MULTIELECTRON ATOMS

1
MULTIELECTRON ATOMS

• ELECTRON SPIN
• Electron has intrinsic angular momentum -
  spin it behaves as if it were spinning,
  i.e. rotating around its axis.
• rotating charge ? magnetic field - the electron
  is a magnetic dipole. S sh with s ?
• remember h h/2? is the unit of angular
  momentum
  
• (In units of angular momentum,) the electron has
  spin it is a member of the family of particles
  with half-integer spin, called Fermions.
• Fermions obey Pauli's exclusion principle.
• direction of spin is quantized, i.e. only
  certain directions are allowed. For spin
  1/2, only two directions are allowed - called
  up and down.
• PAULI'S EXCLUSION PRINCIPLE
• No quantum mechanical state can be occupied by
  more than one fermion of the same kind (e.g.
  more than one electron).
• MULTIELECTRON ATOMS
• The hydrogen atom, having only one electron, is a
  very simple system this is why Bohr's simple
  model worked for it.
• Complications in atoms with many electrons
• in addition to the force between electron and
  nucleus, there are also forces between the
  electrons
• shielding electrons in outer orbits are
  shielded from the force of the nucleus by
  electrons in the inner orbits.
• ? need to solve Schrödinger equation to describe
  multi-electron atoms.

2
QUANTUM NUMBERS

• Schrödinger equation applied to atom ?
• electron's energy, magnitude and direction of
  angular momentum are quantized (i.e. only certain
  values allowed)
• no well-defined orbit, only probability of
  finding electron at given position orbital
• the state of an electron is described by a set of
  four quantum numbers
• n, the principal quantum number
• l , the orbital quantum number
• ml lz, the orbital magnetic quantum number
• ms sz, the spin quantum number
• Meaning of quantum numbers
• the energy level of a state is determined by n
  and l
• most probable value of distance grows with n
• n 1,2,3,.
• l 0,1,2,3,, n -1 (i.e. n different values)
  measures magnitude of angular momentum in
  units of h value of l influences the energy and
  the shape of the orbital
• l 0 spherical
• l 1 dumbbell shaped,....
• ml 0, ?1, ?2, ? l , i.e. (2 l 1) different
  values specifies direction of angular momentum
  (gives component of angular momentum vector in
  specified direction) ? determines orientation of
  orbital
• ms ? ? denotes direction of spin ms ?
  spin up ms ? ? spin down
  

3
orbitals

• Orbital shapes

4
Electron shells

• Some definitions
• collection of orbitals with same n electron
  shell shells named K,L,M,N,..
• one or more orbitals with same n and l
  subshell
• spectroscopic notation for orbitals orbitals
  denoted by value of n and a letter code for the
  value of l
• l 0 s
• l 1 p
• l 2 d
• l 3 f
• l 4 g
• and alphabetic after that
• e.g. 2s refers to the subshell n2, 0
• number of electrons in the subshell is added as
  a superscript
• e.g. 2p6 means a configuration where 6
  electrons are in the subshell 2p, i.e the
  subshell with n 2 and l 1.
• PAULI EXCLUSION PRINCIPLE ?
• No two electrons in the same atom can have the
  same set of four quantum numbers
• ? the number of electrons in a given subshell is
  limited to 2x(2l 1) (factor of 2 is due to
  orientation of spin),
• number of electrons in a given shell is limited
  to 2n2 .
• ? in multi-electron atom, electrons cannot all
  sit in the lowest energy levels.

5
Electron configurations of the elements

• Periods 1,2, 3, 4
• period 5

6
Electron configuration, contd

• Period 6

7
Electron configuration, contd

• Period 7