increasing the accelerating voltage increase the electrons’ energy and momentum; greater momentum means shorter wavelength, which in turn means that the electrons are diffracted through a smaller angle. Hence the diameters of the diffraction rings get smaller. Students could make measurements of the rings and relate these to the accelerating voltage. A log-l graph will reveal the relationship between them. It is reasonable to say that ring diameter is proportional to wavelength; a log-log graph of diameter against voltage will thus be a straight line with gradient (-1/2). Apparatus electron diffraction tube power supply (6.3 V) for cathode e.h.t. supply (0 – 5000 V dc) with voltmeter connecting leads Great care must be taken to set the tube up correctly. The graphite can be damaged by incorrect connections. Notice that the positive e.h.t supply terminal is used without the protective resistor in some set ups. Take care. As the discussion in this section is almost entirely in terms of electron diffraction, students might get the idea that only electrons exhibit wave–particle duality whereas in fact it applies to all particles. You might like to mention that neutron diffraction is also used as a tool for probing material structure. Large bio-molecules have now been diffracted. The chosen method is to introduce wave particle duality via the experiment however a little mathematics may be of use. This mathematics is given so an experimental or theoretical route can be chosen or the mathematics later used to back up the experiment. E=hf and since fλ = c then E =hc/λ Taking E = mc2 then mc2 = hc/λ and so mc = h/λ momentum = mass x velocity = p =mc And this gives the de Broglie relation p = h/λ Do notice that the switch from mc to mv has not been justified other than it works. (Note, this derivation really only refers to photons and not to electrons). For the diffraction tube where V is the anode cathode pd and v the electron speed then INDEX
  50. 50. 45 ½ mv2 = eV so v = (2eV/m) 1/2 giving mv = m (2eV/m) 1/2 = (2meV) 1/2 p = h/λ = (2meV) 1/2 Simplifying the Bragg formula into a two dimensional treatment for a transmission grating, for diffraction θ = λ/b (approximately) where b is the separation between the planes of carbon atoms. D, if required, can be obtained from manufacturers details. θ = d/D from geometry so d/D = λ/b or λ proportional to d as diffracting gap size b and target screen distance D are constants. So using the momentum and accelerating pd equation above then p = h/λ = (2meV) 1/2 or 1/λ is proportional to V1/2 or λ is proportional to V-1/2 External references This activity is taken from Salters Horners Advanced Physics, section PRO, activity 18, with extra material added in the last two sections, adapted from Revised Nuffield Advanced Science Physics teachers guide, book 2, section L2. θ Tube screen Graphite Target d D INDEX
  51. 51. 46 TAP 506-2: Diffraction of light Apparatus torch bulb in holder with power supply diffraction gratings, 2 each of various spacing, e.g. 100 lines mm-1 , 300 lines mm-1 red, blue and green filters (one of each colour) 2 glass slides (e.g. microscope slides) lycopodium dust Safety Lycopodium is dried pollen. Some people are allergic to pollen so, before use, it is wise to check for hay-fever sufferer. (See Safeguards in the School Lab 4.4). Lycopodium powder in air will explode so extinguish all flames before using it. Technique Observe what happens when light is diffracted by: • a grating of parallel lines; • a regular grid of crossed lines; • a random array of fine dust particles. Explore the effects of changing the separation of the lines and the wavelength of the light. Set up a small (6 V) lamp. You are going to observe how light from the lamp is diffracted in different situations. Write down or sketch what you observe. Hold a diffraction grating and a colour filter close to your eye. Look through it at the lamp. Rotate the grating. (A diffraction grating consists of many parallel, equally spaced lines, as much as several thousands in each centimetre.) Repeat with a finer or a coarser grating (using the same colour filter as before). Now use two diffraction gratings. Place one on top of the other, so that their lines are at 90 degrees to each other. You have made a grid of lines through which the light is diffracted. Look through the grid at the lamp. Try holding the gratings so that their lines cross at a different angle – say, 60° or 45°. Try combining gratings with different line spacing. Finally, sprinkle fine dust (e.g. lycopodium powder) on to a glass slide. Blow off any excess dust. Look through the slide at the lamp. (Now you are looking at light diffracted by a random array of tiny particles.) INDEX
