Quantum Weirdness: A Beginner’s Guide Dr. Andrew Robinson Part 2 Quantum Physics Wave-Particle Duality 10:34 AM 1 The 3-Polarizer Experiment • Two crossed polarizers block all light • A third polarizer between them can show an image. 10:34 AM 2 Quantized Classical Physics Systems • Water drop suspended in air using an ultrasonic sound wave. • Change the frequency of the sound to the right frequency, and you excite a standing wave vibration https://youtu.be/4z4QdiqP-q8 10:34 AM 3 What is Wrong With Classical Physics? Genesis of Quantum Theory 10:34 AM 4 19th Century Physics • Newton’s Laws • Gravitation • Thermodynamics (heat transfer) • Waves • Electricity and Magnetism (Maxwell’s Equations) 10:34 AM 5 Blackbody Radiation The First Problem with Classical Physics: 10:34 AM 6 Blackbody Radiation • The colour of a hot object. • The colour observed changes with temperature • White hot (very hot) • Red hot (not as hot) 10:34 AM 7 Observing hot objects and looking at the wavelengths of light given off, shows a peak (a preferred wavelength) https://www.youtube.com/watch?v=sUp_WZKZID4 10:34 AM 8 The sun (5525 K = 5200 oC) Peak colour is green-yellow • This is the same colour that our eyes are most sensitive to. • Tennis ball green 10:34 AM 9 Lord Rayleigh (John William Strutt) Sir James Jeans Applied Mathematics, Physics, Astronomy, Cosmology • Applied Maxwell’s equations to predict the shape of the graph and the distribution of wavelengths. 10:34 AM 10 The Ultraviolet Catastrophe ∞ Rayleigh-Jeans theory predicted intensity going to infinity in the ultra- violet part of the spectrum Complete failure of 19th century physics! 10:34 AM 11 Planck Model • The German Physicist Max Planck re- calculated the blackbody radiation curves using a different approach. • His model assumed that matter consisted of many atomic oscillators, each absorbing and emitting radiation • He assumed that the energy of each oscillator was quantized – constrained to certain values https://www.nobelprize.org/prizes/physics/1918/summary/ 10:34 AM 12 • A classical oscillator can have any frequency, and hence can have any energy • Planck’s oscillators were quite different, they could only oscillate at quantized energy levels Energy 퐸4 = ℎ × 5푓 퐸3 = ℎ × 4푓 Planck also assumed that the energy was 퐸2 = ℎ × 3푓 frequency dependent 퐸1 = ℎ × 2푓 퐸0 = ℎ × 푓 The Planck constant h = 6.62606876×10-34 J.s 10:34 AM 13 • Planck’s theory worked very well in explaining the true shape of the intensity curve • However, Planck was very worried that he had managed to find a solution by playing a mathematical trick! By 1918, enough other evidence had been produced for him to get the Nobel Prize 10:34 AM 14 Incandescent Lightbulb: Blackbody Radiator • The filament is heated by passing an electric current through it. • Produces visible light • Produces lots of infra-red (heat) • Not very efficient 10:34 AM 15 The Photoelectric Effect The Second Problem with Classical Physics 10:34 AM 16 The Photoelectric Effect • If UV light shines on a metal in a vacuum, then electrons may be emitted from the metal • They are known as photoelectrons (they are normal electrons, just produced by light) UV light e- An electron is emitted https://www.youtube.com/watch?v=kcSYV8bJox8 10:34 AM 17 Einstein’s Explanation • Light consists of particles (wave packets) which have both wavelike AND particle properties Wave (Young’s Experiment) Particles (Newton’s Corpuscular theory) Stream of wave packets • The individual wave packet is called a photon 10:34 AM 18 • A photon collides with an electron in the metal. • The electron absorbs the energy of the photon and is emitted UV Photons Photoelectron 10:34 AM 19 Energy of the Photon • Einstein calculated the energy of a single photon to be 퐸 = ℎ푓 퐸푛푒푟푔푦 = 푃푙푎푛푐푘′푠 퐶표푛푠푡푎푛푡 × 푓푟푒푞푢푒푛푐푦 Wave property • Uses the Planck equation • Nobel Prize in 1921 10:34 AM 20 Momentum and the Photon • Newton defined the momentum of an object to be 푚표푚푒푛푡푢푚 = 푚푎푠푠 × 푣푒푙표푐푡푦 풑 = 푚풗 • The force applied is equal to the rate of change of momentum 10:34 AM 21 푚표푚푒푛푡푢푚 풑 = 푚푎푠푠 × 풗풆풍풐풄풊풕풚 • In the Newtonian approximation, a particle with no mass can have no momentum • In 1916, Einstein, whilst discussing the photoelectric effect proposed that the photon, a particle with zero mass, did have momentum Planck’s Constant ℎ 푝 = 휆 Wavelength 10:34 AM 22 Compton Scattering • The American physicist Arthur Compton did a crucial experiment to test this • He scattered X-rays from electrons in a carbon sample • The X-rays were scattered and changed wavelengths Incoming X-rays - 휃 10:34 AM 23 Incoming X-rays (Higher energy) Scattered X-rays (Lower energy) - 휃 • Compton analysed the angles of scattering and the difference in energy (indicated by a difference in wavelength) • He concluded that Einstein was