Download multi-electron atoms

MULTI-ELECTRON ATOMS
„
ORBITAL APPROXIMATION
„
ELECTRON SPIN
„
PAULI EXCLUSION PRINCIPLE
„
AUFBAU BUILDING BLOCK PRINCIPLE
„
HUND’S RULE
„
PENETRATION AND SHIELDING, ZEFF
„
ENERGY LEVEL SPLITTING
„
ORBITAL FILLING AND ELECTRON
CONFIGURATION
MULTI-ELECTRON ATOMS
• Schrödinger equation was for only one e-.
• Electron-electron repulsion in multielectron atoms.
• Hydrogen-like orbitals (by approximation).
ELECTRON SPIN
MULTI-ELECTRON ATOMS
• The existence of more than one electron
requires us to consider three features not
relevant in the case of hydrogen:
– need for a 4th quantum number;
– a limit on the number of electrons allowed in a
given orbital; and
– a more complex set of orbital energy levels
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ROLE OF MAGNETISM
PAULI EXCLUSION
PRINCIPLE
• “No two electrons in an atom may have all
four quantum numbers alike”.
Paramagnetic
Diamagnetic
unpaired electrons
all electrons paired
2p
• An atomic orbital can hold a maximum of
two electrons. These must have opposite
spins.
2p
ENERGY OF ORBITALS IN A
SINGLE ELECTRON ATOM
Energy only depends on principal quantum number n
ENERGY OF ORBITALS IN A
MULTI-ELECTRON ATOM
Energy depends on n and l
n=3
n=3 l = 2
n=2
En = -RH (
1
n2
n=3 l = 1
)
n=2 l = 0
n=2 l = 1
n=1
n=1 l = 0
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FACTORS AFFECTING
ATOMIC ORBITAL ENERGIES
THE EFFECT OF NUCLEAR
CHARGE ON ORBITAL ENERGY
• The Effect of Nuclear Charge (Zeffective):
– Higher nuclear charge lowers orbital energy (stabilizes the system)
by increasing nucleus-electron attractions.
• The Effect of Electron Repulsions (Shielding):
– Additional electron in the same orbital:
• An additional electron raises the orbital energy through
electron-electron repulsions.
– Additional electrons in inner orbitals:
• Inner electrons shield outer electrons more effectively than do
electrons in the same sublevel.
EFFECTIVE NUCLEAR CHARGE
SHIELDING
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THE EFFECT OF
ORBITAL SHAPE
Radial probability plots for the
1s, 2s and 2p orbitals. The 1s
electrons effectively shield
both the 2s and 2p electrons
from the nucleus. The 2s
orbital is more penetrating
than the 2p orbital.
PENETRATION AND
SHIELDING
Penetration of 2s
DARTBOARD ANALOGY
Zeff is the effective nuclear charge.
ELECTRON
CONFIGURATIONS
Rules for assigning electrons to orbitals:
• Aufbau process:
– Build up and minimize energy. The lowest energy
(most stable) orbitals are occupied first.
• Pauli exclusion principle:
– No two electrons can have all four quantum numbers
alike
• Hund’s rule:
– When degenerate orbitals are available, electrons
initially occupy these orbitals singly, and with parallel
spins.
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ORBITAL ENERGIES
ORDER OF ORBITALS (FILLING) IN
MULTI-ELECTRON ATOMS
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
Hund’s rule: The most stable arrangement of
electrons in subshells is the one with the greatest
number of parallel spins.
AUFBAU PROCESS AND
HUND’S RULE
Ne97
C
N
O
F
6
810
electrons
electrons
electrons
2
2
2
22p
5
246
3
C
N
2s222p
Ne
O
F 1s
1s2s
5
FILLING THE p ORBITALS
FILLING THE d ORBITALS
N
O
F
Ne
1s
2s
2p
ELECTRON CONFIGURATION
ELECTRON CONFIGURATIONS AND
THE PERIODIC TABLE
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Problem Number 83:
Wolfgang Pauli
Wolfgang Paul
Problem No. 84:
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