Transcript ppt

Exam 3 covers
Lecture, Readings, Discussion, HW, Lab
Exam 3 is Tue. Nov. 25, 5:30-7 pm, 2103 Chamberlin (here)
Biot-Savart Law - currents produce magnetic fields
Ampere’s law - shortcut to determining mag. fields from currents.
Magnetic flux, Faraday effect, Lenz’ law, inductance, inductors
Electromagnetic waves:
Wavelength, freq, speed
E&B fields, intensity, power, rad. pressure, Poynting vec
Polarization
Modern Physics (quantum mechanics)
Photons & photoelectric effect
Bohr atom: Energy levels, absorbing & emitting photons
Tue. Nov. 25, 2008
Physics 208, Lecture 25
1
Last Time…
Photons as particles
Photon absorption and emission
Bohr atom
Photon properties of light





Photon of frequency f has energy hf
 E
photon  hf  hc / 

h  6.626 1034 J  s  4.14 1015 eV  s

hc 1240eV  nm
Red light made of ONLY red photons

The intensity of the beam can be increased by
increasing the number of photons/second.

(#Photons/second)(Energy/photon) =
energy/second = power
Tue. Nov. 25, 2008
Physics 208, Lecture 25
3
Photon
interference?
Only one photon present here
Do an interference
experiment again.
But turn down the
intensity until only
ONE photon at a
time is between
slits and screen
?
Is there still
interference?
A. Yes
Tue. Nov. 25, 2008
B. No
C. I’m confused
Physics 208, Lecture 25
4
Single-photon interference
1/30 sec
exposure
Tue. Nov. 25, 2008
1 sec
exposure
Physics 208, Lecture 25
100 sec
exposure
5
Probabilities

Quantum mechanic says:

Cannot predict where on camera photon will arrive.

Individual photon hits determined probabilistically.

Photon has a probability amplitude through space.


Square of this quantity gives probability that photon will hit
particular position on detector.
The photon is a probability wave.
Tue. Nov. 25, 2008
Physics 208, Lecture 25
6
Matter waves


If light waves have particle-like properties,
maybe matter has wave properties?
de Broglie postulated that the
wavelength of matter
is related to momentum as
h

p

This is called
the de Broglie wavelength.
Tue. Nov. 25, 2008
Physics 208, Lecture 25
Nobel prize, 1929
7
Why h / p ? Works for photons

Wave interpretation of light:



wavelength = (Speed of Light) / Frequency
=c/f
Particle interpretation of light (photons):

Energy = (Planck’s constant) x Frequency

E = hf, so f = E / h
c
c
h
Wavelength =  =


f E /h E /c
But photon momentum = p = E / c…
h

for a photon
p
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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

h
We argue that   applies to everything
p
Photons and footballs
both follow the same relation.


Everything has both
wave-like and particle-like properties
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Wavelengths of massive objects
h
deBroglie wavelength =  
p


p=mv
h

mv


Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Matter Waves


deBroglie postulated that matter has wavelike
properties.
deBroglie wavelength   h / p
Example:
Wavelength of electron with 10 eV of energy:

Kinetic energy
p2
E KE 
 p  2mE KE
2m
h
hc
1240eV  nm



 0.39nm
2
6
2mE KE
2mc E KE
20.51110 eV 10eV 
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Wavelength of a football

Need m, v
to find 

Momentum:

Make the Right Call: The NFL's Own interpretations and
guidelines plus 100s of official rulings on game situations.
National FootBall League, Chicago. 1999:
"... short circumference, 21 to 21 1/4 inches;
weight, 14 to 15 ounces.”
(0.43 - 0.40 kg)
“Sometimes I don’t know how they catch that ball, because
Brett Aaron wings that thing 60, 70 mph,” Flanagan said.
(27 - 32 m/s)
Wells
mv  0.4 kg30 m /s  12 kg m /s
h 6.6 1034 J  s
35
26
 
 5.5 10 m  5.5 10 nm
p 12 kg m /s
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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This is very small




1 nm = 10-9 m
Wavelength of red light = 700 nm
Spacing between atoms in solid ~ 0.25 nm
Wavelength of football = 10-26 nm
• What makes football wavelength so small?
h
h
 
p mv
Tue. Nov. 25, 2008
Large mass, large momentum
short wavelength
Physics 208, Lecture 25
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Suppose an electron is a wave…

Here is a wave:
h

p
x


…where is the electron?

Wave extends infinitely far in +x and -x direction
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Analogy with sound


Sound wave also has the same characteristics
But we can often locate sound waves


E.g. echoes bounce from walls. Can make a sound pulse
Example:




Hand clap: duration ~ 0.01 seconds
Speed of sound = 340 m/s
Spatial extent of sound pulse = 3.4 meters.
3.4 meter long hand clap travels past you at 340 m/s
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Beat frequency: spatial localization

What does a sound ‘particle’ look like?


