Ordering of Outermost Levels
Three aspects determine the
structure of the periodic table.
1.
2.
3.
Energetic
ordering
of
outermost subshell in Hartree
theory.
Limited capacity of subshells
due to the exclusion principle.
The periodic table considers
atoms to be their ground
states. Construct the ground
state configuration using the
“Aufbau-principle“: start with
the lowest energy subshell
and “build up” to the next
lowest subshell and so forth.
For a given n, the outer subshell with the lowest l has the lowest energy.
For a given l, the outer subshell with the lowest n has the lowest energy.
Periodic Table
1s!2s!2p!3s!3p!4s!3d!4p!5s!4d!5p!6s!4f!5d!6p!7s!…
e.g. Nitrogen : 1s22s22p3
shorter:
[He]2s22p3
Titanium : 1s22s22p63s23p64s23d2
[Ar]4s23d2
Change of Ordering with Z
Outer-shell
energy
ordering
Inner-shell
energy
ordering
Schematic representation
of subshell energies as a
function of the atomic
number Z.
Energy scale is non-linear
and changes with Z !
Key message:
Ordering of subshell energy
levels changes as subshells
become occupied.
He Ne
Ar
Kr
Xe
Ionization Energies
Ionization energy: Minimum energy required to detach one electron from an atom
(or a molecule).
e.g.
Ar ! Ar+ + e-
(15.8 eV)
1s22s22p63s23p6
! 1s22s22p63s23p5
e.g.
K ! K + + e-
(4.3 eV)
1s22s22p63s23p64s1 ! 1s22s22p63s23p6
X-Ray Line Spectra
X-ray: Accelerated electrons (kinetic energy ~104
eV) hit a metallic cathode, producing X-ray
emissions.
Broad distribution “Bremsstrahlung”
radiation) is due to scattering by nuclei.
(braking
Sharp peaks due to collisions,
which causes tightly bonded
metal atom electrons to be
ejected. Radiation at defined
frequencies is produced by
emission as higher lying
electrons drop in energy to fill
the hole.
Selection rules apply:
"l=±1 and "j=0, ±1
Note: this figure depicts the transitions of “holes”. Thus,
the diagram is upside down to how we normally show
atomic energy diagrams. (energies are positive).
Moseley’s Formula
Moseley found in 1913, that X-ray transitions (specifically K#) vary smoothly with
the nuclear charge Z.
Empirical formula (based on Bohr’s model)
Rewrite to:
…is linear in Z.
The constant a captures electronic shielding
of the nuclear charge.
The work is particular significant because it established the order of elements in the
periodic table. This lead to some corrections to the table (e.g. Co vs. Ni) and also
identified several gaps (not yet discovered elements, e.g. Tc, Pm, Th …).