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5 Quantum Mechanics G482 Electricity, Waves & Photons 5 Quantum Mechanics G482 Electricity, Waves & Photons 2.5.1 Energy of A Photon 2.5.1 Energy of A Photon Mr Powell 2012 Index 2.5.2 The Photoelectric Effect 2.5.2 The Photoelectric Effect 2.5.3 Wave- Particle Duality 2.5.3 Wave- Particle Duality 2.5.4 Energy Levels in Atoms 2.5.4 Energy Levels in Atoms

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Mr Powell 2012 Index Introduction.... The aim of this module is to introduce the concept of quantum behaviour. How do we know that light is a wave? The evidence for this comes from diffraction of light. However, this wave-like behaviour cannot explain how light interacts with electrons in a metal. A revolutionary model of light (photon model), developed by Max Planck and Albert Einstein, is needed to describe the interaction of light with matter. Physicists expect symmetry in nature. If light can have a dual nature, then surely particles like the electron must also have a dual nature. We study the ideas developed by de Broglie. The final section looks briefly at the idea that electrons in atoms have discrete bond energies and they move between energy levels by either absorbing or by emitting photons. There are many opportunities to discuss how theories and models develop with the history of wave-particle duality.

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Mr Powell 2012 Index Practical Skills are assessed using OCR set tasks. The practical work suggested below may be carried out as part of skill development. Centres are not required to carry out all of these experiments. This module does not lend itself to many experiments carried by the students. However, it does contain many revolutionary ideas and engaging students in discussions is vital when demonstrating some of the experiments. Use a GM tube to ‘count’ gamma ray photons. Determine the wavelength of light from different LEDs Demonstrate the photoelectric effect using a photocell or a negatively charged zinc plate connected to an electroscope. Observe ‘diffraction rings’ for light passing through a tiny hole. Demonstrate the diffraction of electrons by graphite. Observe emission line spectra from different discharge tubes. (A hand-held optical spectrometer can be used to observe Fraunhofer lines in daylight. Caution: Do not look directly at the Sun.)

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Mr Powell 2012 Index Activities... 1.Discuss how wave and particle models of light are both required in different contexts. Discuss how de Broglie posed the question of whether particles like electrons could also behave like waves 2.Demonstrate electron diffraction in cathode ray tube. Illustrate features of demonstration including thin graphite layer 3.View narrow-slit or small hole interference of light and/or see images of X-ray diffraction and compare to electron diffraction patterns 4.Given the de Broglie equation calculate wavelength of wave associated with electron. Use eV = ½ mv 2 to give speed of electron in cathode ray and calculate wavelength. Compare to atomic spacing and discuss gap requirement for diffraction. Give further examples of wavelengths of particles from sub-atomic to every-day 5.Discuss why duality and quantum phenomena only apparent on very small scale 6.Summarise wave-particle duality with “travel as a wave, interact as particles” Resources.... 1.Diffraction tube, E.H.T. supply, darkened lab 2.Laser and small holes or slits, darkened lab 3.Calculate speed required for a person to have wavelength similar to a door. Calculate time taken to travel 1 mm at this speed and compare to, say, age of universe 4.Explain double-slit results with wave and particle model, illustrate difficulty of understanding elements of quantum mechanics and try to give “ interpretation” with waves of probability 5.End of topic test Points to Note… 1.Websites: 2.http://www.upscale.uto ronto.ca/PVB/Harrison/ 3.DoubleSlit/Flash/Histog ram.html and 4.http://www.upscale.uto ronto.ca/PVB/Harrison/ 5.DoubleSlit/Flash/Doubl eSlit.html 6. make good illustrations of point

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Mr Powell 2012 Index 2.5.3 Wave-Particle Duality (p178) Assessable learning outcomes.... (a) explain electron diffraction as evidence for the wave nature of particles like electrons; (b) explain that electrons travelling through polycrystalline graphite will be diffracted by the atoms and the spacing between the atoms; (c) select and apply the de Broglie equation h/mv = (d) explain that the diffraction of electrons by matter can be used to determine the arrangement of atoms and the size of nuclei. Assessable learning outcomes.... (a) explain electron diffraction as evidence for the wave nature of particles like electrons; (b) explain that electrons travelling through polycrystalline graphite will be diffracted by the atoms and the spacing between the atoms; (c) select and apply the de Broglie equation h/mv = (d) explain that the diffraction of electrons by matter can be used to determine the arrangement of atoms and the size of nuclei.

