Transcript Chapter 7

POLYELECTRONIC ATOMS
PERIODICITY OF ELEMENTS
(Part 2; Sec 9-13)
Electronic Configurations
Periodic Trends
POLYELECTRONIC ATOMS
• We will extend the 1-electron results
(energy eqn, quantum numbers, AO shapes,
etc) to the polyelectronic atom (atoms with
> 1 electron).
• Electrostatic forces in the poly-e atom
include nucleus-electron attractions and
electron-electron repulsions.
POLYELECTRONIC ATOMS
• The e-e repulsions prevent the exact
solution of the Schrodinger Eqn for helium
and above. (Electron Correlation Problem)
• The presence of > 1 electron results in
partial shielding of the nuclear charge. I.e.
Zeff = Zactual – electron shielding
POLYELECTRONIC ATOMS (2)
• Also, because of the difference in AO shape
for different ℓ values, electrons with the
same n but in different subshells (ℓ)
experience different attractive forces to the
nucleus.
• As the electron spend more time near the
nucleus, its energy becomes more negative
(is held more tightly).
POLYELECTRONIC ATOMS (3)
• For the 1-e atom, AO energy depends only on n.
As n increases, energy increases (becomes less
positive). So AOs can be ordered from low to
high energy: 1s < [2s, 2p] < [3s, 3p, 3d]... Fig
7.18 (note degeneracy).
• For the many-electron atom, energy depends on n
and ℓ: 1s < 2s < 2p < 3s < 3p, etc. See Fig 7.22
(note that the degeneracy is partially lifted).
Figure 7.22 The Orders of the Energies
of the Orbitals in the First Three Levels
of Polyelectronic Atoms
Figure 7.18 Orbital Energy Levels
for the Hydrogen Atom
PERIODIC TABLE
• Most powerful tool in the study of
chemistry.
• Elements are placed in order by Z.
• Used to predict undiscovered elements and
their properties. Tables 7.3, 7.4
• Quantum mechanics explains the
appearance of the PT and also periodicity of
atomic properties
Table 7.3 Comparison of the Properties of
Germanium as Predicted by Mendeleev and
as Actually Observed
Table 7.4 Predicted Properties of
Elements 113 and 114
From H to Polyelectronic Atoms
• In H, AOs with the same n have the same E.
• In multielectron atoms,
– For a given set of QNs, orbital energies are
lower than in H (larger Z value).
– AOs with the same n value but different ℓ have
different energies (nondegenerate).
– orbitals with the same n and ℓ have the same E.
– 3d and 4s have similar energies
DETERMINING ELECTRONIC
CONFIGURATIONS
• What is the arrangement of electrons in the
atom? What rules govern these
arrangements or electronic configurations?
• There are four quantum numbers [n, ℓ, mℓ,
ms] that have defined relationships to each
other and that are used to define a set of
atomic orbitals (AOs) that electrons fill.
ELECTRON CONFIG. (2)
• Aufbau (building-up) Principle determines
the order of filling AOs; i.e. the electronic
configuration of the atom. The electrons fill
the AOs in order of lowest energy (most
negative) to highest energy.
• The atom’s ground state is the one that has
the lowest energy. All others are called
excited states.
ELECTRON CONFIG. (3)
• Pauli Exclusion Principle: The maximum
number of electrons per orbital is 2 because
no two electrons can have the same 4 q.n.
values in an atom. Since there are two spin
states (up/down; α/β; ↑/↓), the max AO
occupancy number is 2.
ELECTRON CONFIG. (4)
• Hund’s Rule: When filling orbitals of
identical energy, fill the empty orbitals with
one electron before pairing them up; I.e.
maximize number of unpaired spins. This
produces the lowest energy configuration.
• There are exceptions: e.g. 4s fill before 3d;
Cr, Cu have a single 4s electron and fullyor half-filled 3d orbitals (extra stability).
ELECTRON CONFIG. (5)
• Electron configs. of cations (remove from
largest n AO) and anions (add according to
Aufbau Prin.)
• Ways to depict electronic config:
– AO list with # electrons as superscripts
– orbital diagram
– noble gas core for [core electrons] + valence
electrons (VE). Fig 7.25
ELECTRON CONFIG. (6)
• Valence electrons are the outermost
electrons and the most important ones in
chemical bonding.
• Atoms in the same group have the same VE
configuration.
ELECTRON CONFIG. (7)
• Learn electron config.s through Kr; use PT
to identify VEs of atoms beyond Kr.
• Count unpaired electrons
• Fig 7.27 shows how the Periodic Table can
be used to determine electron config.
– Main Group: s- and p- block elements
– Transition Group: d-block elements
– Lanthanide and Actinide: f-block element
Problems
• 65, 68, 70, 72, 74, 76, 80, 82
Figure 7.27 The Orbitals Being Filled for
Elements in Various Parts of the Periodic
Table
Figure 7.28 The Periodic Table with
Atomic Symbols, Atomic Numbers, and
Partial Electron Configurations
PERIODIC LAW
• Now we can see how the electronic
configurations of atoms lead to periodicity
of elements and form the basis for chemical
and physical properties of elements.
• PERIODIC LAW: When the elements are
arranged according to Z, their physical and
chemical properties vary periodically,
regularly and predictably.
PERIODIC LAW (2)
• Elements in the nth A-Group (Main Group)
have n electrons in the valence (outermost
occupied) shell.
• Elements in the nth period have n as the
principal QN of its valence shell.
PERIODICITY OF ATOMIC
PROPERTIES
• Ionization Energy: energy required to
remove one electron from gaseous atom or
ion (kJ/mol)
–
–
–
–
–
Fig 7.7.30, 7.31; Table 7.5, 7.6
Atom (g) -----> Ion+(g) + electron, I1
Across row, I1 increases WHY?
Down group, I1 decreases WHY?
I1 is highest in upper RH corner
Figure 7.30 The Values of First Ionization
Energy for the Elements in the First Six
Periods
Table 7.5 Successive Ionization
Energies in kJ/mol for the Elements
in Period 3
PERIODICITY OF ATOMIC
PROPERTIES (2)
• Electron Affinity: energy associated with
addition of electron to gaseous species
(kJ/mol)
–
–
–
–
–
Fig 7.32, Table 7.7
Atom (g) + electron -----> Ion- (g)
Note most EA values are negative (exothermic)
Trend across row and down group? And WHY?
EA is highest in upper RH corner
Figure 7.32 The Electron Affinity Values
for Atoms Among the First 20 Elements that
Form Stable, Isolated X- Ions
PERIODICITY OF ATOMIC
PROPERTIES (3)
• Atomic Radius: measure of atomic size
– Atomic radii based on covalent or metallic
bond distances (pm)
– Figs 7.34
– Trend across row and down group? And WHY?
– Atomic size is largest in lower LH corner
– Note that size of cation < size of neutral atom
– But size of anion > size of neutral atom
Figure 7.34
Atomic Radii
(in
Picometers)
for Selected
Atoms
PERIODICITY OF ATOMIC
PROPERTIES (4)
• Metallic Character
– Form cations, small I
– lower LH corner
– alkali metals
• Nonmetallic Character
– Form anions, large I
– upper RH corner
Problems
• 85, 90, 96,