Physics Textbooks Boundless Physics Atomic Physics Multielectron Atoms
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Multielectron Atoms

Atoms with more than one electron are referred to as multielectron atoms.

Learning Objective

  • Describe atomic structure and shielding in multielectron atoms

Key Points

    • Hydrogen is the only atom in the periodic table that has one electron in the orbitals under ground state.
    • In multielectron atoms, the net force on electrons in the outer shells is reduced due to shielding.
    • The effective nuclear charge on each electron can be approximated as: $Z_\text{eff} = Z - \sigma$, where $Z$ is the number of protons in the nucleus and $\sigma$ is the average number of electrons between the nucleus and the electron in question.

Terms

  • valence shell

    the outermost shell of electrons in an atom; these electrons take part in bonding with other atoms

  • electron shell

    The collective states of all electrons in an atom having the same principal quantum number (visualized as an orbit in which the electrons move).

  • hydrogen-like

    having a single electron

Full Text

Multielectron Atoms

Atoms with more than one electron, such as Helium (He) and Nitrogen (N), are referred to as multielectron atoms. Hydrogen is the only atom in the periodic table that has one electron in the orbitals under ground state.

In hydrogen-like atoms (those with only one electron), the net force on the electron is just as large as the electric attraction from the nucleus. However, when more electrons are involved, each electron (in the $n$-shell) feels not only the electromagnetic attraction from the positive nucleus, but also repulsion forces from other electrons in shells from '1' to '$n$'. This causes the net force on electrons in the outer electron shells to be significantly smaller in magnitude. Therefore, these electrons are not as strongly bonded to the nucleus as electrons closer to the nucleus. This phenomenon is often referred to as the Orbital Penetration Effect. The shielding theory also explains why valence shell electrons are more easily removed from the atom.

Electron Shielding Effect

A multielectron atom with inner electrons shielding outside electrons from the positively charged nucleus

The size of the shielding effect is difficult to calculate precisely due to effects from quantum mechanics. As an approximation, the effective nuclear charge on each electron can be estimated by: Zeff=Z−σZ_\text{eff} = Z - \sigma, where $Z$ is the number of protons in the nucleus and σ\sigma is the average number of electrons between the nucleus and the electron in question. σ\sigma can be found by using quantum chemistry and the Schrodinger equation or by using Slater's empirical formula.

For example, consider a sodium cation, a fluorine anion, and a neutral neon atom. Each has 10 electrons, and the number of nonvalence electrons is two (10 total electrons minus eight valence electrons), but the effective nuclear charge varies because each has a different number of protons:

$Z_\text{eff}F^{-} = 9 - 2 = 7+$

$Z_\text{eff}Ne = 10 - 2 = 8+$

$Z_\text{eff}Na^{+} = 11 - 2 = 9+$

As a consequence, the sodium cation has the largest effective nuclear charge and, therefore, the smallest atomic radius.

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