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Physics 116
Session 31
De Broglie, duality, and
uncertainty
Nov 21, 2011
R. J. Wilkes
Email: [email protected]
Announcements
• HW 6 due today
• Clicker scores have been updated on Webassign gradebook
• Exam 3 next week (Tuesday, 11/29)
• Usual format and procedures
• I’ll post example questions on Wednesday as usual
• We’ll go over the examples in class Monday 11/28
• Q: in class last week, you mentioned a story about two ways to be
invisible…what is the title?
• Classic short story by Jack London, "the shadow and the flash”
– you can read it online:
http://www.online-literature.com/poe/92/
enjoy. (the physics requires a bit of poetic license, but it is fun.)
Lecture Schedule
(up to exam 3)
Today
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Photoelectric effect experiment
• Vacuum tube with metal plates + battery
light
–
–
–
–
cathode = negative, anode = positive
anode
If wavelength is short enough, e’s escape
Anode attracts any free electron
cathode Vacuum tube
If electrons reach anode, current thru vacuum
V
• Shine light on cathode
+
– Blue light – electrons escape, current flows
Ammeter
Battery
• Electrons have some kinetic energy KE
Flow of electrons =
– Red light – no current: electrons can’t escape
current
• With blue light: try reversing voltage:
–
–
–
–
Now put negative V on anode, + on cathode
Electrons need more than just escape energy!
+
Anode repels e back into cathode, unless it has KE > V eV
Dial down negative voltage, until current just starts again
• Now, value of V gives us a measurement of the KE of e’s
• “work function” = minimum energy needed for escape from
metal surface = (energy of photon hf) – (KE)
V
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Example : work function values
•
What is the longest wavelength light that can
eject electrons from the surface of…
1) Potassium
⎫⎪
−15
h
=
4.13
×
10
eV − s
⎬
−34
h = 6.63 × 10 J − s ⎪⎭
(eV/Hz)
1eV = 1.6 × 10 −19 J
Emin = W0 = hf0
W
f0 = 0
h
2.3eV
=
= 5.5 × 1014 Hz
−15
4.13 × 10 eV − s
c
λ0 = = 5.38 × 10 −7 m = 538nm
f0
( = yellow)
2) Copper Emin = W0 = hf0
f0 =
Notice units: electron-volt
eV = energy gained by e
falling through a 1 volt
potential difference.
eV and h are very small!
Suitable for atom-sized
energy calculations
W0
h
4.7eV
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=
11.4
×
10
Hz
−15
4.13 × 10 eV − s
λ0 = 2.63 × 10 −7 m = 263nm
( = UV)
f0 =
hyperphysics.phy-astr.gsu.edu/
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Unique properties of photons
•
•
•
We know that photons carry energy and momentum (recall: radiation
pressure), and travel at the speed of light
Relativity tells us that
m0 c 2
E=
1 − v 2 c2
v = c but E ≠ 0 → m0 = 0
So photons must be massless
–
–
Any particle moving at the speed of light must have rest mass = 0
Any particle with non-zero rest mass can never reach v=c
⎛
⎞
m0 v
⎜
⎟
m0 v
p ⎜ 1 − v 2 c2 ⎟ v
p=
⇒ =⎜
2
⎟ = c2 ⇒
2
2
E
m
c
1− v c
0
⎜
⎟
⎜⎝ 1 − v 2 c 2 ⎟⎠
Example: photon from He-Ne laser has
•
Momentum of a photon must be
p=
h
λ
=
−34
−34
6.63 × 10 J − s 6.63 × 10 J − s
=
= 1.06 × 10−27 kg − m / s
−7
623nm
6.23 × 10 m
( )
hf
E
h
p= =
=
c
λ
c
Notice: very tiny
momentum per photon,
which is why we don’t
notice quantum effects
in everyday life
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Wave-particle duality
•
•
All this implies light behaves like a stream of particles
Compton experiment (1923): light scattering (collisions) with atomic
electrons
–
–
•
•
Photon collisions are same as for particle with momentum p and energy E
Energy lost knocking an electron out of atom is given by same equation as
for particles with mass – observe a longer wavelength afterward (lower E)
So photons have wave and particle character simultaneously…
De Broglie (1923): perhaps objects known to be particles, with mass
(eg electrons), act like waves also?
