topic 7 Flashcards
(14 cards)
Schrödinger equation for many electron atoms
- need to think ab attractive and repulsive interactions
consequence of electron to electron repulsive potential energy term in SE
- no longer possible to solve the SE equation exactly
- need to make orbital approximations to simplify equation
orbital approximation
- assume total wave function describing all electrons can be understood as a product of one - electron wave functions
- assume each one electron wave function is similar to atomic orbitals determined for H - atom with the same quantum numbers
- assume each electron moves within a time - average charge distribution
orbital energy of many electron atoms depend on
- n and l
- but for hydrogenic atom just depends on n
one way to deal with non - hydrogenic transition energies is to
- define them with an effective principle number (Vnl)
- Vnl = n - quantum defect (measure of shielding)
- substitute Vnl into expression for transition energy of hydrogen
core electrons within the closed shells have
net zero orbital and scion angular momenta
total spin angular momentum vector for 2 unpaired electrons is
- s1 + s2
- it is quantised in the same manner as individual spin angular momentum
- s is restricted to integer values for Ana even number of unpaired electrons and half integer values for an odd number of unpaired electrons
- for 2 unpaired electrons the possible values for S are
1 and 0
total spin angular momentum has 2S + 1 quantised components along the z- direction
s, s-1 ….. -s
- S= 1 known as triplet state, three allowed projections
in general allowed values of total orbital angular momentum quantum number are given by
clebsch - gordan series
max l = l1 + l2 and min l = l1-l2
all in-between allowed
Russell saunders coupling scheme
- three different types of interactions between unpaired electrons that lead to states of the same electronic configuration having different energies
1. spin correlation - there is least electronic repulsion when spins of unpaired electrons are aligned parallel to maximise S
2. coupling of orbital angular momentum - state of highest L has maximum alignment of individual orbital angular momenta and the lowest energy
3. spin orbit coupling - the interaction between the spin and orbital angular momenta of the unpaired electrons
order of important for Russell - saunders coupling scheme for lighter atoms (first row of periodic table)
spin correlation is greater than or equal to coupling of orbital angular momentum which is a lot greater than spin orbit coupling
micro states
- way of looking at how one or more electrons can occupy a set of orbitals by following the magnetic quantum number
- equivilant to number of combinations of magnetic quantum number
micro state coupling Mj
- microstate l + microstate s
