Page 264 - Instant notes

Physical chemistry 250

The kink in the ionization energy trend between the elements Be and B in the second
period, and between Mg and Al in the third period, arises because the outermost electrons
in B and Al occupy p orbitals, which are less strongly bound (less penetration into the
core), than the electrons in the s orbitals of the preceding elements. The additional slight
kink in ionization energy between N and O is due to the extra electron-electron repulsion
that occurs when one of the 2p orbitals becomes doubly occupied. This effect is less
pronounced between P and S in period 3 because their orbitals are larger and more
diffuse.

Atomic transitions and selection rules

Each electron configuration of an atom (also called a state or a level) possesses a well-
defined energy. The movement (or transition) of electrons between any pair of states is
associated with a quantum of energy exactly equal to the difference in energy between
the initial and final state, ∆E=hv. This is the basis of atomic spectroscopy. Examples
include the Rydberg series in the hydrogen atom emission spectrum (see Topic G5) or
the spectra of hydrogen-like atoms (this Topic).
Not all transitions between all possible pairs of energy levels are allowed. The
selection rule for atomic transitions is, ∆l=±1 and ∆m l=0, ±1. The selection rules arise
because angular momentum must be conserved. A photon of electromagnetic radiation
has one unit of angular momentum so the angular momentum of the electron involved in
the transition must change by one unit whenever a photon is emitted or absorbed.
Therefore an s electron (l=0) cannot make a transition into a d orbital (l=2), or υice υersa,
because the photon cannot provide (or carry away) two units of angular momentum.

Spectra of hydrogen-like atoms

The electron configurations of all alkali metal atoms consist of a single electron in an s
orbital surrounding filled core shells, e.g. Li (Z=3), Na (Z=11), have electron
1
1
configurations [He]2s , [Ne]3s , etc. These atoms are termed hydrogen-like since the
single valence electron is comparatively unaffected by the core electrons and behaves
similarly to a hydrogenic atom in which a single electron experiences a Coulomb
potential only from a positive core. The shielding of the nuclear charge by the core
electrons is incorporated into the energy level formula of hydrogenic atoms using an
effective nuclear charge Z effe. The energy level diagram for Li is shown in Fig. 4 and is
similar to the energy level diagram for hydrogen (Topic G5) except that the different
penetration of sub-shells into the core removes the degeneracy of the sub-shells.
The similar pattern of energy levels of alkali metal atoms produces spectra similar in
appearance to the Rydberg series of the hydrogen atom emission spectrum (Topic G5).
Transitions allowed by the atomic selection rule are marked on Fig. 4. The series of
frequencies corresponding to transitions between different sub-shells were historically
called sharp, principal, diffuse and fine. The first letters of these descriptive terms
account for the modern nomenclature of the different types of atomic orbital: s, p, d and
f. The energy levels giving rise to each series are labeled S, P, D and F. The transition