Quantum Weirdness: A Beginners Guide Dr. Andrew Robinson Part 2 - - PowerPoint PPT Presentation

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

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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)

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Blackbody Radiation

The 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 Jeans Applied 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
• nly oscillate at quantized energy levels

Energy

𝐹0 = ℎ × 𝑔 𝐹1 = ℎ × 2𝑔 𝐹2 = ℎ × 3𝑔 𝐹3 = ℎ × 4𝑔 𝐹4 = ℎ × 5𝑔

The Planck constant h = 6.62606876×10-34 J.s Planck also assumed that the energy was frequency dependent

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

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The Photoelectric Effect

The 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 light e- 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 𝐹 = ℎ𝑔

𝐹𝑜𝑓𝑠𝑕𝑧 = 𝑄𝑚𝑏𝑜𝑑𝑙′𝑡 𝐷𝑝𝑜𝑡𝑢𝑏𝑜𝑢 × 𝑔𝑠𝑓𝑟𝑣𝑓𝑜𝑑𝑧

Wave property

• Uses the Planck equation
• Nobel Prize in 1921

10:34 AM 20

Momentum and the Photon

• Newton defined the momentum of an
• bject to be

𝑛𝑝𝑛𝑓𝑜𝑢𝑣𝑛 = 𝑛𝑏𝑡𝑡 × 𝑤𝑓𝑚𝑝𝑑𝑗𝑢𝑧 𝒒 = 𝑛𝒘

10:34 AM 21

• 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 𝑞 = ℎ 𝜇

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𝑛𝑝𝑛𝑓𝑜𝑢𝑣𝑛 𝒒 = 𝑛𝑏𝑡𝑡 × 𝒘𝒇𝒎𝒑𝒅𝒋𝒖𝒛

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

𝜄

• 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)

𝜄

Scattered X-rays (Lower energy)

• Compton shared the Nobel Prize in Physics in 1927

Spectroscopic Observations

The Third Problem with Classical Physics

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Spectroscopy

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

10:34 AM 26

• 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

10:34 AM 28

10:34 AM 29

• 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

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 Visible Infra-red Ultra-violet

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• To predict the wavelengths 𝜇 seen in each of the series,

there are a set of empirical equations

1 𝜇 = 𝑆 1 12 − 1 𝑜2 n = 2,3,4,5... Lyman series 1 𝜇 = 𝑆 1 32 − 1 𝑜2 n = 4,5,6,7... Paschen series 1 𝜇 = 𝑆 1 22 − 1 𝑜2 n = 3,4,5,6... Balmer series 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 𝜇 = 𝑆 1 𝑜𝑔

2 − 1

𝑜𝑗

2

• 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 Atom

The 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

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

10:34 AM

• 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/

10:34 AM 42

• He mixed classical physics (attraction between charged

particles, and circular motion), with a new quantum idea:

+

• The electrons are in circular
• rbitals 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

10:34 AM 44

• 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)

𝑜 = 3 → 𝑜 = 2 𝑜 = 4 → 𝑜 = 2 𝑜 = 5 → 𝑜 = 2 𝑜 = 6 → 𝑜 = 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

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

10:34 AM 51

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 𝜇 = ℎ 𝑛𝑤

10:34 AM 52

Momentum Planck’s Constant

De Broglie Wavelength

• In MOST physical circumstances the wavelength is

very small, so no wave-like properties are seen. 𝜇 = ℎ 𝑛𝑤

10:34 AM 53

Momentum Planck’s Constant

• Use de Broglie’s equation to determine whether you

will diffract whilst walking through a door

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

𝜇𝐸𝐶 = 6.63 × 10−34𝐾. 𝑡 100 kg × 1 m/s = 6.63 × 10−32𝑛

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

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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

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

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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

• 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!

• 10:34 AM

62