  52. 52. 47 Repeat the above, using a different colour filter. Sum up your observations by saying how the diffraction patterns depend on: • the separation of the diffracting objects • the geometry of the diffracting objects • the wavelength of the light. Practical advice This activity is intended to remind students of diffraction effects they may have previously observed. Points to bring out are: • the size of the pattern increases with increasing wavelength (red light is diffracted more than blue) • the size of the pattern depends inversely on the spacing of the diffracting objects (the finer the grating, the more widely spaced the diffraction images) • the geometry of the diffraction pattern depends on the geometry of the diffracting objects • a random arrangement of small obstacles gives rise to a diffraction pattern that is a set of concentric rings. External reference This activity is taken from Salters Horners Advanced Physics, section PRO, activity 17 INDEX
  53. 53. 48 TAP 506-3: Interpreting electron diffraction patterns For this question to make sense, students need to be aware that an obstacle (e.g. a nucleus) is equivalent to a ‘hole’ of the same size. So far they have only met diffraction by ‘gaps’. Use the electron diffraction patterns shown in Figures (a) and (b) to determine the diameters of carbon and oxygen nuclei. The diffraction patterns represented by the two graphs in Figures (a) and (b) were obtained using electrons accelerated to 420 MV. By following the steps below, you will get a flavour of how such diffraction data are interpreted. You will also see some of the equations that must be used when electrons are moving at relativistic speeds (that is, close to the speed of light). INDEX
  54. 54. 49 Calculate the kinetic energy Ek of an electron accelerated through 420 MV. To calculate the momentum of the electron, you cannot use p=mv and EK = ½ mv2 , because these equations don’t apply to relativistic particles. Instead, it turns out that the electron’s momentum p is related to its kinetic energy by Ek ~ pc where c is the speed of light. Calculate the momentum of the electron. The de Broglie relationship p = hλ applies to relativistic and non-relativistic electrons because Relativity Theory is used in its derivation. Calculate the electron’s de Broglie wavelength. The angle of the first minimum θmin on the graph is a clearly identifiable point, and this is used to calculate the diameter of the nuclei. From the graphs in Figure (a) and (b), determine the angle of the first minimum for carbon nuclei, and for oxygen nuclei. The smaller the nucleus, the more it diffracts the electrons. From the angles you found, which are smaller, carbon nuclei or oxygen nuclei? Is this what you would expect from their atomic numbers? The diameter d of the nucleus is related to the electron wavelength and the diffraction angle θmin by Use this relationship to obtain estimates of the diameters of carbon and oxygen nuclei. Explain why your answers are only estimates. INDEX
  55. 55. 50 External references This activity is taken from Salters Horners Advanced Physics, section PHM, activity 19 which was an adaptation of Revised Nuffield Advanced Physics section L question 37(L). Answers and worked solutions Ek = 420 x 106 x 1.60 x 10-19 = 6.72 x 10-11 J Ek ~ pc so p = 6.72 x 10-11 / 3 x 108 = 2.24 x 10-19 N s λ = h/p = 6.63 X 10 -34 / 2.24 x 10-19 . = 2.96 x 10-15 m (a) carbon nuclei, 50° (b) oxygen nuclei. 42° d = 1.22λ θ min where d is the diameter of the nucleus Remember, the angle should be in radians or use sin θ. (a) carbon d = (1.22 x 2.96 x 10-15 ) / 0.766 = 4.7 x 10-15 m (b) oxygen d = (1.22 x 2.96 x 10-15 ) / 0.669 = 5.3 x 10-15 m INDEX
  56. 56. 51 TAP 506- 4: Electron diffraction questions 1 In an electron diffraction experiment using graphite the larger ring formed by rows of carbon atoms 1.23 x 10-10 m apart was formed at an angle of 0.167 radian. (a) What is the wavelength? [θ in radians = λ / b where b is the diffracting object size] (b) Write an expression for the kinetic energy of an electron (½ mv2 ) in terms of its charge, and accelerating voltage V (c) Obtain an expression for momentum, p, in terms of e, V and m. The accelerating voltage was 5000 V (d) Work out h in mv = h/ λ INDEX
  57. 57. 52 Answers (a) 0.205 x 10-10 m (b) KE = 0.5mv2 = Ve (c) p = mv = (2meV) 1/2 (d) h = 7.78 x 10-34 J s (the accepted value is 6.6 x 10-34 J s) External reference This activity is taken from Revised Nuffield Advanced Physics Unit L question 32. INDEX
  58. 58. 53 Episode 507: Electron standing waves You could extend the idea of electrons-as-waves further, to the realm of the atom. Summary Demonstration: Melde’s experiment. (20 minutes) Discussion: Electron waves in atoms. (10 minutes) Demonstration: Standing waves on a loop. (10 minutes) Student Question Electron standing waves (10 mins) Demonstration: Melde’s experiment TAP 507-1: Standing waves – for electrons? In this section we are going to introduce the idea of standing waves within an atom. It is therefore useful first to demonstrate standing waves on a stretched elastic cord. This is known as Melde’s experiment. (A very simple alternative to the vibration generator is an electric toothbrush.) Show that there are only certain frequencies at which standing wave loops occur. Discussion: Electron waves in atoms The waves on the string