PHYS140 Matter Waves 1

The Wave Nature of Matter

• Subatomic particles• De Broglie• Electron beam• Davisson-Germer Experiment• Electron Interference• Matter Waves

PHYS140 Matter Waves 2

Problem

• What is the de Broglie wavelength of a 50 kg persontraveling at 15 m/s?

(h = 6.6 x 10-34 J s)n comparable to spacing

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Subatomic Particles

• We can see the electron tracks• There is evidence of light as a particle from the

collision of light with the electrons at point P

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De Broglie Hypothesis

• Linking momentum and wavelength• Based on the photoelectric effect, de Broglie

surmised that particles should behave by photonsand their wavelength should be related to theirmomentum

!

p =h

"

" =h

p

PHYS140 Matter Waves 5

The electric beam

• To create a beam of electrons for a double slitexperiment, the electrons must have the samewavelength

• To have the same wavelength, the electrons musthave the same momentum or equivalently, energy

!

K =1

2mv

2=p2

2m

!

p = 2Km

!

" =h

p=

h

2Km=

hc

2Kmc2

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Davisson-Germer Experiment• By accident, Davisson and Germer found that

electrons were diffracted by large nickel crystals,similar to diffraction of light by crystals

Matter Waves

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• Like photons and electrons, protons, neutrons, atoms,and even molecules have wave properties

• Electrons have lowest mass• As mass increases, wavelength decreases• For macroscopic molecules, the wavelength is smaller

than any known particles.• it’s impossible to make the slit separation small

enough• The screen must be placed much to far away to

resolve the interference pattern

!

" =hc

2Kmc2

Model of the atom - electrons

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Complementarity

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• Light waves that interfere and diffract deliver theirenergy in particle package of quanta

• Electrons that move through space in straight lines andexperience collisions as if they were particles,distribute themselves spatially in interference patternsas if they were waves

• What you see depends on what facet you look at• When Niels Bohr was knighted for his contributions to

physics, he chose the yin-yang symbol for his coat ofarms

Practice• Quantum Wave Interference

• Worksheet• http://phet.colorado.edu/simulations/sims.php?sim=Quantum_Wave

_Interference

• Movie• Dr. Quantum double slit• http://www.youtube.com/watch?v=DfPeprQ7oGc

• Good Lecture• http://www.youtube.com/watch?v=UXvAla2y9wc&NR=1

• Group Problems• Q4B.1, Q4B.5, Q4S.1

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