Example:‘beat frequency’ between two notes
Two waves of almost same wavelength added.
Qui ckTi me™ a nd a
TIF F (L ZW ) d e co mp re ssor
a re ne e d ed to se e thi s p i cture .
Qui ckTi me ™ a nd a
TI
FF (LZW) d e comp resso r
a re ne e de d to see thi s p i cture.
Constructive
interference
Large
amplitude
Tue. Nov. 25, 2008
Destructive
interference
Small
amplitude
Physics 208, Lecture 25
Constructive
interference
Large
amplitude
16
Making a particle out of waves
440 Hz +
439 Hz
440 Hz +
439 Hz +
438 Hz
440 Hz +
439 Hz +
438 Hz +
437 Hz +
436 Hz
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Adding many sound waves

Six sound waves with different wavelength added together
1=
4= /1.15
2= /1.05
5= /1.20
3= /1.10
6= /1.25
•Wave now resembles a particle, but what is the wavelength?
– Sound pulse is comprised of several wavelength
– The exact wavelength is indeterminate
8
4
0
-4
x
-8
-15
-10
-5
0
5
10
15
J
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Spatial extent of ‘wave packet’
8
4
0
-4
x
-8
-15
-10
-5
0
5
10
15
J


x = spatial spread of ‘wave packet’
Spatial extent decreases as the spread in
included wavelengths increases.
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Same occurs for a matter wave


Localized particle:
sum of waves with slightly different wavelengths.
 = h /p, each wave has different momentum.


There is some ‘uncertainty’ in the momentum
Still don’t know exact location of the particle!


Wave still is spread over x (‘uncertainty’ in position)
Can reduce x, but at the cost of increasing the spread in
wavelength (giving a spread in momentum).
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Heisenberg Uncertainty Principle

Using



x = position uncertainty
p = momentum uncertainty
Planck’s
constant
Heisenberg showed that the product
( x )  ( p ) is always greater than ( h / 4 )
Often write this as
x p ~
/2
h

is pronounced ‘h-bar’
2
where

Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Uncertainty principle question
Suppose an electron is inside a box 1 nm in width.
There is some uncertainty in the momentum of
the electron. We then squeeze the box to make it
0.5 nm. What happens to the momentum
uncertainty?
A. Momentum becomes more uncertain
B. Momentum becomes less uncertain
C. Momentum uncertainty unchanged
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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The wavefunction

Quantify this by giving a physical meaning to
the wave that describing the particle.

This wave is called the wavefunction.


Cannot be experimentally measured!
But the square of the wavefunction is a
physical quantity.

It’s value at some point in space
is the probability of finding the particle there!
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Electron waves in an atom


Electron is a wave.
Its ‘propagation direction’ is
around circumference of
orbit.

Wavelength = h / p

Waves on a circle?
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Waves on a circle
Wavelength





My ‘ToneNut’.
Produces particular pitch.
Sound wave inside has
wavelength =v/f (red line).
Integer number of
wavelengths required around
circumference
Otherwise destructive
interference

Blow in here
Tue. Nov. 25, 2008
wave travels around ring and
interferes with itself
Physics 208, Lecture 25
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Electron Standing Waves

Electron in circular orbit works same way

Integer number of deBroglie wavelengths
must fit on circumference of the orbit.

Circumference = (2)x(orbit radius) = 2r

h
h
So condition is 2r  n  n  n
p
mv

This says mvr  n
This is quantization
angular momentum (L=mvr)

Ln

Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Electron standing-waves on an atom
Wave representing
electron


Electron wave extends around
circumference of orbit.
Only integer number of
wavelengths around orbit
allowed.
Tue. Nov. 25, 2008
Wave representing
electron
Physics 208, Lecture 25
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Hydrogen atom energies


Wavelength gets longer in higher n
states, (electron moving slower) so
kinetic energy goes down.
But energy of Coulomb interaction
between electron (-) and nucleus
(+) goes up faster with bigger n.
Zero energy
n=4
n=3
E3  
13.6
eV
32
n=2
E2  
13.6
eV
22
E1  
13.6
eV
12

Energy

End result is

13.6
E n   2 eV
n
n=1

Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Hydrogen atom question
Here is Peter Flanary’s
sculpture ‘Wave’
outside Chamberlin
Hall. What quantum
state of the hydrogen
atom could this
represent?
A. n=2
B. n=3
C. n=4
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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Another question
Here is Donald Lipski’s sculpture ‘Nail’s
Tail’ outside Camp Randall Stadium.
What could it represent?
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
A. A pile of footballs
B. “I hear its made of plastic. For 200
grand, I’d think we’d get granite”
- Tim Stapleton (Stadium Barbers)
C. “I’m just glad it’s not my money”
- Ken Kopp (New Orlean’s Take-Out)
Tue. Nov. 25, 2008
Physics 208, Lecture 25
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