83. W.N. Catford/P.H. Regan 1AMQ
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.
W.N. Catford/P.H. Regan AMQ

84. 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,…
W.N. Catford/P.H. Regan AMQ

85. W.N. Catford/P.H. Regan 1AMQ
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
W.N. Catford/P.H. Regan AMQ

86. W.N. Catford/P.H. Regan 1AMQ
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 /2 and -1/ projection of S on z
W.N. Catford/P.H. Regan AMQ

87. 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 /2 /2
Electrons in an atom fill the allowed states
(a) beginning at the lowest energy
(b) obeying the Exclusion Principle
W.N. Catford/P.H. Regan AMQ

88. W.N. Catford/P.H. Regan 1AMQ
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 /2 /2 /2 /2 /2
W.N. Catford/P.H. Regan AMQ

89. 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.
W.N. Catford/P.H. Regan AMQ

90. W.N. Catford/P.H. Regan 1AMQ
 = 0
 = 1
Mean values of radius, for various n values
Hydrogen Atom
W.N. Catford/P.H. Regan AMQ

91. W.N. Catford/P.H. Regan 1AMQ

92. Note the notation-Principal Q.N followed by symbol for l
W.N. Catford/P.H. Regan AMQ

93. W.N. Catford/P.H. Regan 1AMQ
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)
W.N. Catford/P.H. Regan AMQ

94. W.N. Catford/P.H. Regan 1AMQ