Matter WavesMatter Waves

Photon DualityPhoton Duality The photon can behave like The photon can behave like

a wave or a particle.a wave or a particle.• Planck’s quantaPlanck’s quanta

It behaves like a wave in It behaves like a wave in diffraction.diffraction.

It behaves like a particle in It behaves like a particle in the photoelectric effect.the photoelectric effect.

Ve

I

md sin

hc

eV

Energy from light is equivalent Energy from light is equivalent to energy from matter.to energy from matter.• Einstein’s relativityEinstein’s relativity

It comes from frequency (or It comes from frequency (or wavelength) for photons.wavelength) for photons.

It comes from rest mass for It comes from rest mass for matter.matter.

Energy DualityEnergy Duality

hc

hfpcE

2mcE

Moving charge

Emitted photon

Matter DualityMatter Duality

The energy from matter and light are equivalent.The energy from matter and light are equivalent.

Light can behave as both a wave and a particle.Light can behave as both a wave and a particle.

Could particles of matter behave like a wave?Could particles of matter behave like a wave?• De Broglie proposal 1923De Broglie proposal 1923• Demonstrated with electron diffraction in 1925Demonstrated with electron diffraction in 1925

De Broglie WaveDe Broglie Wave The de Broglie wave is based The de Broglie wave is based

on the momentum of the on the momentum of the particle.particle.• Momentum relation for lightMomentum relation for light

Duality extends to particles Duality extends to particles with mass.with mass.

Moving particles have an Moving particles have an associated wavelength.associated wavelength.

hc

pc h

p

h

mvp

mv

h

Electron WaveElectron Wave An electron with sufficient An electron with sufficient

energy can be diffracted.energy can be diffracted.

X-ray diffraction of a crystal is X-ray diffraction of a crystal is on the order of on the order of = 0.1 nm. = 0.1 nm.• Energy 12.4 KeVEnergy 12.4 KeV

• Momentum 12.4 KeV/cMomentum 12.4 KeV/c

Electrons of similar momenta Electrons of similar momenta also diffract in crystals.also diffract in crystals.

Image of electron diffraction from gold crystals (MacDiarmid institute)

Human WaveHuman Wave Find the wavelength Find the wavelength

associated with a person of 70 associated with a person of 70 kg moving at 3 m/s.kg moving at 3 m/s.

What conditions are required What conditions are required for human diffraction?for human diffraction?• How big of a doorwayHow big of a doorway

The de Broglie wavelength is The de Broglie wavelength is given by given by = h/mv= h/mv..• 6.6 x 106.6 x 10-34-34 J s / 210 kg m/s J s / 210 kg m/s

• = 3.1 x 10= 3.1 x 10-36-36 m. m.

A proton is about 2 x 10A proton is about 2 x 10-15-15 m. m.

The doorway would have to be The doorway would have to be less than 10less than 10-21-21 the diameter of the diameter of a proton.a proton.• Note 1 kg m/s = 6 x 10Note 1 kg m/s = 6 x 101818 eV/c eV/c

Bohr WavesBohr Waves The de Broglie waves help The de Broglie waves help

explain the Bohr model.explain the Bohr model.• Angular momentum quantizedAngular momentum quantized

• Apply de Broglie to Apply de Broglie to momentummomentum

The quantized state has an The quantized state has an integer number of wavelengths integer number of wavelengths on the circumference.on the circumference.• Standing waveStanding wave

nhrmv )2(

r

nhhpmv

2

nr 2

ComplementarityComplementarity

Duality exists for both light and matter.Duality exists for both light and matter.• Both wave and particleBoth wave and particle• Complementary aspectsComplementary aspects

The energy and momentum are both related to The energy and momentum are both related to hh..• Wave properties frequency and wavelengthWave properties frequency and wavelength• Principle of ComplementarityPrinciple of Complementarity

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