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.

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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

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What is Wrong With Classical Physics?Genesis of Quantum Theory

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19th Century Physics

• Newton’s Laws

• Gravitation

• Thermodynamics (heat transfer)

• Waves

• Electricity and Magnetism (Maxwell’s Equations)

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Blackbody RadiationThe First Problem with Classical Physics:

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Blackbody Radiation

• The colour of a hot object.

• The colour observed changes with temperature

• White hot (very hot)

• Red hot (not as hot)

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Observing hot objects and looking at the wavelengths of light given off, shows a peak (a preferred wavelength)

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https://www.youtube.com/watch?v=sUp_WZKZID4

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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

Lord Rayleigh (John William Strutt)

Sir James JeansApplied Mathematics, Physics, Astronomy, Cosmology

• Applied Maxwell’s equations to predict the shape of the graph and the distribution of wavelengths.

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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!

∞

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Planck Model

• The German Physicist Max Planck re-calculated the blackbody radiation curves using a different approach.

https://www.nobelprize.org/prizes/physics/1918/summary/

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• 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

• 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

𝐸0 = ℎ × 𝑓

𝐸1 = ℎ × 2𝑓

𝐸2 = ℎ × 3𝑓

𝐸3 = ℎ × 4𝑓

𝐸4 = ℎ × 5𝑓

The Planck constant h = 6.62606876×10-34 J.s

Planck also assumed that the energy was frequency dependent

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• 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

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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

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The Photoelectric EffectThe Second Problem with Classical Physics

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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 lighte- An electron is emitted

https://www.youtube.com/watch?v=kcSYV8bJox8

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Einstein’s Explanation

• Light consists of particles (wave packets) which have both wavelike AND particle properties

• The individual wave packet is called a photon

Wave (Young’s Experiment)

Particles (Newton’s Corpuscular theory)

Stream of wave packets

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• A photon collides with an electron in the metal.

• The electron absorbs the energy of the photon and is emitted

UV Photons

Photoelectron

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Energy of the Photon

• Einstein calculated the energy of a single photon to be

𝐸 = ℎ𝑓

𝐸𝑛𝑒𝑟𝑔𝑦 = 𝑃𝑙𝑎𝑛𝑐𝑘′𝑠 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

Wave property

• Uses the Planck equation• Nobel Prize in 1921

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Momentum and the Photon

• Newton defined the momentum of an object to be

𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 𝑚𝑎𝑠𝑠 × 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

𝒑 = 𝑚𝒗

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• The force applied is equal to the rate of change of momentum

• 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

𝑝 =ℎ

𝜆

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𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝒑 = 𝑚𝑎𝑠𝑠 × 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚

Wavelength

Planck’s Constant

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

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-Incoming X-rays

𝜃

• 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.

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Incoming X-rays (Higher energy)

𝜃

Scattered X-rays (Lower energy)

• Compton shared the Nobel Prize in Physics in 1927

Spectroscopic ObservationsThe Third Problem with Classical Physics

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Spectroscopy

http://www.youtube.com/watch?v=ryB-cuv8rT0

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• 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

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

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• A J Ångström studied the light emitted by low pressure gases in discharge tubes in 1853

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

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• 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

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

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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 Paschenseries

Visible Infra-redUltra-violet

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• To predict the wavelengths 𝜆 seen in each of the series, there are a set of empirical equations

1

𝜆= 𝑅

1

12−

1

𝑛2n = 2,3,4,5... Lyman series

1

𝜆= 𝑅

1

32−

1

𝑛2n = 4,5,6,7... Paschen series

1

𝜆= 𝑅

1

22−

1

𝑛2n = 3,4,5,6... Balmer series

R = 1.097×107 m-1 is known as the Rydberg Constant

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• There is a pattern to the characteristic frequencies

1

𝜆= 𝑅

1

𝑛𝑓2 −

1

𝑛𝑖2

• According to classical physics there should be no line spectra at all – all wavelengths should be emitted, not just a few

Integer numbers: suggests a quantum series

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• 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

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The Structure of the AtomThe Fourth Problem with Classical Physics

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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

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• 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

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• 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!

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

• Electrons must remain in “stationary states” which are described by a quantum number

https://www.nobelprize.org/prizes/physics/1922/summary/

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• He mixed classical physics (attraction between charged particles, and circular motion), with a new quantum idea:

+

-

The electrons are in circular orbitals known as stationary states

As the radius of the orbital increases, so does the energy of the electron in the state.

The orbitals (and the radii and energy) can be described by a quantum number n

n=1

n=2

n = 3

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The Quantum Jump

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• 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

• Electrons in high energy orbitals can drop into lower orbits, emitting a photon (light)

𝑛 = 3 → 𝑛 = 2𝑛 = 4 → 𝑛 = 2

𝑛 = 5 → 𝑛 = 2

𝑛 = 6 → 𝑛 = 2

• Balmer series (visible light) electrons drop to the n= 2 level

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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

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Quantum Man Statue

Julian Voss-Andreae is a German sculptor. He is also a quantum physicist.

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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

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Wave-Particle Duality

Particles and Waves

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Light as a Particle or Wave

• Young’s Double Slit Experiment: Light is a wave

• Photoelectric Effect: Light is a particle with wavelike properties

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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

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https://www.nobelprize.org/prizes/physics/1929/broglie/facts/

De Broglie Wavelength

• de Broglie proposed that all physical particles had wave-like properties and the wavelength was related to their momentum:

• This was a generalization of Einstein’s photon momentum equation

𝜆 =ℎ

𝑚𝑣

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Momentum

Planck’s Constant

De Broglie Wavelength

• In MOST physical circumstances the wavelength is very small, so no wave-like properties are seen.

𝜆 =ℎ

𝑚𝑣

10:34 AM 53

Momentum

Planck’s Constant

• Use de Broglie’s equation to determine whether you will diffract whilst walking through a door

𝜆𝐷𝐵 =ℎ

𝑚𝑣

Speed - estimate 1 m/s (walking speed)Mass – 100 kg for a person

𝜆𝐷𝐵 =6.63 × 10−34𝐽. 𝑠

100 kg × 1 m/s= 6.63 × 10−32𝑚

Since the door width is much greater than the de Broglie wavelength, there will be no diffraction

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The Davisson-Germer Experiment

• In 1926 Davisson and Germerdemonstrated that a beam of low energy electrons were diffracted by a single crystal of nickel

• Proved de Broglie’s hypothesis

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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

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•Single crystal

•Well defined diffraction pattern

Low Energy Electron Diffraction

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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

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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

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https://www.youtube.com/watch?v=M4_0obIwQ_U

• https://www.youtube.com/watch?v=A9tKncAdlHQ (9 minute video)

• Now suppose that you fire a single electron through the double slits

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•

•

•

••

••

• •

••

•

The electron can either go through the upper slit, or through the lower slit. We should get only two lines on the screen

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• Now watch what happens when the experiment is carried out

• Akita Tonamora (Hitachi, 1989)

https://www.youtube.com/watch?v=FCoiyhC30bc

Expanded article on this experiment https://physicsworld.com/a/the-double-slit-experiment/

• The single electron produces an interference pattern as if it was a wave

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• 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!

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