are 'trapped' between the two fixed points at the ends of the string and cannot escape. If the electron has wave properties and it is also confined within an atom we could imagine a sort of standing wave pattern for these waves rather like the standing waves on a stretched string. The electrons are 'trapped' within the atom rather like the waves being 'trapped' on a stretched string. The boundaries of these electron waves would be the potential well formed 'within' the atom. This idea was introduced because the simple Rutherford model of the atom had one serious disadvantage concerning the stability of the orbits. Bohr showed that in such a model the electrons would spiral into the nucleus in about 10-10 s, due to electrostatic attraction. He therefore proposed that the electrons could only exist in certain states, equivalent to the loops on the vibrating string. electron nucleus L M (Diagram: INDEX
  59. 59. 54 If your students have met the idea of angular momentum, you could tell them that Bohr proposed that the angular momentum of the electrons in an atom is quantised, in line with Planck's quantum theory of radiation. He stated that the allowed values of the angular momentum of an electron would be integral multiples of h/2π. This implied a series of discrete orbits for the electron. We can imagine the electron as existing as a wave that fits round a given orbit an integral number of times. Demonstration: Standing waves on a loop The wire loop is a two dimensional analogy of electron waves in an atom. As it vibrates at the correct frequency, an integral number of waves fit round the orbit. These waves represent the electron waves in an atom. Student question: Electron standing waves de Broglie waves can be imagined as forming standing waves which fit into an atom TAP 507-2: Electron standing waves INDEX
  60. 60. 55 TAP 507-1: Standing waves - for electrons? Electrons have a frequency too Electrons can be modelled as having a frequency. In another context you have seen how superposition of waves in the laboratory produces standing waves. Here it is useful to put these two together, describing electrons with standing waves, with their wavelength described by de Broglie’s relationship: ./ mvh=λ Here you look at some consequences of this step. You will need: vibration generator signal generator rubber cord G-clamp wooden blocks Vibrating a rubber cord 1 2 3 5 7 8 9 Frequency Adjust 1 10 100 1000 10 100 1000 Frequency range Outputs A power 10Hz 100kHz 1kHz 10kHz100Hz Frequency 10 Hz Wave Make sure that you can get clear patterns with this apparatus. Note that only whole numbers of half wavelengths fit onto the cord. Electrons trapped in an atom are also constrained. Describing them as waves, where the amplitude tells you the chance of find them in any one place, constrains you to draw the waves in a similar way. INDEX
  61. 61. 56 Making links Putting relationships together with these results allows you to predict that electrons will have certain allowed energy levels only. simplest pattern next simplest pattern L λ 2 L λ 2 from kinetic energy Ek = 1 2 mv2 p = mv Ek = p2 2m Ek = h2 8mL2 from diagrams λ = 2L from de Broglie λ = h mv mv = h λ mv = h 2L λ = L mv = h L h2 2mL2 2 ? λ and 4 ? Ek Ek = See if you can continue the series for the next two standing wave patterns that will fit onto the cord. You have 1. Reminded yourself about standing waves. 2. Seen some of the consequences of using standing waves to model electrons in atoms. External reference This activity is taken from Advancing Physics chapter 17, 140E INDEX
  62. 62. 57 TAP 507-2: Electron standing waves If an electron is confined in a definite space, the de Broglie waves can be imagined as forming standing waves that fit into that space. h = 6.6 x 10-34 J s, charge on electron = 1.6 x 10-19 C, mass of electron is 9.1 x 10-31 kg r = 1.0 × 10–10 m de Broglie standing wave diameter 0.2 × 10–10 m r = 0.1 × 10–10 m diameter 2.0 × 10–10 m Suppose the standing wave fits with one half-wavelength across the diameter of the atom. 1. Write down the wavelength of the standing wave if the atom is imagined to have radius r = 1.0 × 10–10 m. 2. Write down the wavelength of the standing wave if the atom is imagined ten times smaller, with radius r = 0.1 × 10–10 m. 3. Other standing waves could fit inside the same diameter. Would their wavelengths be longer or shorter than the waves shown here? Electron momentum The momentum of an electron with de Broglie waves of wavelength λ is m v = h / λ. If the wavelength is the largest possible, the momentum must be the smallest possible. 4. Calculate the smallest possible momentum of the electron, if the atom is imagined to have radius r = 1.0 × 10–10 m. INDEX
  63. 63. 58 5. Calculate, or write down directly from the answer to question 4, the smallest possible momentum of the electron if the atom is imagined to have radius r = 0.1 × 10–10 m. 6. Write a few lines explaining why an electron confined in a smaller space has a larger minimum momentum. INDEX
