De Broglie Waves, Uncertainty, and Atoms

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

• Todays Lecture will cover textbook sections
  27.5, 28.2, 4

2
Compton Scattering
This experiment really shows photon momentum!
Pincoming photon 0 Poutgoing photon
Pelectron
Outgoing photon has momentum p? and wavelength ??
Incoming photon has momentum, p, and wavelength l

Recoil electron carries some momentum and KE

3
ACT Photon Collisions

• Photons with equal energy and momentum hit both
  sides of a metal 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

4
Radiometer
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
5
De Broglie Waves
So far only for 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!!
6
Preflight 23.5
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
7
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
8
ComparisonWavelength of Photon vs. Electron
Example
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

• Electron with 1 eV kinetic energy

9
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

10
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 gt lgolf
• (2) lbowling lgolf
• (3) lbowling lt lgolf

11
Heisenberg Uncertainty Principle
Rough idea if we know momentum very precisely,
we lose knowledge of location, and vice versa.
If we know the momentum p, then we know the
wavelength ?, and that means were not sure where
along the wave the particle is actually located!
12
Heisenberg Test
w
q
Dy w
l/sinq
y
x
13
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.
14
If we make the slit narrower (decrease wDy) 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.
15
to be precise...
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.
16
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) l 10-7 m Electron (1 eV) l
10-9 m Helium atom l 10-11 m
17
Rutherford Scattering
Scattering He atoms off of gold. Mostly go
through, some scattered back!
Only something really small (i.e. nucleus) could
scatter the particles back!
If nucleus was baseball in Memorial Stadium,
electrons would be where?
Atom is mostly empty space with a small (r
10-15 m) positively charged nucleus surrounded by
cloud of electrons (r 10-10 m)
18
Nuclear Atom (Rutherford)
More Black Body Radiation
19
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
20
Our Radiometer
Black side is hottergas molecules bounce off it
with more momentum than on shiny side-this is a
bigger effect than the photon momentum
21
Recap

• Photons carry momentum ph/l
• Everything has wavelength lh/p
• Uncertainty Principle DpDx gt h/(2p)
• Atom
• Positive nucleus 10-15 m
• Electrons orbit 10-10 m
• Classical EM doesnt give stable orbit
• Need Quantum Mechanics!

22
See you next lecture!

• Read Textbook Sections 28.1-28.7