WaveParticle Duality

1
Wave-Particle Duality

• e/m radiation exhibits diffraction and
  interference gt wave-like
• particles behave quite differently - follow well
  defined paths and do not produce interference
  patterns
• when ? ltlt size of opening, wave behaves like a
  particle
• light exchanges energy in lumps or quanta
  just like particles

2
Water waves flare out when passing through
opening of width a
a
?
3
Wave-Particle Duality

• 1900 sound, light, e/m radiation were waves
• electrons, protons, atoms were
  particles
• 1930 quantum mechanics provided a new
  interpretation
• light behaves as a particle photoelectric
  Compton effect
• Ehf hc/?
  ph/?
• particles behave as waves electron diffraction
• gt localized packets of energy gt particle-like
• f, ? wave-particle duality E,p

light
electron
http//www.colorado.edu/physics/2000
4
Double Slit Experiment with electrons (1989)
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Modern Physics
Large objects small speeds Newtonian Physics
F ma
Large objects large speeds relativistic
mechanics F dp/dt
size
Atomic scales small speeds Quantum
Mechanics Schrödinger Equation
Atomic particles Large speeds relativistic
quantum mechanics Dirac Equation
speed
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Electromagnetic Waves

• Maxwell(1860) showed that light is a travelling
  wave of electric and magnetic fields
• E Em sin (kx-?t)
• B Bm sin (kx-?t)
• v ?/k c 3 x 10 8 m/s
• the speed is the same in all reference frames
• v c/n in material media ( n1 for vacuum)

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Transverse Wave E and B are both ? to v and
E ? B
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Light

• Light is a wave c?f
• gt exhibits interference and diffraction
• gt oscillating electric and magnetic fields are
  solutions of Maxwells equations
• gt Maxwells equations predict a continuous range
  of ?s from ?-rays to long radio waves
• electromagnetic spectrum

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Electromagnetic Spectrum
Power ? ?2
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Sensitivity of eye to various ?
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Radiation

• heated objects glow if the temperature
  is high enough
• gtembers in a fire, stove element
• gt bar of steel heated to 12000 K glows in
  deep red colour
• thermal radiation
• charges in material vibrate in SHM(accelerate)
  and produce e/m radiation
• also occurs at lower T but ? is longer gt
  infra-red and not visible

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R(?,T)
14500K
Classical prediction for 14500 K
Cannot explain the peak
Watts m-2s-1
12500K
10000K
As T decreases, ? of peak increases
?
Partially explained by Planck 1900
13
Modern Physics

• 1905 Einstein proposed
• when an atom emits or absorbs light, energy
• is not transferred in a smooth continuous fashion
  but rather in discrete packets or lumps of
  energy
• photons have energy Ehf

Frequency c?f
Plancks constant h6.63x10-34 J.s
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Modern Physics

• h plays a similar role to c in relativity
• if c ? ? then no relativity! v/c ltlt1
  always gt signals transmitted instantaneously
• if h ? 0 then no quantum mechanics gt no
  stable atoms!

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Example

• Consider a 100W sodium vapour lamp with ?
  590 nm
• what is the energy of a single photon?
• Ehf hc/? (6.63x10-34
  J.s)(3x108 m/s)/590x10-9 m) 3.37x10-19 J
• Power dE/dt number of
  photons/sec x 3.37x10-19 J 100 W
• number of photons/sec 3 x 1020

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Example

• The amount of sunlight hitting the earth is about
  1000 W/m2 and ? 500 nm
• photons/sec/m2 2.5x 1021
• we do not see the grainy character of the energy
  distribution gt appears continuous
• photoelectric effect (lab 4)
• if we shine a beam of light of short enough ?
  onto a clean metal surface, the light will knock
  electrons out of the metal surface