  64. 64. 59 Answers and worked solutions 1. The waves have half a wavelength fitting into the diameter, so λ = 4.0 × 10–10 m. 2. The radius is 10 times smaller so the wavelength is 10 times shorter: λ = 0.4 × 10–10 m. 3. More half-wavelength loops have to be fitted into the same length, so the wavelengths will all be smaller. 4. .smkg1065.1 m104.0 sJ106.6 124 10 34 −− − − ×= × × = = λ h mv 5. As for question 4 with the wavelength 10 times smaller, so the momentum is 10 times larger: mv = 16.5 × 10–24 kg m s–1 . 6. The smaller the space the shorter the wavelength. But the shorter the wavelength the greater the momentum, since mv = h / λ. External reference This activity is taken from Advancing Physics chapter 17, and uses part of question 160s. INDEX
  65. 65. 60 Episode 508 See Episode 513 INDEX
  66. 66. 61 Episode 509: Radioactive background and detectors This episode introduces the ubiquitous nature of radioactivity, and considers its detection. It draws on students’ previous knowledge, and emphasises the importance of technical terminology. Summary Demonstration: Detecting background radiation (10 minutes) Discussion: Sources of background radiation (15 minutes) Demonstration: Radioactive dust (10 minutes) Discussion + survey: Sources of radiation – should we worry? (15 minutes) Demonstration + discussion: Am-241 source, plus use of correct vocabulary. (10 minutes) Demonstration: Spark detector (10 minutes) Demonstration: Detecting background radiation Use a Geiger counter to reveal the background radiation in the laboratory. What is the ‘signal’ like? (It is discrete, erratic / random.) Does it vary from place to place in the room? (No; it may appear to; this is an opportunity to discuss the need to make multiple or longer-term measurements.) Does it vary from time to time? (No, it’s roughly constant.) Count for 30 s to get a total count N; repeat several times to show random variation. Calculate the average value of N. (Note: a good rule of thumb is that the standard deviation is √Nave, so roughly two-thirds of values of N will be within ± √Nave.) Which is better: 10 counts of 30 s, averaged to get the activity, or one count of 300 s? (They amount to the same thing. The statistics of this is probably beyond most A-level students.) Calculate the background count rate from the data (typical value is 0.5 counts per second or 30 counts per minute, but this varies a lot geographically.) Discussion Sources of background radiation Look at charts showing sources of background radiation. Consider how these might vary geographically, with time, occupation etc. to scaler/ratemeter INDEX
  67. 67. 62 Pie chart for background radiations Note that pie charts in text books etc showing relative contributions are often calibrated in units of equivalent dose of radiation called sieverts (symbol Sv); sievert is a unit which takes account of the effects of different types of radiation on the human body. 1 Sv = 1 J kg-1 = 1 m2 s-2 TAP 509-1: Doses TAP 509-2: Whole body dose equivalents Demonstration: Radioactive dust Airborne radioactive substances are attracted to traditional computer and TV screens that use a high voltage. Similarly a ‘charged’ balloon will also accumulate radioactive dust and have an activity larger than the average background. The fresh dust in vacuum cleaner bags has a noticeably higher activity too. Set up a Geiger counter to measure the activity of vacuum cleaner dust; don’t forget to measure background rate also. TAP 509-3: Radiation in dust 0.4% fallout 10% cosmic rays 12% internal such as food etc. 12% medical, X rays etc. 14% gamma rays from the ground 50% radioactive gases in the home 0.4% air travel <0.1% nuclear waste 0.2% occupational (Diagram: INDEX
  68. 68. 63 Discussion + survey: Sources of radiation – should we worry? So “radiation is all around us”. Indeed, most substances, and things, are radioactive. Students are radioactive! Typically 7000 Bq. So “it’s dangerous to sleep with somebody”! However, most of the resulting radiation is absorbed within the ‘owners’ body. Introduce activity of a sample as a quantity, measured in becquerels (Bq). Mass of typical student = 70 kg, so specific activity = 7000/70 = 100 Bq kg-1 . The Radiation Protection Division of the Health Protection Agency (formerly the National Radiological Protection Board, NRPB) defines a radioactive substance as having specific activity ≥ 400 Bq kg-1 . Should we worry about this? Ask students to complete this survey, and then re-visit at the end of the topic. For each statement, indicate whether they think it is true or false, or they don’t know. S1 Radioactive substances make everything near to them radioactive. S2 Once something has become radioactive, there is nothing you can do about it. S3 Some radioactive substances are more dangerous than others. S4 Radioactive means giving off radio-waves. S5 Saying that a radioactive substance has a half life of three days means any produced now will all be gone in six days. Demonstration + discussion: Am-241 source, plus use of correct vocabulary Radioactive sources Follow the local rules for using radioactive sources, in particular do not handle radioactive sources without a tool or place them in close proximity to your body. Place an Am-241 source close to the GM tube and measure the count rate, which will be impressive, compared to background. (Some end window GM tubes will not detect alpha emission from AM-241 but only weak gamma). Geiger Muller tube Radioactive source (Diagram: INDEX
