De Broglie Waves, Uncertainty, and Atoms

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De Broglie Waves, Uncertainty, and Atoms
Physics 102 Lecture 23
Hour Exam 3

• Monday, April 14
• Covers
• lectures through Lecture 20 (last Mondays
  lecture)
• homework through HW 10
• discussions through Disc 10
• Review, Sunday April 13, 3 PM, 141 LLP

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Hour Exam 3 Review

• Fall 2007, HE2, problems 18-25
• Fall 2007, HE3, all except 22,27

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Photoelectric Effect Summary

• Each metal has Work Function (W0) which is the
  minimum energy needed to free electron from atom.
• Light comes in packets called Photons
• E h f h6.626 X 10-34 Joule sec
• Maximum kinetic energy of released electrons
• K.E. hf W0

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Photoelectric Effect Summary

• Maximum kinetic energy of released electrons
• K.E. hf W0

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Compton Scattering
This experiment really shows photon momentum!
Pincoming photon 0 Poutgoing photon
Pelectron
Outgoing photon has momentum p? and wavelength ??
Incoming photon has momentum, p, and wavelength l

Recoil electron carries some momentum and KE

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Is Light a Wave or a Particle?

• Wave
• Electric and Magnetic fields act like waves
• Superposition, Interference, and Diffraction
• Particle
• Photons
• Collision with electrons in photo-electric effect
• Compton scattering from electrons
• BOTH Particle AND Wave

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ACT Photon Collisions

• Photons with equal energy and momentum hit both
  sides of the plate. The photon from the left
  sticks to the plate, the photon from the right
  bounces off the plate. What is the direction of
  the net impulse on the plate?
• 1) Left 2) Right 3) Zero

Photon that sticks has an impulse p
Photon that bounces has an impulse 2p!
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Radiometer
Preflight 23.1
Photon A strikes a black surface and is absorbed.
Photon B strikes a shiny surface and is
reflected back. Which photon imparts more
momentum to the surface?
Photon A Photon B
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Ideal Radiometer
Photons bouncing off shiny side and sticking to
black side. Shiny side gets more momentum so it
should rotate with the black side leading
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Our Radiometer
Black side is hottergas molecules bounce off it
with more momentum than on shiny side-this is a
bigger effect than the photon momentum
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Are Electrons Particles or Waves?

• Particles, definitely particles.
• You can see them.
• You can bounce things off them.
• You can put them on an electroscope.
• How would know if electron was a wave?

Look for interference!
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Youngs Double Slit w/ electron

• JAVA

Source of monoenergetic electrons
L
Screen a distance L from slits
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Electrons are Waves?

• Electrons produce interference pattern just like
  light waves.
• Need electrons to go through both slits.
• What if we send 1 electron at a time?
• Does a single electron go through both slits?

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Electrons are Particles and Waves!

• Depending on the experiment electron can behave
  like
• wave (interference)
• particle (localized mass and charge)
• If we dont look, electron goes through both
  slits. If we do look it chooses 1.

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De Broglie Waves
So far only photons have wavelength, but De
Broglie postulated that it holds for any object
with momentum- an electron, a nucleus, an atom, a
baseball,...
Explains why we can see interference and
diffraction for material particles like
electrons!!
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Preflight 23.3
Which baseball has the longest De Broglie
wavelength?
(1) A fastball (100 mph) (2) A knuckleball (60
mph) (3) Neither - only curveballs have a
wavelength
31 60 8
Lower momentum gives higher wavelength.
pmv, so slower ball has smaller p.
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ACT De Broglie Wavelength
A stone is dropped from the top of a building.
What happens to the de Broglie wavelength of the
stone as it falls?
1. It decreases 2. It stays the same 3.
It increases
Speed, v, KEmv2/2, and momentum, pmv, increase.
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ComparisonWavelength of Photon vs. Electron
Example
Say you have a photon and an electron, both with
1 eV of energy. Find the de Broglie wavelength
of each.

• Photon with 1 eV energy

• Electron with 1 eV kinetic energy

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Preflights 23.4, 23.5
Photon A has twice as much momentum as Photon B.
Compare their energies.

• EA EB
• EA 2 EB
• EA 4 EB

21 47 33
Electron A has twice as much momentum as Electron
B. Compare their energies.

• EA EB
• EA 2 EB
• EA 4 EB

22 40 38
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ACT De Broglie

• Compare the wavelength of a bowling ball with the
  wavelength of a golf ball, if each has 10 Joules
  of kinetic energy.
• (1) lbowling gt lgolf
• (2) lbowling lgolf
• (3) lbowling lt lgolf

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Heisenberg Uncertainty Principle
Rough idea if we know momentum very precisely,
we lose knowledge of location, and vice versa.
This seems weird but
OK this is weird but it is also true.
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Heisenberg Uncertainty PrincipleA Consequence
of the Wave Nature of Particles
w
q
Dy w
l/sinq
y
x
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Electron entered slit with momentum along x
direction and no momentum in the y direction.
When it is diffracted it acquires a py which can
be as big as h/w.
The Uncertainty in py is Dpy? h/w.
An electron passed through the slit somewhere
along the y direction. The Uncertainty in y is
Dy ? w.
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If we make the slit narrower (decrease wDy) the
diffraction peak gets broader (Dpy increases).
If we know location very precisely, we lose
knowledge of momentum, and vice versa.
Remember earlier we saw that a particle whose
momentum (and therefore wavelength) is known
precisely is very uncertain in position.
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to be precise...
Of course if we try to locate the position of the
particle along the x axis to Dx we will not know
its x component of momentum better than Dpx,
where
and the same for z.
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Early Model for Atom

• Plum Pudding
• positive and negative charges uniformly
  distributed throughout the atom like plums in
  pudding

But how can you look inside an atom 10-10 m
across?
Light (visible) l 10-7 m Electron (1 eV) l
10-9 m Helium atom l 10-11 m
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Rutherford Scattering
Scattering He atoms off of gold. Mostly go
through, some scattered back!
Flash
Only something really big (i.e. nucleus) could
scatter the particles back!
If nucleus was baseball in Memorial Stadium,
electrons would be
A) Front Row B) Back Row B) Quad C) Savoy
D) Moon
Atom is mostly empty space with a small (r
10-15 m) positively charged nucleus surrounded by
cloud of electrons (r 10-10 m)
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Nuclear Atom (Rutherford)
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Recap

• Photons carry momentum ph/l
• Everything has wavelength lh/p
• Uncertainty Principle DpDx gt h/(2p)
• Atom
• Positive nucleus 10-15 m
• Electrons orbit 10-10 m
• Classical EM doesnt give stable orbit
• Need Quantum Mechanics!

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Reminder Review Sunday