1. De Broglie Waves, Uncertainty, and Atoms
Physics 1161: Pre-Lecture 29
De Broglie Waves, Uncertainty, and Atoms
Sections 30.1 – 30.7 1

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

3. 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!!

4. 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

5. 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 we’re not sure where along the wave the particle is actually located! l y

6. Heisenberg Test Dpy = p sinq Dy = w = l/sinq Use de Broglie l
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

7. 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.

8. 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.

9. Rutherford Scattering
Scattering He++ atoms off of gold. Mostly go through, some scattered back!
(Alpha particles = He++)
Only something really small (i.e. nucleus) could scatter the particles back!
Atom is mostly empty space with a small (r = m) positively charged nucleus surrounded by cloud of electrons (r = m)

10. Nuclear Atom (Rutherford)
Large angle scatterings
nuclear atom
Classic nuclear atom is not stable!
Electrons will radiate and spiral into nucleus
Need quantum theory

11. Recap Photons carry momentum p=h/l Everything has wavelength l=h/p
Uncertainty Principle DpDx > h/(2p)
Atom
Positive nucleus m
Electrons “orbit” m
Classical E+M doesn’t give stable orbit
Need Quantum Mechanics!