correct • This is regarded as the experiment which confirmed Einstein’s theory. • Compton shared the Nobel Prize in Physics in 1927 10:34 AM 24 Spectroscopic Observations The Third Problem with Classical Physics 10:34 AM 25 Spectroscopy • Study of light emitted or absorbed by materials • Low pressure gases in glass tubes with a voltage applied at each end of the tube produce a coloured light • Different gases produce different colours http://www.youtube.com/watch?v=ryB-cuv8rT0 10:34 AM 26 • A J Ångström studied the light emitted by low pressure gases in discharge tubes in 1853 https://commons.wikimedia.org/wiki/File:Emission_Line_Spectra.webm • Different gases emit different wavelengths of light (different colours). • They do not emit all colours (which classical physics predicts 10:34 AM 27 Spectroscopy • Separate out the various colours of light emitted from the tube The diffraction grating is a piece of glass with lines drawn on it. It acts like a series of multiple slits 10:34 AM 28 • Reflection diffraction grating (Glass or plastic with a reflective coating) CD-DVD • Transmission Diffraction Grating (Just glass or plastic, light goes through it) 600 lines/mm 10:34 AM 29 Diffraction Grating • A Diffraction Grating is a multiple- slit aperture • More slits mean sharper diffraction spots • Light of different colours emerges at different angles Emission Spectra • Gases emitted discrete wavelengths, not a continuous spectrum • Each gas emits a different characteristic line spectrum • The spectrum for hydrogen was the simplest https://commons.wikimedia.org/wiki/File:Emission_Line_Spectra.webm 10:34 AM 32 Line Spectrum of Hydrogen • The lines in the visible region are known as the Balmer Series • At short wavelengths (Ultra violet) there is another series - the Lyman series • At long wavelengths (infra red) there is the Paschen series Ultra-violet Visible Infra-red 10:34 AM 33 • To predict the wavelengths 휆 seen in each of the series, there are a set of empirical equations 1 1 1 = 푅 − n = 2,3,4,5... Lyman series 휆 12 푛2 1 1 1 = 푅 − n = 3,4,5,6... Balmer series 휆 22 푛2 1 1 1 = 푅 − n = 4,5,6,7... Paschen series 휆 32 푛2 R = 1.097×107 m-1 is known as the Rydberg Constant 10:34 AM 34 • There is a pattern to the characteristic frequencies 1 1 1 = 푅 2 − 2 휆 푛푓 푛푖 Integer numbers: suggests a quantum series • According to classical physics there should be no line spectra at all – all wavelengths should be emitted, not just a few 10:34 AM 35 • The equation only works for Hydrogen gas • The spectrum for Helium from a discharge tube is much more complicated and does not follow the simple formulae for hydrogen 10:34 AM 36 The Structure of the Atom The Fourth Problem with Classical Physics 10:34 AM 37 Structure of the Atom • Each atom consists of a very small nucleus, which contains most of the mass, and has a positive electrical charge. • Around the atoms (in a cloud) are the negatively charged electrons. https://www.youtube.com/watch?v=5pZj0u_XMbc&feature=youtu.be 10:34 AM 38 • This picture is known as a “Rutherford Atom”, after Earnest Rutherford, who proposed the structure. • It is not really correct, as the electrons do not move in circular orbits 10:34 AM 39 • This model is not stable in classical physics • The electron should spiral into the nucleus! The lifetime was predicted to be ~10-8 seconds 0.00000001 seconds Matter would be unstable! 10:34 AM 40 Image Search for “Quantum” 10:34 AM 41 The Bohr Model • The Danish physicist Niels Bohr proposed a model to explain the emission spectrum of hydrogen • He mixed classical physics (attraction between charged particles, and circular motion), with a new quantum idea: • Electrons must remain in “stationary states” which are described by a quantum number https://www.nobelprize.org/prizes/physics/1922/summary/ 10:34 AM 42 The electrons are in circular orbitals known as stationary states - + As the radius of the orbital increases, so does the energy of n=1 the electron in the state. n=2 The orbitals (and the radii and n = 3 energy) can be described by a quantum number n 10:34 AM 43 The Quantum Jump • An electron in the Bohr model can make a quantum jump between states. • If it goes to higher energy, it emits a photon (light) • If it drops to lower energy, it must absorb a photon of exactly the right energy 10:34 AM 44 • Electrons in high energy orbitals can drop into lower orbits, emitting a photon (light) • Balmer series (visible light) electrons drop to the n= 2 level 푛 = 4 → 푛 = 2 푛 = 3 → 푛 = 2 푛 = 5 → 푛 = 2 푛 = 6 → 푛 = 2 10:34 AM 45 Quantum Leap • The Bohr model can work in reverse: • A photon can push an electron into a higher orbital • Photon energy must be exactly the same energy as the difference between the two levels 10:34 AM 46 Quantum Man Statue Julian Voss-Andreae is a German sculptor.