the wave nature of matter - siena collegemmccolgan/gp140s10/q4.pdf · · 2010-04-08phys140 matter...
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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
PHYS140 Matter Waves 3
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
PHYS140 Matter Waves 4
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
PHYS140 Matter Waves 6
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
PHYS140 Matter Waves 7
• 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
Complementarity
PHYS140 Matter Waves 9
• 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
PHYS140 Matter Waves 10
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