  69. 69. 64 From here on, start to use appropriate technical vocabulary, drawing on students’ earlier experience. For example: Substances are radioactive, they emit ‘radiation’ when they decay. Why are some substances radioactive? (They contain unstable nuclei inside their respective atoms.) The unstable nucleus is called the mother and when it (she?) decays a daughter nucleus is produced (it’s not quite like human procreation!). Eventually the activity of a radioactive substance must cease. However, point out that the decay of the americium doesn’t seem to be getting any less. There are a very large number of nuclei in there! Am-241 is used in smoke alarms, so it won’t ‘run out’. They are supplied with 33.3 kBq sources. The half-life is 458 years. What particular property does nuclear radiation have – what does it do to the matter through which it passes? (It is ionizing radiation. It creates ions when it interacts with atoms.) What is an ion? (A neutral atom which has lost or gained (at least one) electron.) Simplified diagram of a smoke alarm To knock an electron from an atom, the ionizing radiation transfers energy to the atom – this is how nuclear radiation is detected. It is not difficult to detect the presence of a single ion – electron pair, so it’s easy to detect the decay of single radioactive nucleus. Chemists can detect microgrammes or nanogrammes of chemical substances, physicists can detect individual atomic events. Demonstration: Spark detector Show a spark detector responding to the proximity of an alpha source. (NB At first, do not refer to the source as an alpha source.) Move the source away a few centimetres; you do not need much distance in air to absorb this radiation. Ask students to recall which type of radiation is easily absorbed by air. (Alpha.) Alpha source Current due to ionisation flows from + to - Current flow stopped by smoke (Diagram: INDEX
  70. 70. 65 TAP 509-4: Rays make ions Comment that a GM tube is not dissimilar to a spark counter, but rolled up to have cylindrical symmetry. At this point, you could discuss the sophisticated design of a GM tube and associated counter. The end window is usually made of mica and has a plastic cover, with holes, to protect the mica. +450 V 0 V low pressure neon or argon gas thin end window anode radioactive particle anode Radioactive source or flame 0 V + 5000 V sparking here thin wire gauze (Diagram: INDEX
  71. 71. 66 TAP 509-1: Doses Radiation dose measurements and units activity in becquerel = disintegrations per second Radiation quality factors alpha beta gamma x-rays neutrons 20 1 1 1 10 20 Sv 1 Sv 1 Sv 1 Sv 10 Sv radiation factor dose equivalent of 1 gray dose in gray = energy deposited per kg dose equivalent in sievert = dose in gray × quality factor energy in different types of radiation radiation source dose in gray INDEX
  72. 72. 67 Practical advice This gives a simple view of the connection between gray and sievert as units of radiation dose measurements. It may be best to change the size of the diagram and use it as an OHT. External reference This activity is taken from Advancing Physics chapter 18, display material 20O INDEX
  73. 73. 68 TAP 509-2: Whole body dose equivalents Typicalwholebodydoseequivalentperyearfromvarioussources(Europe) Artificialsources 530µSv 22%oftotal Naturalsources 1860µSv 78%oftotalwork9µSv airtravel8µSv nuclearpower3µSv nuclearweaponsfallout10µSv cosmicandsolarradiation 310µSv gammaradiationfrom groundandbuildings 380µSv radongasfromground andbuildings800µSvfoodanddrink370µSv medicalprocedures 500µSv INDEX
  74. 74. 69 Practical advice This shows the breakdown of whole body doses, from different sources. It may be best to change the size of the diagram and use it as an OHT. External reference This activity is taken from Advancing Physics chapter 18, display material 30O. INDEX
  75. 75. 70 TAP 509-3: Radiation in dust Ionisation in the home Radon gas is present in the atmosphere of our homes; its daughter products can contribute to the background count as constituents of household dust. In this activity you are asked to collect dust and assess its level of radioactivity. You will need two sheets of kitchen paper towel radiation sensor, alpha sensitive (NB not a standard GM tube) stop watch rubber band What to do 1. Collect some household dust on a sheet of kitchen paper towel. One way to do this is to cover your finger with the paper and then to wipe your finger over the surface of a dusty television or computer monitor screen. Do this for the whole screen, more than one screen if possible – you need a substantial layer of dust. Put the paper carefully to one side. Do not dislodge the dirt. (Incidentally, one reason for suggesting the dust from a television screen is because it is charged. It therefore attracts the ionised daughter products from, amongst other things, radon decays.) 