Spin-Orbit Effect

1
Spin-Orbit Effect

• In addition to its motion about the nucleus, an
  electron also has an intrinsic angular momentum
  called spin
• similar to the earth moving about the sun and
  spinning on its axis
• orbital angular momentum L r x p
• spin angular momentum S cannot be written in
  terms of coordinates
• total angular momentum of the electron is J L
  S
• if L // S, then JLS
• if L antiparallel S, then JL-S
• in quantum mechanics angular momentum is
  quantized and has magnitude given by

• Electrons have spin s1/2 and are fermions

2
Spin-Orbit Effect

• Consider a state with l1 and s1/2 . What are
  the possible values of j
• j 1-1/21/2 and j11/2 3/2

• Quantum states with the same values of n and l
  but different j have small energy differences gt
  fine structure due to spin

3
Electron moving about a proton with angular
momentum L
Magnetic field due to apparent motion of charged
proton is up
When electron spin is up, its magnetic moment is
down and energy is higher
When electron spin is down, its magnetic moment
is up and energy is lower
E L.S
4
Fine Structure
n2 l0,1 gt S or P 2S level has j1/2 2P level
has j1/2 or 3/2
n1 l0 gt 1S j1/2
E L.S
5
Periodic Table

• Atoms with more than one electron cannot be
  solved exactly
• assume the Z electrons do not interact with one
  another but rather only see the nucleus with
  charge Z
• the state of each electron is described by four
  quantum numbers
• n, l ,m and ms
• the fourth number, ms ?1/2 is the spin
  quantum number
• l 0, 1, 2, 3, 4, 5, correspond to
• s p d f g h
• Pauli principle no two electrons can have the
  same set of values of n, l ,m and ms
• eg. Hydrogen (Z1) has only one electron
• lowest energy state has n1 gt l0 gt m0 and ms
  ?1/2
• 1s state

6
Periodic Table

• Helium ( Z2) has two electrons
• we can put both in the n1 energy state with l0
  and m0 but with opposite spin
• hence total spin is zero, total orbital angular
  momentum is zero, and total (spin orbital)
  angular momentum is zero gt j0.
• Denote as 1s2
• Lithium (Z3) has three electrons
• first two as in He but third must go into n2
  level gtl0 or 1
• l0 has lower energy
• denote as 1s22s
• Beryllium (Z4) has 1s22s2 electron
  configuration

7
Periodic Table

• An s state (l0) can hold a maximum of 2
  electrons
• a p state (l1) can hold a maximum of 6
  electrons
• a d state (l2) can hold a maximum of 10
  electrons
• in general, 2(2l1) states
• neon (Z10) has ten electrons
• configuration is 1s22s22p6
• Hunds rules

• argon (Z18) has eighteen electrons
• configuration is 1s22s22p63s23p6

E L.S
8
configurations
Periodic table