The statement that core electrons occupy orbitals with high symmetry while valence electrons occupy orbitals with low symmetry is not accurate. In reality, the symmetry of electron orbitals is determined by the shape of the atomic or molecular system and is not directly linked to whether the electrons are core or valence electrons.
Symmetry in atomic and molecular systems is described by mathematical models such as symmetry groups and symmetry operations. These models help us understand and classify the arrangement of orbitals and the overall shape of molecules.
In an atom, core electrons occupy the innermost energy levels, closer to the nucleus. The specific arrangement of these electrons is determined by the atomic structure and the rules of electron configuration. The core electrons do not generally participate in chemical reactions, and their symmetry properties depend on the particular atom.
On the other hand, valence electrons are found in the outermost energy levels of an atom and are responsible for chemical bonding and reactivity. The valence electrons occupy a variety of orbitals, which can have different shapes and symmetries depending on the atom or molecule involved. The symmetry properties of valence orbitals are dictated by the overall molecular symmetry, bonding interactions, and the specific arrangement of atoms in the molecule.
In summary, the symmetry of electron orbitals, whether they are core or valence electrons, depends on the molecular or atomic system in question and is not directly determined by their core or valence nature.