Atomic Structure and Atomic Radiation - Atoms, Radiation, and-Radiation Protection - page 35

repeated with the actinide elements from Z = 90 (Th) to Z = 103 (Lr), in which the
5f subshell is being filled.
The picture given here is that of an independent-electron model of the atom,
in which each electron independently occupies a given state. In reality, the atomic
electrons are indistinguishable from one another and an atomic wave function is
one in which any electron can occupy any state with the same probability as any
other electron. Moreover, hybrid atomic states of mixed configurations are used to
explain still other phenomena (e.g., the tetrahedral bonds in CH 4 ) .
2.8
Molecules
Quantum mechanics has also been very successful in areas other than atomic
structure and spectroscopy. It has also explained the physics of molecules and
condensed matter (liquids and solids). Indeed, the nature of the chemical bond
between two atoms, of either the same or different elements, is itself quantum
mechanical in nature, as we now describe.
Consider the formation of the H 2 molecule from two H atoms. Experimentally, it
is known from the vibrational spectrum of H 2 that the two protons' separation os-
cillates about an equilibrium distance of 0.74 Å and the dissociation energy of the
molecule is 4.7 eV. The two electrons move very rapidly about the two nuclei, which,
by comparison, move slowly back and forth along the direction between their cen-
ters. When the nuclei approach each other, their Coulomb repulsion causes them
to reverse their directions and move apart. The electrons more than keep pace and
move so that the separating nuclei again reverse directions and approach one an-
other. Since the electrons move so quickly, they make many passes about the nuclei
during any time in which the latter move appreciably. Therefore, one can gain con-
siderable insight into the structure of H 2 and other molecules by considering the
electronic motion at different fixed separations of the nuclei (Born-Oppenheimer
approximation).
To analyze H 2 , we begin with the two protons separated by a large distance R ,
as indicated in Fig. 2.5(a). The lowest energy of the system will then occur when
each electron is bound to one of the protons. Thus the ground state of the H 2
system at large nuclear separations is that in which the two hydrogen atoms, H A
and H B , are present in their ground states. We denote this structure by writing
(H A 1, H B 2), indicating that electron number one is bound in the hydrogen atom
H A and electron number two in H B . Another stable structure at large R is an ionic
one, (H A 12 - ,H B ), in which both electrons orbit one of the protons. This structure
is shown in Fig. 2.5(b). Since 13.6 eV is required to remove an electron fromH and
its binding energy in the H - ion is only 0.80 eV, the ionic structure in Fig. 2.5(b)
has less binding energy than the natural one in (a). In addition to the states shown
in the figure, one can consider the same two structures in which the two electrons
are interchanged, (H A 2, H B 1) and (H A 21 - ,H B ).