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By the end of this section, you will be able to:
  • Derive the predicted ground-state electron configurations of atoms
  • Identify and explain exceptions to predicted electron configurations for atoms and ions
  • Relate electron configurations to element classifications in the periodic table

Having introduced the basics of atomic structure and quantum mechanics, we can use our understanding of quantum numbers to determine how atomic orbitals relate to one another. This allows us to determine which orbitals are occupied by electrons in each atom. The specific arrangement of electrons in orbitals of an atom determines many of the chemical properties of that atom.

Orbital energies and atomic structure

The energy of atomic orbitals increases as the principal quantum number, n , increases. 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. [link] depicts how these two trends in increasing energy relate. The 1 s orbital at the bottom of the diagram is the orbital with electrons of lowest energy. The energy increases as we move up to the 2 s and then 2 p , 3 s , and 3 p 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 3 d orbital is higher in energy than the 4 s orbital. Such overlaps continue to occur frequently as we move up the chart.

A table entitled, “Subshell electron capacity,” is shown. Along the left side of the table, an upward pointing arrow labeled, “E,” is drawn. The table includes three columns. The first column is narrow and is labeled, “2.” The second is slightly wider and is labeled, “6.” The third is slightly wider yet and is labeled, “10.” The fourth is the widest and is labeled, “14.” The first column begins at the very bottom with a horizontal line segment labeled “1 s.” Evenly spaced line segments continue up to 7 s near the top of the column. In the second column, a horizontal dashed line segment labeled, “2 p,” appears at a level between the 2 s and 3 s levels. Similarly 3 p appears at a level between 3 s and 4 s, 4 p appears just below 5 s, 5 p appears just below 6 s, and 6 p appears just below 7 s. In the third column, a dashed line labeled, “3 d,” appears just below the level of 4 p. Similarly, 4 d appears just below 5 p and 5 d appears just below 6 p. Six d however appears above the levels of both 6 p and 7 s. The far right column entries begin with a dashed line labeled, “4 f,” positioned at a level just below 5 d. Similarly, a second dashed line segment appears just below the level of 6 d, which is labeled, “5 f.”
Generalized energy-level diagram for atomic orbitals in an atom with two or more electrons (not to scale).

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 5 p orbitals fill immediately after the 4 d , and immediately before the 6 s . 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 (1 s through 3 p ), 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.

Questions & Answers

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Practice Key Terms 7

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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