p=
–
h
λ
for photons
⇒ λ=
h
for electrons
p
More on this soon…
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Uncertainty principle (Heisenberg, 1927)
•
Let’s look again at single slit diffraction
–
–
–
–
–
Illuminate single slit (width W) with light that includes some small range of
wavelengths ( = small range of photon momenta)
We can deduce wavelength of light from locations of fringes
Photons making up the diffraction pattern came from all across the slit
If we make the slit narrower, we have less uncertainty about where the
photon came from
But then the diffraction peaks get wider: we have more uncertainty about
the wavelength (momentum) of the photons
Plane waves in x direction should have py=0, but light
appearing at angle θ indicates there is a y component, ∆py
Slit width represents uncertainty in y coordinate of each
photon arriving at slit. Then
λ
sin θ ≈ θ =
tan θ ≈ θ =
W
∆py
px
→
∆pyW = h = ∆py ∆y
∆py
px
=
λ
W
=
py
px
∆py
h/λ
Heisenberg Uncertainty principle
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Heisenberg principle
• What does this mean?
∆py ∆y = h (=very small number!)
• If you measure position of an electron very precisely, you cannot
measure its momentum very precisely
– You know where the electron is, but not where it is going
• If you measure momentum of an electron very precisely, you
cannot measure its position very precisely
– You know where the electron is going, but not where it is now
• You never notice this limitation, unless you are looking at very
tiny objects or effects
– Try calculating uncertainty limits for a baseball:
• Say p = 100 kg-m/s, and you measure it to +1%
• What is Heisenberg limit on how well you can find its position?
…we’ll come back to this later…
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Back to Young’s Double Slit Experiment
Deep Thought for today:
Is light a particle?
…or a wave?
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Two slits - no certainty
•
How can we explain the 2-slit experiment for photons (particles)?
– Use very low intensity of light, so only one photon arrives per second
– Use an array of photomultiplier tubes to detect single photons arriving one
by one at the screen
• Find: expected fringe pattern builds up as photon count rises
– Fringe pattern = probability distribution for photon arrival locations
•
•
Non-intuitive combination of wave-like and particle-like
How does a photon know about “the other” slit?
– Quantum theory says: it’s impossible to simultaneously observe
interference (wave property) and know which slit a particular photon
came through (particle)
• To determine which slit it went through, you must absorb the photon!
– We say: probability distribution is determined by the wave character of
light, and its arrival (bundle of energy transferred at some specific point in
space and time) is defined by its particle character
• Photon is both things at once: Wave-particle duality
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Building up the 2-slit pattern
10 particles
• Wave interference picture:
What you actually get
with particles:
Particles arrive as
individual “events” but
as numbers build up,
we see the interference
pattern forming.
• Particle picture: what you expect:
2-slit pattern =
probability
distribution:
Statistical, not
determinist!
100
3000
20,000
70,000
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Wave or Particle? Neither/Both/Take your pick
•
Quantum theory says: light is both
– Interferes like a wave, but energy transfer occurs like a particle (photon)
– But exactly same for “actual particles” like electrons and protons !
•
How do we know this?
1. We can do the 2-slit experiment with electrons and get the same result !
2. We can build a device which detects single photons (photomultiplier tube )
based on the photoelectric effect
•
Modern picture of fundamental interactions (Richard Feynman, 1948)
– Matter as we know it is made of particles called fermions
• Electron, proton, neutron
• …plus other short-lived particles produced in collisions of nuclei
– Forces = interactions:
photon
transfers of energy/momentum between particles
e
• Mediated by particles called bosons:
e
Feynman Diagram:
Photon, gluon, W/Z bosons, graviton
E-M Strong Nuclear
Force Force
Weak nucl. Gravity
Force
Force
electron emits photon
which hits another
electron. Like charges
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repel!
Let’s back up a bit: Subatomic discoveries ~100 years ago
•
•
J. J. Thomson (1897) identifies electron: very light, negative charge
E. Rutherford (1911) bounces “alpha rays” off gold atoms
• We now know: α = nucleus of helium: 2 protons + 2 neutrons
• “Scattering experiment” = model for modern particle physics
– Size of atoms was approximately known from chemistry
– He finds: scattering is off a much smaller very dense core (nucleus )
• Rutherford’s nuclear model of atom: dense, positively charged nucleus
surrounded by negatively charged lightweight electrons
•
Niels Bohr (1913): applies Planck/Einstein quanta to atomic spectra
–
–
–
–
Atoms have fixed energy states: they cannot “soak up” arbitrary energy
Quanta are emitted when atom “jumps” from high to low E state
Assumed photon’s energy E=hf, as Planck and Einstein suggested
Simple model of electrons orbiting nucleus, and “classical” physics (except
for quantized E) gives predictions that match results well (at least, for
hydrogen spectrum)
Next topics: atoms, nuclei, radioactivity, subatomic particles
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