Question

(a) Because an exact outer boundary cannot be measured or even calculated for an atom, how are atomic radii determined? (b) What is the difference between a bonding radius and a nonbonding radius? (c) For a given element, which one is larger? (d) If a free atom reacts to become part of a molecule, would you say that the atom gets smaller or larger?

Short answer

(a) Atomic radii are determined indirectly by measuring the distance between the nuclei of two bonded atoms of the same element and dividing that distance by two. This is done through methods such as X-ray diffraction or electron microscopy. (b) Bonding radius (covalent radius) is the measure of atomic size when an atom is part of a chemical bond, while nonbonding radius (van der Waals radius) is the measure of atomic size when an atom is not bonded to another atom. (c) The nonbonding radius is generally larger than the bonding radius for a given element, as it represents the entire electron cloud surrounding the nucleus without sharing. (d) When a free atom reacts to become part of a molecule, it generally gets smaller due to the sharing of electrons between the two nuclei leading to a more compact arrangement. However, the size may vary depending on the type of bond and interacting atoms.

Step-by-step solution

(a) Determination of Atomic Radii

Since it is impossible to measure or calculate the exact outer boundary of an atom, atomic radii are determined indirectly. The atomic radius of an element is generally determined by measuring the distances between the nuclei of two atoms of the same element which are bonded together, and then dividing that distance by two. For example, if the atom is part of a molecule, the distance between the nuclei of the two bonded atoms can be measured through X-ray diffraction or other experimental methods like electron microscopy. This measured distance helps to infer the atomic radius.

(b) Bonding Radius and Nonbonding Radius

The bonding radius is the measure of atomic size when an atom is part of a chemical bond with another atom. It is also referred to as the covalent radius. The bonding radius refers to the distance between the two nuclei involved in the bond, halved. Nonbonding radius, also known as van der Waals radius, is the measure of the atomic size when an atom is not bonded to another atom. It represents the size of an isolated atom due to its electron cloud and it's a measure of how close such an atom can approach another without forming a chemical bond.

(c) Comparing Bonding and Nonbonding Radii

Generally, the nonbonding radius is larger than the bonding radius for a given element. This is because when an atom forms a bond with another atom, the electron cloud is shared between the two nuclei. This results in a more compact arrangement of electrons and the distance between the two nuclei in the bond is reduced. On the other hand, in a non-bonding situation, the electron cloud is not shared, and the atomic size is determined by the entire electron cloud surrounding the nucleus.

(d) Atom Size in a Molecule

When a free atom reacts to become a part of a molecule, the atom generally gets smaller. This can be explained by considering the fact that when an atom forms a bond with another atom, the electrons are shared between the two nuclei. This leads to a more compact arrangement of the electron cloud, and hence the atomic size decreases when an atom becomes part of a molecule. However, depending on the type of bond formed and the interacting atoms, the size of the atom in the molecule may be subjected to some variations.

Key concepts

Bonding Radius

The bonding radius, also called the covalent radius, is an essential concept in understanding the size of atoms when they form chemical bonds. When we talk about atomic size in a molecule, this is the measure we often refer to. The bonding radius is defined as half the distance between the nuclei of two identical atoms that are bonded together. This essentially means that the bonding radius is a convenient way to estimate half of the length of a single covalent bond between two atoms.

• It's used as a standard measurement because the exact size of an atom is hard to pinpoint due to the diffuse nature of the electron cloud.
• Bonding radius is particularly useful in chemistry, as it helps predict how atoms will interact and bond in molecules.

To measure the bonding radius, scientists use techniques like X-ray diffraction or electron microscopy, which involve bouncing high-energy particles off atoms and measuring how they scatter. This scattering pattern reveals the spacing between atoms, allowing scientists to calculate the bonding radius. Understanding bonding radius is key to making sense of how molecules form and how stable they might be.

Nonbonding Radius

The nonbonding radius, also known as the van der Waals radius, describes an atom's size when it is not bonded to another atom. Unlike the bonding radius, which only considers bonded atoms, the nonbonding radius takes into account an atom as it exists in free space, without interatomic interactions. This gives a picture of the maximum "reach" of an atom, or how close it can come to another atom without forming a bond.

• The nonbonding radius is usually larger than the bonding radius because it includes the entire electron cloud enveloping the nucleus.
• It highlights the space in which electrons exist when the atom is not energetically interacting with others.
• This radius is critical for understanding phenomena like intermolecular forces or London dispersion forces, which can occur even without direct bonding.

In practical terms, knowing the nonbonding radius can help scientists understand how atoms in a large structure (like crystals) influence each other through their sheer size rather than bonding interactions. This concept also assists in predicting molecular shapes and the stability of atoms in various states of matter.

Atomic Size in Molecules

The atomic size within molecules is an intriguing subject, as atoms often "shrink" upon forming bonds within a molecule. When atoms come together to form a molecule, the shared electrons in bonds result in a more compact electron cloud. This is why the bonding radius in molecules tends to be smaller than the nonbonding radius.

• As atoms share electrons, the proximity of other atomic nuclei compresses the electron cloud, resulting in reduced atomic size in molecules.
• This compact nature of atom sizing in molecules affects many properties, such as bond strength and molecular geometry.
• When bonds are formed, atoms tend to stick closer together, making the structure more stable in most cases.

Factors like bond type (single, double, triple bonds) and the presence of lone electron pairs can influence the atom's effective size within a molecule. By understanding the reduction in atomic size, scientists can predict and manipulate the properties of molecules in chemical reactions, materials science, and pharmaceuticals.