Transcript De Broglie Waves, Uncertainty, and Atoms

Physics 102: Lecture 23
De Broglie Waves, Uncertainty, and Atoms
Hour Exam 3
• Monday, April 14
• Covers
– lectures through Lecture 20 (last Monday’s
lecture)
– homework through HW 10
– discussions through Disc 10
• Review, Sunday April 13, 3 PM, 141 LLP
Hour Exam 3 Review
• Fall 2007, HE2, problems 18-25
• Fall 2007, HE3, all except 22,27
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=hf
h=6.626 X 10-34 Joule sec
• Maximum kinetic energy of released electrons
– K.E. = hf – W0
30
Photoelectric Effect Summary
• Maximum kinetic energy of released electrons
– K.E. = hf – W0
hf
KE
W0
30
Compton Scattering
This experiment really shows photon momentum!
Pincoming photon + 0 = Poutgoing photon + Pelectron
Electron at
rest
Incoming photon has
momentum, p, and
wavelength 
E  hf 
hc

p
Energy of a photon
h

Outgoing photon
has momentum p
and wavelength 
Recoil electron
carries some
momentum and KE
5
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
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
Photon that
sticks has an
impulse p
2) Right
3) Zero
Photon that bounces
has an impulse 2p!
10
Radiometer
Incident photons
Black side
(absorbs)
Shiny side
(reflects)
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
38%
63%
11
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
12
Our Radiometer
Black side is hotter:gas molecules bounce off it with
more momentum than on shiny side-this is a bigger
effect than the photon momentum
13
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!
Young’s Double Slit w/ electron
• JAVA
d
Source of
monoenergetic
electrons
L
2 slitsseparated
by d
Screen a distance
L from slits
41
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?
43
Electrons are Particles and Waves!
• Depending on the experiment electron
can behave like
– wave (interference)
– particle (localized mass and charge)
• If we don’t look, electron goes through
both slits. If we do look it chooses 1.
46
De Broglie Waves
p
h

h

p
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!!
15
Preflight 23.3
Which baseball has the longest De Broglie wavelength?
31% (1)
A fastball (100 mph)
60%(2)
A knuckleball (60 mph)
8% (3)
Neither - only curveballs have a wavelength
h

p
Lower momentum gives higher wavelength.
p=mv, so slower ball has smaller p.
18
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, KE=mv2/2,
and momentum,
p=mv, increase.
h
h
p
 

p
20
Equations are different - be careful!
Comparison:
Wavelength of Photon vs. Electron
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:
E
hc

 
hc 1240 eV nm

 1240 nm
E
1 eV
• Electron with 1 eV kinetic energy:
2 Big difference!
1
p
KE  mv 2 and p = mv, so KE =
2
2m
Solve for p  2m(K.E.)

hc
h
1240 eV nm


2m(KE)
2(511,000 eV)(1 eV)
2mc 2 (KE)
 1.23nm
23
Preflights 23.4, 23.5
Photon A has twice as much momentum as Photon B.
Compare their energies.
21%
•
47%
• EA = 2 EB
33%
•
EA = EB
EA = 4 EB
h
hc
E  and   so E  cp
p

double p then double E
Electron A has twice as much momentum as Electron B.
Compare their energies.
22%
•
EA = EB
40%
•
EA = 2 EB
38%
•
EA = 4 EB
1 2 p2
KE  mv 
2
2m
double p then quadruple E
25
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) bowling > golf
(2) bowling = golf
(3) bowling < golf
h

p
h

2m(KE)
27
Heisenberg Uncertainty Principle
h
p y y 
2
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.
29
Heisenberg Uncertainty Principle:
A Consequence of the Wave Nature of
Particles
h
Number of electrons
arriving at screen
w
sin  

electron
beam
p y y 

w
2
 w

sin 
y = w = /sin
screen
y

x
p y y  p sin 

sin 
py = p sin
 p  h
Use de Broglie 
33
to be precise...
h
p y y 
2
Of course if we try to locate the position of the particle
along the x axis to x we will not know its x component of
momentum better than px, where
h
p x x 
2
and the same for z.
Preflight 23.7
According to the H.U.P., if we know the x-position of a
particle, we can not know its:
(1)
y-position
(2)
x-momentum
(3)
y-momentum
(4)
Energy
35
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)
 = 10-7 m
Electron (1 eV)
 = 10-9 m
Helium atom
 = 10-11 m
38
Rutherford Scattering
Scattering He++ atoms off of gold. Mostly go through,
some scattered back!
Flash
(Alpha particles = He++)
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)
42
Nuclear Atom (Rutherford)
Large angle scatterings
nuclear atom
Classic nuclear atom is not stable!
Electrons will radiate and spiral into
nucleus
Need
quantum
theory
45
Recap
• Photons carry momentum p=h/
• Everything has wavelength =h/p
• Uncertainty Principle px > h/(2)
• Atom
–
–
–
–
Positive nucleus 10-15 m
Electrons “orbit” 10-10 m
Classical E+M doesn’t give stable orbit
Need Quantum Mechanics!
50
Reminder: Review Sunday