Question

Explain why the radius of a sodium ion \((0.095 \mathrm{nm})\) is about half that of a sodium atom \((0.186 \mathrm{nm})\).

Short answer

A sodium ion has a smaller radius than a sodium atom because it loses an electron, resulting in a decrease in the number of electron shells.

Step-by-step solution

Understand Atomic vs. Ionic Radius

The atomic radius is the distance from the center of the nucleus to the outermost electron shell of a neutral atom. The ionic radius is similar but refers to an ion which has gained or lost electrons, adjusting its electron shell structure.

Compare Electron Configurations

A neutral sodium atom ( ext{Na}) has an electron configuration of ext{1s}^2 ext{2s}^2 ext{2p}^6 ext{3s}^1. When it becomes a sodium ion ( ext{Na}^+), it loses one electron, resulting in an electron configuration of ext{1s}^2 ext{2s}^2 ext{2p}^6, which is stable and has an outer orbital of ext{2p}.

Analyze the Decrease in Electron Shells

When the sodium atom loses its outermost electron to form ext{Na}^+, it essentially loses its third shell, leading to the second shell ( ext{n} = 2) becoming its outermost occupied shell. This significantly reduces the overall radius of the ion.

Understand Electron Shielding and Nuclear Charge

In the neutral ext{Na} atom, the outer electron experiences both the positive nuclear charge and the electron shielding effect from inner electrons, leading to a larger radius. In ext{Na}^+, the loss of an electron reduces both shielding and the radius due to the remaining electrons being more strongly attracted closer to the nucleus.

Key concepts

Atomic Radius

The atomic radius is a fundamental concept in chemistry that refers to the size of a neutral atom. It represents the distance from the nucleus's center to the outermost electron shell. The atomic radius can vary significantly across the periodic table.

Factors influencing the atomic radius:

• When moving down a group in the periodic table, the atomic radius increases due to the addition of electron shells.
• Across a period, from left to right, the atomic radius generally decreases. This is because electrons are added to the same shell while the nuclear charge increases, pulling the electron cloud closer.
• The atomic radius of an element determines its ability to engage in bonding with other atoms. The larger the radius, the further the outer electrons are from the nucleus, which can influence chemical reactivity.

Simply put, the larger the atomic radius, the more spread out the atom's electrons, affecting its interactions and potential size of the ionic form.

Electron Configuration

Electron configuration is a method to represent the distribution of electrons in an atom's electron shells. It plays a crucial role in determining the chemical properties and reactivity of an element.

The basics of electron configuration:

• Electrons occupy orbitals in a specific order according to the "Aufbau principle," which predicts the order of electron filling in the atom's orbitals.
• The configuration is represented by noting the energy level (n), type of orbital (s, p, d, f), and the number of electrons in those orbitals, e.g., \( 1s^2 2s^2 2p^6 \) for a stable noble gas configuration.
• Transition from a neutral atom to a cation (positive ion) involves the loss of one or more electrons, affecting both its electron configuration and its physical characteristics, such as its ionic radius.

An essential aspect of the sodium ion formation is the removal of the outermost 3s electron, which results in a more compact electron configuration and affects its ionic radius drastically.

Electron Shielding

Electron shielding, also known as screening, refers to the reduction in effective nuclear charge felt by an electron in an atom with multiple electrons. This mechanism influences the size of the atom and its reactivity.

Key points about electron shielding:

• When electrons in inner shells repel electrons in outer shells, they reduce the full nuclear charge effect on the outer electrons.
• As a result, these outer electrons are "shielded" from the strong positive charge of the nucleus.
• In Na⁺, losing an electron reduces this shielding effect. The remaining electrons are drawn closer to the nucleus due to the unopposed nuclear charge.

This reduced electron shielding in ions like the sodium ion leads to a smaller ionic radius compared to its atomic form, explaining why Na⁺ is considerably smaller than a neutral sodium atom.