Quantum Theory

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Quantum Theory
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Outline

• The ultraviolet catastrophe
• Photoelectric effect
• Wave-particle duality
• Atomic models

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Quantum Theory

• "Anyone who is not shocked by quantum theory does
  not understand it" - Niels Bohr

Niels Bohr 1885-1962
"Nobody understands quantum theory" - Richard
Feynman "It is often stated that of all the
theories proposed in this century, the silliest
is quantum theory. Some say the the only thing
that quantum theory has going for it, in fact, is
that it is unquestionably correct" - Richard
Feynman
Richard Feynman 1918-1988
"The universe is not only stranger than we know,
it is stranger than we CAN know. (variously
attributed to Arthur C. Clarke, J. B. S. Haldane
and "an ancient philosopher")
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A Clockwork Universe?

• Newtons laws would mean you could predict the
  motion of everything
• every planet
• every particle

Philosophical implications!
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The Ultraviolet Catastrophe
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Background - Maxwell

• Maxwell developed a theory based on
  probabilities that a molecule in a gas would have
  a certain velocity

James Clerk Maxwell
Quincunx
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Background - Boltzmann

• Statistical mechanics - based on probabilities.

S k log W
Work attacked throughout his life statistical
nature not understood Maxwell-Boltzmann
distribution (1871)
Ludwig Boltzmann 1844-1906
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Stefan-Boltzmann

• Rate of emitting radiation e?AT4 ?
  5.67 x 108 W m-2 K-4
• At normal temperatures low intensity, little
  effect
• Higher temperatures we start to feel heat

Observe red/white glow
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Not just physicists!

• Joseph Wedgewood, 1792

500ºC dark red 750ºC cherry red 900ºC orange 10
00ºC yellow 1200ºC white
Statue of Wedgewood, Stoke-on-Trent
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Black-body Radiation

• A black body is a perfect absorber of
  electromagnetic radiation - also a perfect emitter

Height increases with T, as in Stefan-Boltzmann
equation. Colour represents temp, not f
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Wien

• 1896 Peak is displaced according to ?pT 2.90 x
  10-3 m K
• e.g. sun at 6000K ?p 500nm (visible)
• Peak moves to lower ? (higher f) as T increases

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Wien

• Then tried fuller explanation
• Questionable basis, but worked at higher
  frequencies.

Wilhelm Wien 1864-1928
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Rayleigh-Jeans1900

• Used same assumptions as Maxwell
• Good agreement at low frequencies but

John Strutt Lord Rayleigh 1842-1919
Sir James Jeans 1877 - 1946
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Ultraviolet Catastrophe!

• Predicted infinite intensity for the UV region

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Planck

• Obtained correct formula empirically

2 months later developed theory to fit! Energy
divided into small chunks E n h f (n
an integer, f frequency) Thought that h would
reduce to zero but it didnt! h 6.626 x
10-34 Js-1 - Plancks constant See spreadsheet
on web-page
Max Planck 1858-1947
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Emin hf
Max Planck 1858-1947
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Quanta

• Energy was thus divided into small packets,
  defined by
• E n h f
• So the energy of an atomic oscillator could only
  have discrete values
• The energy in electromagnetic radiation is
  quantized
• Quantum means how much in Latin

Remember this was all being done before anyone
had a clue about atomic structure so atomic
oscillators were an abstract concept.
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3K background radiation

• Uniform radiation, microwave region, observed in
  all directions in the sky

• Big Bang model

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The photoelectric effect
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Photoelectric effect

• Noted by Hertz in 1887 (pre-electron)
• Characterised by Lenard in 1902
• Light shining on surface electrons ejected

Phillip Lénard 1862-1947
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Comments

• Increasing the intensity of the light increased
  the number of photoelectrons, but not their
  energy
• Red light (low f) would not cause ejection of
  electrons

• Weak high frequency (violet) light would result
  in few, high energy electrons

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Einstein, 1905

• Proposed that light consisted of quanta called
  photons
• Each incident photon has E hf
• Thus increasing f increases E of emitted
  electrons
• Increasing intensity does just gives more photons
• Generalised Plancks result to light

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Photons

• In converting electrical energy to light energy,
  a 60W bulb operates at 2 efficiency. Assuming
  all the light is 555nm (green!) determine the
  number of photons per second given off by the
  bulb.

