Chem111
Fall, 2005
23
Wave- particle Duality
••
particles
:
specific location, velocity, mass; countable, distinct
••
waves
:
delocalized; interference effects
Æ
2 particles cannot occupy the same space, but 2 waves can!
So …
when do light and matter act like particles and when do they act
like waves?
Light
: depends on how we measure
•
λ
α
1/
ν
and
E= h
ν
Æ
high frequency (energy) radiation
Æ
particles
low frequency (energy) radiation
Æ
waves
•
Atomic dimensions (0.5 to 2 Å= 0.5 to 2 x 10
-19
m )
λ
> 10 Å
Æ
wave behavior (radiowaves, IR, visible, ultraviolet)
λ
< 10 Å
Æ
particle behavior (gamma rays)
Matter
: de Broglie
λ
= h/p
matter is composed of "wavicles"
•
λ
for macroscopic objects is very
small (< 10
-30
m)
→
definitely particle
•
on an atomic scale we see different behavior:
•
e- at 300 K (v~0.04% c)
61Å
Æ
wave behavior
•
e- at 3 x 10
5
m/s
(v~0.1% c)
24 Å
•
e- at 3 x 10
7
m/s
(v~10% c)
0.24 Å
•
He nucleus at 300K (v~0.04% c)
0.72 Å
Æ
particle behavior
Lecture 11:
•
Introduction to QM (continued)
•
The Schrödinger Equation
•
The Hydrogen Atom
diffraction pattern
(wavelike)
no diffraction pattern
(particle like)

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Chem111
Fall, 2005
24
Heisenberg Uncertainty Principle
•
wave- particle duality places limitations on what can be measured (and the
precision of the measurement ) problem of probabilities
•
another way to think about this … when the measurement process is on the
same scale as the effect being measured, the effect is perturbed by the
measurement ( i.e. don't know what the system is doing afterwards)
consider a slit diffraction experiment:
Δ
x = uncertainty in the knowledge of the position of the particle in x.
Δ
p
x
= uncertainty in our knowledge of the velocity (momentum) of the particle in
the x-direction
before the screen
after the screen
Δ
x = infinity (we have no idea
where the particle is in x)
Δ
x = w
Δ
p
x
= 0
(we know it's traveling in
the y-direction)
Δ
p
x
= 2h/w
(geometry,
interference conditions, de
Broglie)
microscopic particle travels in
the y direction (v
x
= 0)
we want to know its x position
Æ
measure x by passing the
particle through a slit
x
y
w
classical result = all particles
with x value within w appear
on the screen here
quantum mechanical result =
interference pattern (wave!)
•
what is the position?
•
clearly some particles have
traveled in the x direction!
(v
x
≠
0 any more)
we have learned something about x
but at the expense of
knowledge of p
x