Transcript Document

Many Electron Atoms
• Spectroscopic Notation, Pauli Exculsion
Principle
• Electron Screening, Shell and Sub-shell
Structure
• Characteristic X-rays and Selection Rules.
• Optical Spectra of atoms and selection
rules.
• Addition of Angular Momentum for Two
electrons.
•K.Krane, Modern Physics, Chapter 8
• Eisberg and Resnick, Quantum Physics,
Chapters 9 and 10.
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Pauli Exclusion Principle
and
Spectroscopic Notation.
A complete description of the state of an
electron in an atom requires 4 quantum
numbers, n, l, ml and ms.
For each value of n, there are 2n2
different combinations of the other
quantum numbers which are allowed.
The values of ml and ms have, at most, a
very small effect on the energy of the
states, so often only n and l are of
interest for example for chemistry.
Spectroscopic Notation uses letters to
specify the l value, i.e. l = 0, 1, 2, 3, 4, 5….
have the designation
s, p, d, f, g, h,…
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Spectroscopic Notation
This notation has its origins in the early optical spectroscopy
of atoms.
The first few letters are named by the way the lines associated
with them look in optical spectra.
Thus:
s---l = 0 related to lines that looked sharp
p---l = 1 related to lines that are strong-Principal lines
d—l = 2 related to lines that looked diffuse
f---l = 3 related to lines that were narrow-Fine
g
h
i
k
Then the others follow in alphabetical order.-------------------
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Summary of the Quantum Numbers
Specifying the Allowed States of
Electrons in Atoms.
Symbol
Name
n
principal quantum number
l
orbital quantum number
ml
magnetic quantum number
ms
spin quantum number
Symbol Allowed Values
Physical Property
n
n=1,2,3,4,…
size of orbit, rn=a0 n2
l
l=0,1,2,3,…,(n-1)
| L | & orbit shape
ml
-l, -l+1,…..,(l-1),+l
projection of L on z
ms
+1/2 and -1/2
projection of S on z
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Atoms with Many
Electrons
Electrons do not all collect in the lowest
energy orbit (evident from chemistry).
This experimental fact can be accounted for
using the Pauli Exclusion Principle which
states that “no two electrons in a single
atom can have the same set of quantum
numbers (n,l,ml ,ms).” (Wolfgang Pauli, 1929).
For example the n=1 orbit (K-shell) can hold
at most 2 electrons,
n
l
ml
ms
1
0
0
+1/2
1
0
0
-1/2
Electrons in an atom fill the allowed states
(a) beginning at the lowest energy
(b) obeying the Exclusion Principle
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Pauli Principle
Electrons do not all collect in the lowest
energy orbit (evident from chemistry).
This experimental fact can be accounted for
using the Pauli Exclusion Principle which
states that “no two electrons in a single
atom can have the same set of quantum
numbers (n,l,ml ,ms).” (Wolfgang Pauli, 1929).
For example the n=2 orbit (L-shell) can hold
at most 8 electrons,
n
l
ml
ms
2
0
0
+1/2
2
1
0
-1/2
2
1
+1
+1/2
2
1
+1
-1/2
2
1
-1
+1/2
2
1
-1
-1/2
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Energies of Orbitals in
Multielectron Atoms.
Shell Structure of Atoms
The n values dominates the determination of
the radius of each subshell (as shown in the
solutions to the Schrödinger equation).
For the penetrating orbitals (s and p), the
probability of being found at a small radius is
balanced by some probability of also being
found at a larger radius.
We see that subshells with the same n but
different l are grouped into “shells” with about
the same average radius from the nucleus.
The energies of outer “subshells”
are affected by the presence of
other electrons, particularly by
screening of the nuclear charge.
In high-Z atoms, the inner subshells are also
affected by the electrons in the outer shells.
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n=1
n=2
=0
=1
Mean values of radius, for various n values
Hydrogen Atom
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W.N. Catford/P.H. Regan
notation-Principal Q.N 1AMQ
Note the
followed by symbol for l
92
Conventionally, the shells are designated by
letter, eg, K shell, n=1
L shell, n=2
M shell, n=3
Subshells correspond to different l values
within each shell.
According to the Pauli Principle, each
subshell has a maximum occupancy
(number of electrons) which is given by,
(2l+1) x 2 = number of possible ml values
.
× no. of ms values for each ml .
Examples:
s subshells (20 +1) × 2 = 2 electrons
p subshells (2 ×1+1) × 2 = 6 electrons
Periodic Table of the Elements.
Inspection of the table of electronic structure
shows that this determines the chemical
properties of the elements (in particular, the
number of valence electrons, i.e. number in
outermost shell, is very important)
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