Quantum Numbers, Electron Configurations, and Periodic Table

Quantum Numbers

By solving the equations of quantum mechanics for an atom, quantum numbers appear as a mathematical consequence. These describe the behavior of electrons in the atom.

• The principal quantum number, n: Represents an energy level. It can assume any positive integer (1, 2, ...). The first level is the lowest energy, and subsequent levels, increasingly distant from the nucleus, have greater energies.
• The orbital angular momentum quantum number, l: Determines the orbital shape and energy within each level. It takes values between 0 and n-1 inclusive.
• The magnetic quantum number, m_l: Describes the orientation of the orbital in space. Among other things, it explains the splitting of spectral lines when an external magnetic field is applied.
• The electron spin quantum number, m_s: Gives the intrinsic value of a property of the electron and other elementary particles: the spin. It determines if the electron is aligned parallel or antiparallel to an external magnetic field. It can have two values. Electrons with the same spin quantum number are said to have parallel or unpaired spins.

Electron Configurations

As we have seen, electrons are distributed around the nucleus at different levels and orbitals. To learn how to arrange them, we must take into account the following rules:

• Pauli Exclusion Principle: Two electrons in a single atom cannot have the same four quantum numbers. Thus, each orbital can only contain two electrons.
• Orbitals are filled according to their relative energies, starting with the lowest energy.
• Hund's Rule: Two orbitals with the same quantum numbers n and l have the same energy. For filling, one electron is first placed in each orbital, and then the orbitals are completed with the second electron.

The distribution of electrons in an atom at different levels and orbitals around the nucleus is called the electronic configuration or electronic structure.

The ground electronic configuration (or simply electron configuration) is the ground state or lowest energy state of the atom.

Any other configuration is called an excited electronic configuration and corresponds to an excited state of higher energy.

Orbitals are usually represented by boxes, and electrons by arrows.

Classification of Periodic Elements

In the early nineteenth century, the number of known elements was large enough to warrant classification.

In 1869, the Russian chemist Dmitri Mendeleev (1834-1907), and in 1870, the German chemist Lothar Meyer (1830-1895), independently presented the elements ordered by their atomic masses.

Mendeleev's periodic classification, more elaborate than Meyer's, contained all the elements known so far, ordered according to their atomic mass and the similarity of their properties.

Some elements had to be placed in reverse order of their atomic masses to respect their physical and chemical properties.

This problem was resolved after 1914, when Henry Moseley identified the elements by their atomic number. This allowed a final statement of the periodic law: When the elements are placed in order of increasing atomic number, a periodic repetition of many physical and chemical properties occurs.

The most common way to classify the chemical elements in the Periodic Table is called the long form. The columns, consisting of elements with similar properties, are called groups. The rows are called periods.

Periodic Properties

As we have seen, some physical and chemical properties vary regularly along the groups and periods. Therefore, they are called periodic properties.

Atomic Radius

• Within a group, the atomic radius increases with increasing atomic number. Descending from one period to another, the number of electronic levels increases, causing an increase in the size of the atom.
• Within a period, the atomic radius increases as the atomic number decreases. When the atomic number increases, the nuclear charge increases while the number of electronic levels remains constant. Thus, the attractive force increases on these levels, and the size of the atom decreases.

Ionic Radii

When an atom is ionized, its volume changes. If it loses electrons, it becomes a cation, and its radius decreases. If it gains electrons, it becomes an anion, and its radius increases.