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Dr. P. Lucas
U of A
MSE 110
Quantized atom
SUMMARY FROM LAST CLASS
•
Bohr’s model of the hydrogen atom was rationalized by de Broglie’s
principle: since the electrons behave as waves, only the orbits which
satisfy n
λ
= 2
π
r are stable.
•
There must be an integral number of wavelength around the orbit
otherwise the wave interfere destructively and disappear.
•
The electron forms a standing wave on the stable orbits.
•
The standing wave is a general concept that also applied to the waves
of a string of length L between two pegs, In this case
•
The wave nature of particles is the source of quantization.
•
Schrodinger used established wave equation and applied it to electron
using de Broglie’s principle to obtain his famous equation.
,
3
,
2
,
1
2
=
=
n
n
L
λ
0
)
(
8
2
2
2
2
=
−
+
∂
∂
ψ
π
V
E
h
m
x
•
Ψ
is a wave function corresponding to each
stable state of the electron around the nucleus.
•
The Schrodinger equation allow us to calculate
Ψ
and E for each
stable state (orbit) of the electron, and
Ψ
2
the region of space of orbits.
•
These states correspond to the familiar orbitals of the atoms.
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View Full Document Dr. P. Lucas
U of A
MSE 110
Bohr’s Model
ATOMIC STRUCTURE
•
Bohr’s model is powerful in its simplicity to describe the quantized
character of atoms, which rationalize observation such as atomic
spectra.
•
Provides a rational to the concept
of stable orbits, or electronic
states.
•
Illustrate the link between wave
nature of electrons in atoms and
quantization through de Broglie’s
principle.
•
However, that model is too simplistic and can not explain all
properties of atoms.
•
There are actually additional stable states for the electron that Bohr
can not explain but which are well describe using Scrodinger equation
Dr. P. Lucas
U of A
MSE 110
Bohr vs Schrödinger
ATOMIC STRUCTURE
•
One example of the limitation of Bohr’s model is the observation that the
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This note was uploaded on 11/19/2009 for the course MSE 110 taught by Professor Lucas during the Spring '08 term at University of Arizona Tucson.
 Spring '08
 Lucas

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