Orbital Energies and Atomic Structure

The energy of atomic orbitals increases as the principal quantum number, n, increases. As our n increases, the size of the orbital increases and the electrons spend more time farther from the nucleus. Thus, the attraction to the nucleus is weaker and the energy associated with the orbital is higher (less stabilized). In any atom with two or more electrons, the repulsion between the electrons makes energies of subshells with different values of l differ so that the energy of the orbitals increases within a shell in the order s < p < d < f. This is due to the fact that there is less electron density found close to the nucleus due to an increased number of planar nodes (electrons are less penetrating). The figure below depicts how these two trends in increasing energy relate. The 1s orbital at the bottom of the diagram is the orbital with electrons of lowest energy. The energy increases as we move up to the 2s and then 2p, 3s, and 3p orbitals, showing that the increasing n value has more influence on energy than the increasing l value for small atoms. However, this pattern does not hold for larger atoms. The 3d orbital is higher in energy than the 4s orbital. Such overlaps continue to occur frequently as we move up the chart [Curious to understand why this is?].

Generalized energy-level diagram for atomic orbitals in an atom with two or more electrons (not to scale).
Curious to understand why 3d is higher in energy than 4s? Click here!

Electrons in successive atoms on the periodic table tend to fill low-energy orbitals first. Thus, many students find it confusing that, for example, the 5p orbitals fill immediately after the 4d, and immediately before the 6s. The filling order is based on observed experimental results, and has been confirmed by theoretical calculations. As the principal quantum number, n, increases, the size of the orbital increases and the electrons spend more time farther from the nucleus. Thus, the attraction to the nucleus is weaker and the energy associated with the orbital is higher (less stabilized). But this is not the only effect we have to take into account. Within each shell, as the value of l increases, the electrons are less penetrating (meaning there is less electron density found close to the nucleus), in the order s > p > d > f. Electrons that are closer to the nucleus slightly repel electrons that are farther out, offsetting the more dominant electron–nucleus attractions slightly (recall that all electrons have −1 charges, but nuclei have +Z charges). This phenomenon is called shielding and will be discussed in more detail in the next section. Electrons in orbitals that experience more shielding are less stabilized and thus higher in energy. For small orbitals (1s through 3p), the increase in energy due to n is more significant than the increase due to l; however, for larger orbitals the two trends are comparable and cannot be simply predicted. We will discuss methods for remembering the observed order.

The arrangement of electrons in the orbitals of an atom is called the electron configuration of the atom. We describe an electron configuration with a symbol that contains three pieces of information (Figure 2):

  1. The number of the principal quantum shell, n,
  2. The letter that designates the orbital type (the subshell, l), and
  3. A superscript number that designates the number of electrons in that particular subshell.

For example, the notation 2p4 (read “two–p–four”) indicates four electrons in a p subshell (l = 1) with a principal quantum number (n) of 2. The notation 3d8 (read “three–d–eight”) indicates eight electrons in the d subshell (i.e., l = 2) of the principal shell for which n = 3.

The diagram of an electron configuration specifies the subshell (n and l value, with letter symbol) and superscript number of electrons.