2. Take a new clean piece of identical kitchen paper. Fix it around the thin window end of the sensor using a rubber band. Take a background measurement for a substantial time, several thousand seconds or even overnight if possible. Automating the capture of the data will prove useful. 3. Without changing any other conditions replace the clean paper with the dusty paper. Wrap it around the GM tube with the dust fingerprint side next to the window so that alpha particles are not absorbed by the paper. Take care not to get the dust onto the sensor. 4. Measure the radioactive count from the dust for the same length of time as before. 5. Look critically at the results. Are they significantly different? Remember that variation in a radiation experiment is equal to the square root of the measurement itself. Do the two results differ by substantially more than this? You have Measured some of the ambient radiation from a household. INDEX
  76. 76. 71 Practical advice This experiment needs care but it does yield interesting results. It requires long timings and not a little luck. Household dust has radioactive products from a number of decays. In trials a count for 600 s produced the following results: background count (no paper): about 230 counts; background count (with paper): about 240 counts; dust count: about 295 counts. There was a substantial amount of dust on the paper from three computer monitors. Alternative approaches The use of TASTRAK plastic is a possible substitute here. The plastic known as CR-39 was developed in 1933 and in 1978 it was found to be an excellent detector of charged particles, which could be revealed by etching the plastic. TASTRAK is a version of CR-39 developed specifically to detect alpha particle tracks. It can be used to demonstrate the detection of radon. The suppliers, TASL, offer kits of TASTRAK plastic for class use which may then be returned to the Track Analysis Group for processing free of charge. This arrangement is STRICTLY for UK schools, colleges and universities only. Track Analysis Systems operate a free etching service. It is not recommended that you attempt the etching process yourself. When returning the exposed slides, remember to declare whether you require them to be in microscope or slide projector form. Be safe Students should wash their hands before eating after collecting the dust. External references This activity is taken from Advancing Physics chapter 18, activity 20H. You can find more information about TASTRAK from or Track Analysis Systems Ltd, H H Wills Physics Laboratory, Tyndall Avenue, Bristol. BS8 1TL, U.K. Tel: +44 (0)117 926 0353, Fax: +44 (0)117 925 172 INDEX
  77. 77. 72 TAP 509- 4: Rays make ions The particles and rays that come from radioactive (unstable) nuclei are known generically as ionising radiation. Ionising radiations do just what their name says – they ionise atoms by removing one or more of the electrons outside the nucleus. It is this property that helps us to detect the radiations in many of the instruments that may already be familiar to you. In this activity you will learn to use a simple detector of ionising radiation – the spark detector. You will need spark counter EHT power supply, 0 – 5 kV, dc leads almost pure alpha source (The only ‘pure’ alpha source available in schools is Pu-239. Am-241 emits gammas too. However, since the spark counter only responds to the alphas, any alpha-emitting source will do here) forceps or tweezers for handling the radioactive source (or source holder) Ionisation and its effects First, some ideas about ionisation and its effects. Ionisation is the name given to the process in which an atom or molecule gains or loses one or more electrons. In the detection of radioactivity we are normally concerned with the loss of an electron. The mechanism is that radiation is emitted from an unstable nucleus; the particle or ray carries energy away with it. It is this loss of energy that allows the radioactive atom to become more stable. As the particle moves away through the air or a more dense substance it comes close to atoms, sometimes sufficiently close to interact. The particle can simply bounce off the atom – an elastic collision – or it can interact inelastically and transfer some its energy to the atom. This gain of energy by the atom leads to the removal of one of its electrons. You can think of the particle or ray as having knocked the electron free of its atom. Energy taken from the incoming particle or ray is needed for this to occur. Can you think of examples in which ionisation is used to detect radiation? Getting going 1. Now, before setting it up, look closely at the spark detector. You should be able to see a grid or array of very fine wires running parallel and close to the surface of a metal plate or above a wire. There may also be an arrangement for holding a radioactive source a fixed distance from the wire array. Your power supply will maintain a high potential difference between the plate and the wires. There will be a large electric field in the space between the wires and the plate. Radioactive sources Follow the local rules for using radioactive sources, in particular do not handle radioactive sources without a tool or place them in close proximity to your body. INDEX