First we find the energy of the light emitted at
555 nm E hf but f c/? so Ehc/ ?
6.626 x 10-34 x 3 x 108/(555 x 10-9) 3.6 x
10-19 J Next we find the amount of light energy
emitted each second 1 W 1 J/s so 60W 60
J/s. 2 efficiency 0.02 x 60 1.2 J/s Finally
we want to find the number of photons per second
1.2 J/s / 3.6 x 10-19J 3.4 x 1018 photons/s
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Equation

• Einsteins relation described the photoelectic
  effect
• hf kinetic energy ?
• where ?work done by electron work function.

Example The work function for silver is 4.73 eV.
Find the minimum frequency to eject electrons
from silver.
Minimum frequency when kinetic energy 0 So
hfmin ? or fmin ?/h ? 4.73 eV 4.73
x 1.6 x 10-19J 7.57 x 10-19J So fmin
1.14 x 1015 Hz
(uv ?263nm)
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Millikan

• Einstein had shown theoretically that
• hf kinetic energy ?
• which could also be written as
• qVo hf - ?
• q charge of electron, hPlancks constant,
  ?work done by electron
• Vo (cutoff voltage) was proportional to f
• Millikan tried to disprove thisover 1912-1917

Robert Millikan 1868-1953
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Millikans results
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Compton Effect

• X-rays lost frequency (and hence E) on
  interaction with material

Arthur Compton 1892-1962
Classically there would have been no frequency
shift - confirmed photon theory
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Wave-particle Duality
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Waves and Particles

• Newton thought light consisted of corpuscles
• Huygens believed that it was a wave.
• By the end of the 19th century, everyone knew
  it was a wave
• Youngs Slits

Thomas Young 1773-1829
Photoelectric effect - photons Back to particles!
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Youngs Slits

• Constructive and destructive interference

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Wave-particle Duality in Light

• Bohr - principle of complementarity.

Can use either wave or particle explanation Need
to be aware of both
Niels Bohr 1885-1962
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Electrons a history

• Cathode rays
• Electrical discharge through evacuated tubes
• Deflected by magnetic field - ? particles

J.J. Thomson 1897 direct measurement of
charge/mass ratio
Millikan followed with measurement of charge and
mass
J. J. Thomson 1856-1940
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De Broglie

• Extended the idea of wave-particle duality
• 1923 particles can be wavelike
• Idea that everything has a wavelength!

Louis de Broglie 1892-1987
E mc2 (mc)c but momentum, pmv and for
a photon vc E pc p f ? but Ehf
(Planck/Einstein) hf p f ? so
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Example
h 6.626 x 10-34 Js

• For everyday objects, we do not notice the
  wavelength

For a baseball (m0.15kg) moving at 30 ms-1 ?
1.5 x 10-34 m For an electron (m9.1 x 10-31kg)
moving at 3 x 106 ms-1 (?) ? 2.4 x 10-10
m de Broglie proposed that crystal diffraction
would confirm wave property of electron
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Diffraction

• Why?
• Separation of atoms in a crystal is of the order
  of 10-10 m (1 Å)

By analogy with diffraction of light, expect
anything with a wavelength similar to the
separation to be diffracted X-rays (? ? 10-10
m) Electrons from example above Neutrons..
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X-ray Diffraction

• 1912 - Friedrich Knipping, under direction of
  Laue
• Extended by W. H. and W. L. Bragg (father and son)

Max von Laue 1879 -1960
W. H. Bragg 1862 -1942
W. L. Bragg 1890 -1971
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G. P. Thomson

• Experiments performed at Marischal College in the
  late 1920's
• (also Lester Werner and Clinton Davisson at Bell
  labs in New York)

George Paget Thomson 1892-1975
100 keV electrons His father had won the Nobel
prize for showing electrons were particles. G.
P. won the prize for showing that they were waves!
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Electron Diffraction
George Paget Thomson 1892-1975
Picture of diffraction taken by Thomson
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Double slit experiment

• With electrons - thought experiment?

Easy to follow wave explanation - but what
happens if one electron passes at a time? How
about bullets?
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Double slit experiment - particles?
?

• If we have both slits open and let one electron
  pass at a time.

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Pattern

• After 70,000 electrons (gradual build up)

Am. J. Phys. 57 117 (1989)
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Quantum Theory - development

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