R. J. WilkesEmail: ph116@u.washington.edu

Physics 116

Session 31De Broglie, duality, and

uncertaintyNov 21, 2011

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.)

3

Lecture Schedule (up to exam 3)

Today

Ammeter Battery

light

Vacuum tube

Flow of electrons = current

V

Photoelectric effect experiment

• Vacuum tube with metal plates + battery– cathode = negative, anode = positive– If wavelength is short enough, e’s escape– Anode attracts any free electron– If electrons reach anode, current thru vacuum

• Shine light on cathode– Blue light – electrons escape, current flows

• Electrons have some kinetic energy KE– Red light – no current: electrons can’t escape

• 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)4

V

+

+

cathode

anode

5

Example : work function values

• What is the longest wavelength light that can eject electrons from the surface of…1) Potassium

2) Copper

hyperphysics.phy-astr.gsu.edu/

Emin =W0 = hf0

f0 =W0

h

=2.3eV

4.13×10−15 eV − s= 5.5 ×1014 Hz

λ0 =cf0= 5.38 ×10−7 m = 538nm

1eV = 1.6 ×10−19 J

h = 6.63×10−34 J − s

⎫⎬⎪

⎭⎪h = 4.13×10−15 eV − s

Emin =W0 = hf0

f0 =W0

h

f0 =4.7eV

4.13×10−15 eV − s= 11.4 ×1014 Hz

λ0 = 2.63×10−7 m = 263nm

( = yellow)

( = UV)

(eV/Hz)

Notice units: electron-volteV = energy gained by e falling through a 1 volt potential difference.eV and h are very small!Suitable for atom-sized energy calculations

6

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

• 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

• Momentum of a photon must be

Example: photon from He-Ne laser has

E =m0c

2

1− v2 c2

v = c but E ≠ 0 → m0 = 0

p =m0v

1− v2 c2⇒

pE=

m0v

1− v2 c2

m0c2

1− v2 c2

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟

=vc2 ⇒ p =

Ec=

hf( )c

=hλ

p =

hλ=

6.63×10−34 J − s623nm

=6.63×10−34 J − s

6.23×10−7 m= 1.06 ×10−27 kg − m / s

Notice: very tinymomentum per photon, which is why we don’t notice quantum effects in everyday life

7

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?

– More on this soon…

p =

hλ

for photons ⇒ λ =hp

for electrons

8

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

sinθ ≈θ =λW

tanθ ≈θ =∆py

px→

∆py

px=λW

=∆py

h / λ∆pyW = h = ∆py∆y

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

px

py

Heisenberg Uncertainty principle

Heisenberg principle

• What does this mean?

• 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…

9

∆py∆y = h (=very small number!)

10

Back to Young’s Double Slit Experiment

Is light a particle? …or a wave?

Deep Thought for today:

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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

• Wave interference picture:

• Particle picture: what you expect:

What you actually get with particles:

Particles arrive as individual “events” but

as numbers build up, we see the interference

pattern forming.

2-slit pattern = probability

distribution:Statistical, not

determinist!

10 particles

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: transfers of energy/momentum between particles

• Mediated by particles called bosons:Photon, gluon, W/Z bosons, graviton Feynman Diagram:

electron emits photon which hits another

electron. Like charges repel!

photon

ee

E-M Strong Nuclear Weak nucl. GravityForce Force Force Force

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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