1. De Broglie Waves, Uncertainty, and Atoms
Physics 102: Lecture 23
De Broglie Waves, Uncertainty, and Atoms 1

2. 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 h=6.626 X Joule sec
Maximum kinetic energy of released electrons
K.E. = hf – W0
All puzzles explained with quantum theory.

3. Photoelectric Effect Summary
Maximum kinetic energy of released electrons
K.E. = hf – W0 hf W0 KE
All puzzles explained with quantum theory.

5. Compton Scattering This experiment really shows photon momentum!
Pincoming photon + 0 = Poutgoing photon + Pelectron
Electron at rest
Experiment: Outgoing photon has longer wavelength 
Incoming photon has momentum, p, and wavelength l
Recoil electron carries some momentum and KE
Momentum of a photon
Energy of a photon

6. Compton Scattering
Incident photon loses momentum, since it transfers momentum to the electron
Lower momentum means longer wavelength
This is proof that a photon has momentum

7. Is Light a Wave or a Particle?
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

9. 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

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

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

13. 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

14. 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!

15. Young’s Double Slit w/ electron
2 slits-separated by d
JAVA
Electrons produce interference pattern just like light waves.
Go to physics 2000 web site for JAVA version
Source of monoenergetic electrons L
Screen a distance L from slits

17. Electrons are Particles and Waves!
Depending on the experiment electron can behave like
wave (interference)
particle (localized mass and charge)
If we do an experiment that tells us which slit the electron went through, then there is no interference pattern

18. 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!!

19. 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
Lower momentum gives higher wavelength.
p=mv, so slower ball has smaller p.

21. 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

22. Some Numerology
1 eV = energy gained by a charge e when accelerated through a potential difference of 1 Volt
e = 1.6 x C
so 1 eV = 1.6 x J
h = x J-sec
c = 3 x 108 m/s
hc = x J-m = 1240 eV-nm
Mass of electron m = 9.1 x kg
mc2 = 8.2 x J = 511,000 eV = 511 keV

23. Comparison: Wavelength of Photon vs. Electron
Example
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.
Equations are different - be careful!
Photon with 1 eV energy:
Big difference!
Electron with 1 eV kinetic energy:
Solve for

25. 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
Electron A has twice as much momentum as Electron B. Compare their energies.
EA = EB
EA = 2 EB
EA = 4 EB

26. 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 > lgolf
(2) lbowling = lgolf
(3) lbowling < lgolf

27. 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.

29. Heisenberg Uncertainty Principle: A Consequence of the Wave Nature of Particles
screen
Number of electrons arriving at screen w
Dpy = p sinq p q p q
electron beam
Dy = w
= l/sinq y x
Use de Broglie l

30. The “Uncertainty in py” is Dpy h/w.
Electron diffraction
electron beam
screen
Number of electrons arriving at screen w x y py
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.

31. electron beam
screen
Number of electrons arriving at screen w x y py
If we make the slit narrower (decrease w=Dy) 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.

33. to be precise... Preflight 23.7
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.
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
51% correct