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5. The Quantum Mechanical Model of the Atom
Wave mechanics
or
Quantum mechanics
By analogy with a guitar string,
fastened at both ends:
⎪
⎭
⎪
⎬
⎫
DeBroglie
L
dinger
o
Schr
E
Heisenberg
W
.
.
.
&
&
Particles take on wave properties:
view the electron as a
standing wave!
• If we assume a circular trajectory
, we should have:
Circumference
≡
a whole number of wavelengths
Cancellation by destructive
interference
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2
2
rn
h
mr n
n
h
But
m
πλ
π
λ
=
⎫
⎪
⇒=
=
⎬
=
⎪
⎭
(De Broglie)
h
v
v
Bohr assumption!
±
Schr
ö
dinger (1925):
Wave equation to calculate the total
energy of the atom.
Idea
:
particle is distributed in space just like the
amplitude of a wave. A high intensity is equivalent
to a
high probability
of finding the particle!
Schrödinger wave equation
(SWE)
Ψ
E
Ψ
H
=
ˆ
⎪
⎪
⎩
⎪
⎪
⎨
⎧
≡
≡
≡
E
H
ˆ
Ψ
wave function
Hamiltonian operator
Total energy
z)
y,
(x,
Ψ
≡
V
T
ˆ
ˆ
+
≡
E
P
E
K
.
.
+
≡
of the moving electron
of
attraction between
e
−
and the nucleus
²
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 Summer '07
 sultan

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