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Mr Powell 2012 Index Discovery of the ElectronDiscovery of the Electron Video 3mins

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2.5.3 Wave-Particle Duality

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Mr Powell 2012 Index Wave Particle Duality – p41

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Mr Powell 2012 Index Concept Maps By the end of this module of work you should understand how some of the elements you have studied fit in with this map;

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Mr Powell 2012 Index Main Themes – coming together hf = Φ + KE max hf = E 2 - E 1 λ = h/mv = h/p E=hf = hc/ λ Waves & Particle Duality Photons Photoelectric effect Intensity of Light Atomic Energy Levels Line Spectra Lasers Particle behaviours Wave behaviours De Broglie Equation Size of Atom

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Mr Powell 2012 Index The dual nature of light: The diffraction of light provides evidence of light being wavelike in nature The photo electric effect provides evidence of light being particle-like in nature The dual nature of matter: The diffraction of an electron beam directed at a thin metal film provides evidence of matter being wavelike in nature ( also electron deflection in electric and magnetic fields) The rows of atoms in the metal crystals behave like light passing through slits for it to happen should be similar to size of atoms. Duality

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Mr Powell 2012 Index Diffraction Rings

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Mr Powell 2012 Index Duality Speed of electrons effects the size of rings… Higher Anode Voltage = Faster Electrons Diffraction Rings are smaller The wavelength is smaller λ = h/mv = h/p

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Mr Powell 2012 Index Reasons by formulae…. Mass of photon zero! if light are not waves but quanta Sub in wave equation Work out the root and rearrange Equate Wave with a mass?

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Mr Powell 2012 Index HSW - Wave nature of the electron Louis de Broglie (1892 - 1987) If light can be modeled as a particle or as a wave, can an electron be modeled as a wave? The wavelength of a matter wave (1923) is given by: Everyday objects are too massive to give observable wavelengths; however, electrons are light enough to give observable wavelengths. Diffraction of electrons was observed by two groups in 1927, Davisson & Germer and George Thomson. The Bohr model could also be explained using standing waves. Whole numbers (1,2,3,etc.) of de Broglie wavelength give the allowed radii found in the Bohr model.

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Mr Powell 2012 Index Energy levels explained: The de Broglie wavelength of an orbiting electron has to fit the shape and size the electron’s shell. Eg for a circular orbit the circumference = n λ ( a whole number of de Broglie wavelengths)

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Mr Powell 2012 Index The de Broglie wavelength λ In 1923 de Broglie hypothesised: * Matter particles have a dual wave-particle nature * The wave like behaviour is characterised by a wavelength λ λ = h mv h = Planks constant m = mass v = velocity h = Planks constant m = mass v = velocity λ = h p Change the by changing a particle’s speed Change the by changing a particle’s speed λ

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Mr Powell 2012 Index Example…. Use of “nu” for frequency… 18

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Mr Powell 2012 Index Quantum Stuff.. TEM (transmission electron microscope) Electrons are accelerated to a high speed to produce a very short de Broglie wavelength. Very detailed images can then be resolved MRI scan (magnetic resonance imaging) Radio waves are emitted when hydrogen nuclei ( eg in water molecules) change energy states in a strong magnetic field. SQUID superconducting quantum interference device - magnetic field detector Used to detect very weak magnetic fields from tiny electrical currents inside the brain and for feotal examinations Quantum tunnelling occurs at a thin slice of an insulating barrier placed in a superconducting ring. When more current is induced the barrier becomes resistive and produces a measureable voltage. (Brian Josephson 1962 ) http://www.abdn.ac.uk/physics/case/squids.html Quantum tunnelling occurs at a thin slice of an insulating barrier placed in a superconducting ring. When more current is induced the barrier becomes resistive and produces a measureable voltage. (Brian Josephson 1962 ) http://www.abdn.ac.uk/physics/case/squids.html

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Mr Powell 2012 Index De Broglie Hypothesis & KE NB: Take a note of how this is derived....

