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 × 푣푒푙표푐𝑖푡푦
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. He is also a quantum physicist.
10:34 AM 47 The Problem With the Bohr Model • Only works where you have a single charge orbiting around a nucleus • If you have any more than one electron in the atom (every element except hydrogen!) then it doesn’t explain the number of lines, or their wavelength
Helium Emission lines
10:34 AM 48 Wave-Particle Duality
Particles and Waves
10:34 AM 49 Light as a Particle or Wave
• Young’s Double Slit Experiment: Light is a wave
• Photoelectric Effect: Light is a particle with wavelike properties
10:34 AM 50 Wave -Particle Duality
• Proposed by Louis de Broglie in his 1924 PhD thesis • Recherches sur la théorie des quanta
• All matter possesses wavelike properties Louis-Victor-Pierre- Raymond, 7th duc de Broglie https://www.nobelprize.org/prizes/physics/1929/broglie/facts/
10:34 AM 51 De Broglie Wavelength
• de Broglie proposed that all physical particles had wave-like properties and the wavelength was related to their momentum: Planck’s Constant ℎ 휆 = 푚푣 Momentum
• This was a generalization of Einstein’s photon momentum equation
10:34 AM 52 De Broglie Wavelength
• In MOST physical circumstances the wavelength is very small, so no wave-like properties are seen.
Planck’s Constant ℎ 휆 = 푚푣 Momentum
• Use de Broglie’s equation to determine whether you will diffract whilst walking through a door
10:34 AM 53 ℎ 휆 = 퐷퐵 푚푣
Speed - estimate 1 m/s (walking speed) Mass – 100 kg for a person
6.63 × 10−34퐽. 푠 휆 = = 6.63 × 10−32푚 퐷퐵 100 kg × 1 m/s
Since the door width is much greater than the de Broglie wavelength, there will be no diffraction
10:34 AM 54 The Davisson-Germer Experiment
• In 1926 Davisson and Germer demonstrated that a beam of low energy electrons were diffracted by a single crystal of nickel • Proved de Broglie’s hypothesis
10:34 AM 55 The Davisson-Germer Experiment
• The regular inter-atomic spacing in the nickel acted like a diffraction grating • Electrons (a charged particle) had wavelike properties and would diffract like a wave
10:34 AM 56 Low Energy Electron Diffraction
•Single crystal •Well defined diffraction pattern
10:34 AM 57 J.J. Thompson and G.P. Thompson
• J.J. Thomson received the Nobel Prize in 1906, demonstrating that the electron was a particle
• His son, G.P. Thomson shared the Nobel Prize in 1937 (with Davisson), demonstrating that the electron was also a wave
10:34 AM 58 Electrons in the Double Slit Experiment
• Repeat of Young’s experiment, but firing streams electrons through double slits. • They show the striped diffraction patterns – acting like a wave https://www.youtube.com/watch?v=M4_0obIwQ_U
• https://www.youtube.com/watch?v=A9tKncAdlHQ (9 minute video)
10:34 AM 59 • Now suppose that you fire a single electron through the double slits
• • • - • ••
• • •• - • •
The electron can either go through the upper slit, or through the lower slit. We should get only two lines on the screen
10:34 AM 60 • Now watch what happens when the experiment is carried out • Akita Tonamora (Hitachi, 1989)
https://www.youtube.com/watch?v=FCoiyhC30bc
• The single electron produces an interference pattern as if it was a wave
Expanded article on this experiment https://physicsworld.com/a/the-double-slit- experiment/
10:34 AM 61 • This implies that the wave representing the electron does not pass through a single slit, but passes through both slits simultaneously -
• The particle has to be in two places at once!
62 10:34 AM