  78. 78. 73 Wire carefully, EHT supply I use Although school EHT supplies are current-limited and safe, using the extra limiting resister (50 MΩ) reduces the shock current to a trivial level. 2. Now connect up the detector to the power supply. Ask for help if you are not certain how to do this. To be safe the wires (the part you are most likely to touch) should be at earth (0 V) potential. Adjust the EHT until sparks just pass, then reduce it slightly. 3. Insert a source of alpha particles into the holder and ensure that the source is pointing towards the wire array and about 10 mm from it. Take the usual handling precautions with the source. + e.h.t. – + 5 kV0 V 5 kV 0 V 4. Does an increase in the potential difference make a significant change in the sparking rate? INDEX
  79. 79. 74 The alpha particles ionise the air molecules as they travel from the source. The sparking is a result of what happens when the ionisation occurs in the strong electric field produced by the spark detector. Look at the diagram. The field is directed between the wire and the gauze, or between the wires and the plate. So, once the electron and its ion (the original atom) are separated, the electron moves towards the wire and the ion moves towards the plate. The ion has a large mass and so gains speed slowly. The electron, however, has a low mass so its acceleration is large. (You might want to estimate how large it is: to do this use the distance from wire to plate and the voltage setting to make a reasonable estimate of the electric field strength, hence the force and the acceleration.) If an electron can gain enough energy from the field it will be able to collide with another gas atom and cause a further ionisation. So one electron has now produced two: the original one plus the one from this second ionisation. Both of these can go on to accelerate and ionise again. The number of electrons in the space builds up rapidly and eventually the air contains enough electrons in one region to allow a spark to jump from wire to plate. This is known as a cascade process. You have seen that 1. Radioactive particles are often detected using ionisation. Examples include the spark detector, the Geiger–Müller tube, the cloud and bubble chambers, and photographic detection methods. 2. Such methods show us where the particles have caused ionisation. They are not direct detections of the particles themselves. 3. Some methods rely on a cascade process in which ions are multiplied by successive ionisations in a strong electric field. Also try TAP 519: Particle Detectors INDEX
  80. 80. 75 Practical advice Students may need close supervision in using this apparatus. They will also need guidance in the correct earth setting to avoid electric shock. The instructions provided in the activity may need to be altered to suit the style of spark detector you have. Radioactive sources Follow the local rules for using radioactive sources, in particular do not handle radioactive sources without a tool or place them in close proximity to your body. Wire carefully, EHT supply in use Social and human context Every time your teeth are x-rayed, ionisation processes are used to expose the film. The ubiquitous Geiger–Müller tube involves a controlled cascade between the central wire and the outer cylinder inside the tube. We rely heavily on the ionising effects of radiation for its detection. External reference This activity is taken from Advancing Physics chapter 18 activity 50E INDEX
  81. 81. 76 Episode 510: Properties of radiations The focus of this episode is the properties of ionizing radiations. It is a good idea to introduce these through a consideration of safety. Summary Discussion: Ionising radiation and health. (10 minutes) Demonstration: Deflection of beta radiation. (10 minutes) Student activity: Completing a summary table. (10 minutes) Student experiment: Inverse square law for gamma radiation. (30 minutes) Discussion: Safety revisited. (5 minutes) Discussion: Ionising radiation and health Why are radioactive substances hazardous? It is the ionising property of the radiation that makes it dangerous to living things. Creating ions can stimulate unwanted chemical reactions. If the radiation has enough energy it can split molecules. Disrupting the function of cells may give rise to cancer. Absorption of radiation exposes us to the risk of developing cancer. Thus it is prudent to avoid all unnecessary exposure to ionising radiation. All deliberate exposure must have a benefit that outweighs the risk. Radioactive contamination is when you get a radioactive substance on, or inside, your body (by swallowing it or breathing it in or via a flesh wound). The contaminating material then irradiates you. How can you handle sources safely in the lab? Point out that you will be safe if you follow your local rules which will incorporate the following: • always handle sources with tongs • point the sources away from your body (and not at any anybody else) • fix the source in a holder which is not adjacent to where your body will be when you take measurements • replace sources in lead-lined containers as soon as possible • wash hands when finished INDEX