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Mr Powell 2012 Index Question…. What is the debroglie wave length of an electron accelerated in a CRO tube using a voltage of 4500V? What is the debroglie wave length of an electron travelling at 3.00 x 10 7 ms -1 Harder Basic

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Mr Powell 2012 Index Question…. What is the debroglie wave length of an electron accelerated in a CRO tube using a voltage of 4500V? What is the debroglie wave length of an electron travelling at 3.00 x 10 7 ms -1 Harder Basic 2.43 x 10 -11 m 0.0183nm = 1.83 x 10 -11 m

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Mr Powell 2012 Index Experiments of GP Thompson

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Mr Powell 2012 Index Microstructure of Nickel Superalloys These pictures are taken using electron diffraction. They are trying to establish the structure and if there are any problems in the structure of Nickel alloys used in aeroplane manufacture. It is important that any micro fissures are detected early on.

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Mr Powell 2012 Index Summary We can think of electrons as waves We can think of electrons as particles Newtonian Mechanics works in certain cases (simple stuff) If we think of electrons in a quantum way (as waves) the maths always works out but the calculations are more complex To build the structure, the scientists used a scanning tunneling microscope (STM) to individually place 48 iron atoms on a copper surface in a circle roughly 143 angstroms across. Then, using the STM again to sense electron behavior inside the corral, they detected "local densities," which appear as waves, at the very intervals predicted by quantum mechanics -- specifically, the Schrodinger equation for a particle in a hard-wall enclosure. The standing waves appear when iron atoms scatter the copper's superface electrons.

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Mr Powell 2012 Index Debroglie by formulae…. Handout

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Mr Powell 2012 Index Make an A3 revision map of key points…. Ionisation? Excitation (electron) Excitation (electron) Excitation (photon) 3 Types of Spectrum Transitions Photoelectric effect Fluorescent Tube Duality? Bohr Model Levels 1)Formulae (basic) 2)Example Calcs (med) 3)Explanations (harder) Quantum Technology

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Mr Powell 2012 Index Connection Connect your learning to the content of the lesson Share the process by which the learning will actually take place Explore the outcomes of the learning, emphasising why this will be beneficial for the learner Connection Connect your learning to the content of the lesson Share the process by which the learning will actually take place Explore the outcomes of the learning, emphasising why this will be beneficial for the learner Demonstration Use formative feedback – Assessment for Learning Vary the groupings within the classroom for the purpose of learning – individual; pair; group/team; friendship; teacher selected; single sex; mixed sex Offer different ways for the students to demonstrate their understanding Allow the students to “show off” their learning Demonstration Use formative feedback – Assessment for Learning Vary the groupings within the classroom for the purpose of learning – individual; pair; group/team; friendship; teacher selected; single sex; mixed sex Offer different ways for the students to demonstrate their understanding Allow the students to “show off” their learning Activation Construct problem-solving challenges for the students Use a multi-sensory approach – VAK Promote a language of learning to enable the students to talk about their progress or obstacles to it Learning as an active process, so the students aren’t passive receptors Activation Construct problem-solving challenges for the students Use a multi-sensory approach – VAK Promote a language of learning to enable the students to talk about their progress or obstacles to it Learning as an active process, so the students aren’t passive receptors Consolidation Structure active reflection on the lesson content and the process of learning Seek transfer between “subjects” Review the learning from this lesson and preview the learning for the next Promote ways in which the students will remember A “news broadcast” approach to learning Consolidation Structure active reflection on the lesson content and the process of learning Seek transfer between “subjects” Review the learning from this lesson and preview the learning for the next Promote ways in which the students will remember A “news broadcast” approach to learning

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