Transcript of 09) Introduction 9
- provides estimates of the Effective nuclear charges, Zeff,
experienced by electrons in different atomic orbitals.
- based on experimental ionization energies
Zeff = Z - S
S = screening (or shielding) constant
Values of S may be estimated as follows:
1. Write out the electronic configuration of the
element in the following order and groupings:
2. Electrons in any group higher in this sequence
than
the electron under consideration contribute
nothing to S.
3. Consider a particular electron in an ns or
np orbital:
(i) Each of the other electrons in the (ns, np)
group contributes S = 0.35.
(ii) Each of the electrons in the (n - 1) shell
contributes S = 0.85.
(iii) Each of the electrons in the (n - 2) or lower
shells
4. Consider a particular electron in an nd or
nf orbital:
(i) Each of the other electrons in the (nd, nf ) group
contributes S = 0.35.
(ii) Each of the electrons in a lower group than the
one being considered contributes S = 1.00.
Application of Slater’s rules
Confirm that the experimentally observed electronic
configuration of K, 1s2 2s2 2p6 3s2 3p6 4s1, is
energetically more stable than the configuration 1s2
2s2 2p6 3s2 3p6 3d1.
The effective nuclear charge experienced by the 4s
electron for the configuration
1s2 2s2 2p6 3s2 3p6 4s1 is:
Zeff = Z - S
= 2.20
For the configuration
1s2 2s2 2p6 3s2 3p6 3d1 is:
Zeff = Z - S
= 1.00
Electronic Configurations of Transition Metals, including
Lanthanides and Actinides
Solid lines surrounding elements designate filled or half-filled d
or f subshells.
Dashed lines surrounding elements designate irregularities in
orbital filling.
Schematic Energy Levels for Transition Elements (TE)
a) Schematic interpretation of electronic configurations for
TE in terms of interorbital repulsion and trend in subshell
energies.
b) A similar diagram for ions
The diagram shows that s electrons are removed before d
electrons.
The electrons with highest n are always removed first in the
formation of ions from the transition elements.
Ex. Sc+: 4s1 3d1 not 4s2
Ex. Cr: 4s1 3d5 not 4s2 3d4
Exercises:
1. Use Slater’s rules to estimate values of Zeff for (a) a 4s and
(b) a 3d electron in a V atom.
2. Based on Zeff values, which is the possible valence
configuration of the ground state of a V+ ion, 3d3
4s1 or 3d2
4s2.
Ionization energies, IE
The first ionization energy, IE1, of an atom is the internal energy
change at 0 K, !U(0 K), associated with the removal of the
first
valence electron in the gas phase.
X(g) " X+(g) + e-
The second ionization energy, IE2 is based on the equation
X+(g) " X+2(g) + e-
Apparent repeating patterns and some features of IEs:
- the high values of IE1 associated with the noble gases
- the very low values of IE1 associated with the group 1
elements
- the discontinuity in values of IE1 on going from an element in
group 15 to its neighbour in group 16
- the decrease in values of IE1 on going from an element in group 2
or 12 to its neighbour in group 3 or 13
- the rather similar values of IE1 for a given row of d-block
elements.
m i n o r c h a n g e
m
a
j o
The break in the trend at B is attributed to occupation of
new p orbital that has most of its electron density farther away
from the nucleus than the other electrons.
At the fourth p electron, at O, a similar drop in ionization energy
occurs.
The new (8th) electron shares an orbital with one of the previous
2p electrons.
The pairing energy, or repulsion between two electrons in the same
region of space, reduces the ionization energy.
Filled and half-filled shells are often referred to as possessing a
‘special stability’.
The key is actually the exchange energy, K!
Consider two electrons in different orbitals.
The repulsion between the electrons if they have anti parallel
spins is greater than if they have parallel spins
e.g. for a p2 configuration:
versus
Electron affinities
The first electron affinity (EA1) is minus the internal
energy change (EA = -!U) for the gain of an electron by a
gaseous
atom.
Y(g) + e " Y-(g)
The second electron affinity of atom Y is defined for process
Y-(g) + e " Y-2(g)
The attachment of an electron to an atom is usually
exothermic.
The pattern of electron affinities with changing Z is similar to
that of the IEs, but with smaller absolute numbers.
The noble gases have smallest EAs.
Covalent and Ionic Radii (Size)
As the nuclear charge increases, the electrons are pulled in toward
the center of the atom, and the size of any particular
orbital (thus the size of atom) decreases.
On the other hand, as the nuclear charge increases, more electrons
are added to the atom and their mutual repulsion keeps the outer
orbitals large.
Opposing factors:
Anions are generally larger than cations with similar numbers of
electrons (F -
and Na+ differ only in nuclear charge, but the radius of
fluoride is 37% larger)
126
170
O2-
S2-
8
16
The radius decreases as nuclear charge increases for ions
with the same electronic structure, such as O2-, F-, Na+, and Mg+2,
with a much larger change for the cations.
Within a family, the ionic radius increases as Z increases because
of the larger number of electrons in the ions and, for the same
element, the radius decreases with increasing charge on the
cation.
861012Mg2+
1161011Na+
119109F-
126108O2-
Crystal Radius and Total Number of Electrons
Crystal Radius and Ionic Charge
2075452Te2-
1843634Se2-
1701816S2-
126108O2-