Download Wave-Particle Duality

16.107 L01 Mar 4/02
Wave-Particle Duality
• e/m radiation exhibits diffraction and interference
=> wave-like
• particles behave quite differently - follow well
defined paths and do not produce interference
patterns
• when λ << size of opening, wave behaves like a
particle
• light exchanges energy in “lumps” or ‘quanta’ just
like particles
Water waves flare out when passing through opening of width a
a
λ
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Wave-Particle Duality
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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
E=hf = hc/λ
p=h/λ
particles behave as waves: electron diffraction
=> localized packets of energy => particle-like
f, λ “wave-particle duality”
E,p
light
http://www.colorado.edu/physics/2000
electron
Double Slit Experiment with electrons (1989)
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Modern Physics
Large objects
Large objects
small speeds
large speeds
“Newtonian Physics”
“relativistic mechanics”
F = ma
size
F = dp/dt
Atomic scales
small speeds
Quantum Mechanics
“Schrödinger
Equation”
Atomic particles
Large speeds
relativistic quantum
mechanics
“Dirac Equation”
speed
Electromagnetic Waves
• Maxwell(1860) showed that light is a
travelling wave of electric and magnetic
fields
• E = Em sin (kx-ωt)
• B = Bm sin (kx-ωt)
• v= ω/k = c ~ 3 x 10 8 m/s
• the speed is the same in all reference frames
• v= c/n in material media ( n=1 for vacuum)
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Transverse Wave
E and B are both ⊥ to v and E ⊥ B
Light
• Light is a wave
c=λf
• => exhibits interference and diffraction
• => oscillating electric and magnetic fields are
solutions of Maxwell’s equations
• => Maxwell’s equations predict a continuous range
of λ’s from γ-rays to long radio waves
• electromagnetic spectrum
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Electromagnetic Spectrum
Power ∝ ω2
Sensitivity of eye to various λ
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Radiation
• heated objects “glow” if the temperature is
high enough
• =>embers in a fire, stove element
• => 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 λ is longer => infra-red
and not visible
R(λ,T)
14500K
Classical prediction
for 14500 K
Cannot explain the peak
R (λ , T ) =
Watts m-2s-1
2π ckT
λ4
12500K
10000K
As T decreases, λ of peak increases
Partially explained by Planck 1900
λ
R (λ , T ) =
2π c 2 h
1
λ 5 e hc / λ kT − 1
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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 E=hf
Frequency
Planck’s constant
h=6.63x10-34 J.s
c=λf
Modern Physics
• h plays a similar role to c in relativity
• if c → ∞ then no relativity! v/c <<1 always
=> signals transmitted instantaneously
• if h → 0
then no quantum mechanics
=> no stable atoms!
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Example
• Consider a 100W sodium vapour lamp with
λ= 590 nm
• what is the energy of a single photon?
• E=hf = hc/λ
=(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
Example
• The amount of sunlight hitting the earth is about
1000 W/m2 and λ ~ 500 nm
• photons/sec/m2 ~ 2.5x 1021
• we do not see the grainy character of the energy
distribution => appears continuous
• photoelectric effect (lab 4)
• if we shine a beam of light of short enough λ onto a
clean metal surface, the light will knock electrons
out of the metal surface
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