Final answer:
It is true that half-filled and fully-filled orbitals have lower energies and higher stability. The anomalies in electron configurations of elements like Cr and Cu support this, where electrons are repositioned to achieve half-filled or filled subshells that confer greater stability. Bonding orbitals also indicate lower energy configurations enhancing system stability.
Step-by-step explanation:
The statement that half-filled and fully-filled orbitals have lower energies (higher stability) than other states is TRUE. Half-filled (such as in the element chromium) and completely filled subshells (such as in copper) are associated with greater stability. This stability is evident in the electron configuration anomalies of certain elements, where an electron may shift from a higher energy 4s orbital to a 3d orbital to achieve this preferred stability. In the case of Cr, the stability of the half-filled 3d subshell is such that one 4s electron is promoted to the 3d orbital. Similarly, in the case of Cu, one electron from 4s is promoted to the 3d orbital to achieve a filled 3d subshell, thus lowering the energy of the system and contributing to the atom's ground state stability.
In addition to these specific exceptions, the formation of bonding molecular orbitals generally results in a lower energy state than the separate atomic orbitals that combined to form them. The specific shapes of the ground-state wave functions, which have high charge densities at points between bonding nuclei, also contribute to the stabilization of the system.