Download Electron

Physics 1161: Pre-Lecture 29
De Broglie Waves, Uncertainty, and Atoms
• Sections 30.1 – 30.7
Compton Scattering
This experiment really shows photon momentum!
Pincoming photon + 0 = Poutgoing photon + Pelectron
Electron at
rest
Incoming photon has
momentum, p, and
wavelength 
E  hf 
hc

p
Energy of a photon
h

Outgoing photon
has momentum p
and wavelength 
Recoil electron
carries some
momentum and KE
De Broglie Waves
p
h

h

p
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!!
Equations are different - be careful!
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.
•
Photon with 1 eV energy:
E
hc

 
hc 1240 eV nm

 1240 nm
E
1 eV
• Electron with 1 eV kinetic energy:
2 Big difference!
1
p
KE  mv 2 and p = mv, so KE =
2
2m
Solve for p  2m(K.E.)

hc
h
1240 eV nm


2m(KE)
2(511,000 eV)(1 eV)
2mc 2 (KE)
 1.23nm
Heisenberg Uncertainty Principle
h
p y y 
2
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!
y

h
p y y 
2
Heisenberg Test
Number of electrons
arriving at screen
w
sin  

electron
beam

w
 w

sin 
y = w = /sin
screen
y

x
p y y  p sin 

sin 
py = p sin
 p  h
Use de Broglie 
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 = 10-15 m)
positively charged nucleus surrounded by cloud of
electrons (r = 10-10 m)
Nuclear Atom (Rutherford)
Large angle scatterings
nuclear atom
Classic nuclear atom is not stable!
Electrons will radiate and spiral into
nucleus
Need
quantum
theory
Recap
• Photons carry momentum p=h/
• Everything has wavelength =h/p
• Uncertainty Principle px > h/(2)
• Atom
–
–
–
–
Positive nucleus 10-15 m
Electrons “orbit” 10-10 m
Classical E+M doesn’t give stable orbit
Need Quantum Mechanics!