  82. 82. 77 Radioactive sources Follow the local rules for using radioactive sources, in particular do not handle radioactive sources without a tool or place them in close proximity to your body. Demonstration: Deflection of beta radiation Show the deflection of β  by a magnetic field. (Make sure you have a small compass to determine which are the N and S poles of the magnet.) Is the deflection consistent with the LH rule? (Yes; need to recall that electron flow is the opposite of conventional current.) Why is this demo is no good with the α source? (α particles are absorbed too quickly by the air.) NB The diagram above is common in textbooks, but is ONLY illustrative. For the curvature shown of beta particles, the curvature of the alpha tracks would be immeasurably small. Student activity: Completing a summary table Display the table, with only the headings and first column completed. Ask for contributions, or set as a task; compile results. TAP 510-1: α, β and γ radiation alpha gamma betamagnetic field INDEX
  83. 83. 78 Can you see any patterns in the table? (Most ionising - the largest electrical charge - is the least penetrating.) Can you explain this? (The most ionising lose energy the quickest.) How can the electrical charge determined? Deflection in a magnetic field.) * NB Gamma radiation is never completely absorbed (unlike alpha and beta) it just gets weaker and weaker until it cannot be distinguished form the background. Student experiment: Inverse square law for gamma radiation Note: since you are unlikely to have sufficient gamma sources for several groups to work simultaneously, this experiment can be part of a circus with others in the next episode. Alternatively, it could be a demonstration. Gamma radiation obeys an inverse square law in air since absorption is negligible. (Radiation spreads out over an increasing sphere. Area of a sphere = 4 π r2 , so as r gets larger, intensity will decrease as 1/r2 . The effect of absorption by the air will be relatively small. TAP 5102: Range of gamma radiation (Some students could do an analogue experiment with light, with an LDR or solar cell as a detector.) When detecting γ radiation with a Geiger tube you may like to aim the source into the side of the tube rather than the window at the end. The metal wall gives rise to greater ‘secondary electron emission’ than the window and this increase the detection efficiency. Correct readings for background. How can we get a straight line graph? We expect I ∝ r-2 , so a plot of I versus r–2 should be direct proportion (i.e. a straight line through the origin). It is much easier to see if a graph is a straight line, rather than a particular curve. Lift the graph and look along the line – it’s easy to spot a trend away from linear. However, two points are worth noting: (i) Sealed γ sources do not radiate in all directions, so do not expect perfect 1/r2 behaviour, and (ii) you do not know exactly name symbol nature elec charge "stopped by" ionising "power" what is it? alpha α particle +2 mm air; paper very good He nucleus beta β particle -1 mm Al medium very fast electron gamma γ wave 0 cm Pb * relatively poor electromagnetic radiation to scaler/ratemeter Radioactive source INDEX
  84. 84. 79 where in the Geiger tube the detection is taking place, so plotting I-1/2 against r gives an intercept, the systematic error in the measurement. Discussion: Safety revisited Return briefly to the subject of safe working. Background radiation is, say, 30 counts per minute. How far from a gamma source do you have to be for the radiation level to be twice this? Would this be a safe working distance? (Probably.) How much has your lifetime dose of radiation been increased by an experiment like the above? (Perhaps one hour at double the background radiation level – a tiny increase. It will be safe enough to carry out a few more experiments.) INDEX
  85. 85. 80 TAP 510-1: α, β and γ radiation Using your knowledge from pre-16 level work, or using information from textbooks, draw up a table to summarise the properties of α, β and γ radiation. The table below provides a framework for your summary. Write items from the following list into appropriate cells of the table. Note that some of the items are not needed and some may be used more than once. INDEX
  86. 86. 81 Practical Advice Some text books may be needed. External reference This activity is taken from Salters Horners Advanced Physics, section DIG, activity 25 INDEX