# Wave-Particle Duality d

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```					Wave-Particle Duality
wave properties and
particle properties
Principle of Complementarity
To understand any given experiment,
use either the wave or the photon
theory, but not both.
Not possible to visualize the “true”
EM SPECTRUM

Low frequency (radio, microwaves) – WAVES
High frequency (x-rays, gamma rays) – PARTICLES

Middle frequency (visible light) –
WAVES/PARTICLES
Waves: v = λf
8
v = c = 3.00 x 10 m/s
Energy is continuous;
depends on amplitude of wave

x-ray

If electron loses all its energy à
max frequency photon

Nucleus slows down the electron.
Decelerated electron emits energy
as an x-ray photon.
K-shell capture

High-speed electron knocks K-shell
electron out of orbit. When outer-
shell electron fills gap, it emits x-ray
x-ray tube operated at 50 kV
shortest-wavelength x-ray
photon emitted?
KE = eV           E = hf = hc/λ
-11
2.5 x 10      m
MOMENTUM OF A PHOTON

Matter particles:   p = mv

Energy particles: p = h/λ
PARTICLES AS WAVES
Waves (energy) have particle properties.

Particles (matter) have wave properties.

1924 – de Broglie wavelength:

λ = h/p     p = mv
Wavelength of a person
A 75 kg-boy runs at 9.0 m/s.
What is his wavelength?
-34
λ = (6.626 x 10 )/(75 x 9.0) =
-37
9.8 x 10 m

Too small to be detected!
Wavelength of an electron
An electron is accelerated across
100 V. Wavelength?
λ = h/√(2eVm)
1.2 x 10-10 m
-10
Size of atom ~ 10         m

MEASURABLE !
Davisson-Germer (1927)

Electrons produce an interference
(diffraction) pattern.
Electrons have wave
Conclusion:
properties.
Wave-particle duality also
applies to material objects
Principle of Complementarity
also applies to matter

What is an electron?
-14
b) 1.408 x 10         m
-20
c) 4.706 x 10         kg m/s
-14
d) 8.08 x 10         J

```
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 views: 1 posted: 3/19/2014 language: English pages: 18