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7.2 Wave Nature of Matter
De Broglie Wavelength
Diffraction of electrons
Uncertainty Principle
Wave Function
Tunneling
Wave properties of matter
Material particles behave as waves with a wavelength given by the De
Broglie wavelength (Planck’s constant/momentum)
The particles are diffracted by passing through an aperture in a similar
manner as light waves.
The wave properties of particles mean that when you confine it in a
very small space its momentum (and kinetic energy) must increase.
(uncertainty principle) This is responsible for the size of the atom.
Wave properties are only dominant in very small particles.
h
p
λ =
De Broglie Wavelength
Momentum of a photon
 inverse to wavelength.
E
p
c
=
Einstein’s special
relativity theory
h
p
=
λ
since
hc
E
=
λ
Wavelength of a particle inverse to momentum.
h
p
λ=
Lois De Boglie
De Broglie proposed that this wavelength
applied to material particles as well as
for photons. (1924)
Wave properties
a
λ
θ
Diffraction of waves
Increases as the ratio
λ
/a
de Broglie wavelength of a baseball
mv
h
p
h
=
=
λ
A baseball with a mass of 0.15 kg is pitched at 45 m/s
What is its De Broglie wavelength?
m= 0.15 kg
v= 45 m/s
m
10
x
8
.
9
)
s
/
m
45
)(
kg
15
.
0
(
10
x
6
.
6
35
s
.
j
34
−
−
=
=
Diffraction effects of a baseball are negligible
de Broglie wavelength of an
electron
meV
2
h
p
h
=
=
λ
eV
m
2
p
m
2
v
m
mv
2
1
KE
2
2
2
2
=
=
=
=
V = 1000 V
+

e

Find the de Broglie wavelength of a 1000 eV
electron.
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 Spring '09
 Smith
 Diffraction

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