Chapter 3: Wave Properties of Particles

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• Chapter 3 Wave Properties of Particles
• De Broglie Waves
• photons

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Example 3.1 Find the de Broglie wavelengths of a
46 g golf ball with a velocity of 30 m/s and an
electron with a velocity of 107 m/s.
Example 3.2 Find the kinetic energy pf a proton
whose de Broglie wavelength is 1.00 fm (10-15 m),
which is roughly the proton diameter.
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Waves of what? normal waves are a disturbance
in space carry energy from one place to
another often (but not always) will
(approximately) obey the classical wave
equation matter waves disturbance is the wave
function Y(x, y, z, t ) probability amplitude
Y probability density p(x, y, z, t ) Y2
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wave properties
phase velocity does not describe particle motion
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Generic wave properties
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phase and group velocities simple plane wave
inadequate to describe particle motion problems
with phase velocity and infinite wave
train represent particle with wave packet (wave
group) simplified version superposition of two
waves of slightly different wavelength
-if wave velocity is independent of wavlength,
each wave (and thus the packet) travel at the
same speed -if wave velocity is depends upon
wavlength, each wave travels at a different
speed, in turn different from the wave packet
speed.
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de Broglie waves for massive particles
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Example 3.3 An electron has a de Broglie
wavelength of 2.00 pm Find its kinetic energy,
as well as the phase and group velocity of the
waves.
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Particle Diffraction The Davisson-Germer
experiment scattering of electrons from annealed
surface (single crystal) classically, diffuse
scattering waves produce constructive/destructive
interference ala x-ray diffraction
electron detector
smaller wavelength gt finer resolution as in
electron microscope
Example 54 eV electrons are scattered off of a
surface with a strong maximum at an angle of 50o
with respect the incoming beam of electrons. If
the spacing between the atomic planes is .091 nm,
what is the wavelength of the electrons from
diffraction theory? What is the de Broglie
wavelength of the electrons?
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Particle in a box
Examples electron in 0.10 nm box, neutron in
1.00 fm box, Gallis in room
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The Uncertainty Principle limits on
probabilities with wave packets probability
density Y2 maximum near center of wave
packet (or near average) non-zero near
maximumgt uncertainty in position Dx combination
of several wavelengths gt uncertainty in wave
number gt uncertainty in momentum Dp uncertainty
principle decreasing Dx (Dp)will eventually
drive up Dp (Dx). It is impossible to know both
the exact position and exact momentum of an
object at the same time.
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Wave function as a superpopsition of cosine
waves at a particular instant in time
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Example 3.6 A measurement establishes the
position of a proton with an accuracy of
/-.001nm. Find the uncertainty in the protons
position 1.00 s later. assume vltltc.
Uncertainty principle II measurement as
interaction observe a particle by bouncing
photons off of the particle
BUT this uncertainty is an intrinsic limit, not
an artifact of measurement!!!
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Applications of the uncertainty principle
Example 3.7 A typical atomic nucleus is about 5
fm in radius. Use the uncertainty principle to
estimate a lower limit for the energy of an
electron confined to the nucleus.
Example 3.8 A a hydrogen atom is about .053 nm
in radius. Use the uncertainty principle to
estimate a lower limit for the energy of an
electron confined to the atom
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Energy-Time uncertainty
Example 3.9 An excited atom gives up its
excess energy by emitting a photon of a
characteristic frequency. The average time
between the excitation of the atom and the
emission of the photon is 10.0 ns. What is the
inherent uncertainty in the frequency of the
photon?
Chapter 3 problems 2,3,4,5,7,9,16,17,22,24,27,28,
35,37,38