Atomic Radius of Chemical Elements

Atomic Radius of Chemical Elements

It must be noted, atoms lack a well-defined outer boundary. The atomic radius of a chemical element is a measure of the distance out to which the electron cloud extends from the nucleus. However, this assumes the atom to exhibit a spherical shape, which is only obeyed for atoms in vacuum or free space. Therefore, there are various non-equivalent definitions of atomic radius.

• Van der Waals radius. In principle, Vana der Waals radius is half the minimum distance between the nuclei of two atoms of the element that are not bound to the same molecule.
• Ionic radius. An ionic radius is one-half the distance between the nuclei of two ions in an ionic bond.
• Covalent radius. Covalent radius is the nominal radius of the atoms of an element when covalently bound to other atoms.
• Metallic radius. A metallic radius is one-half the distance between the nuclei of two adjacent atoms in a crystalline structure, when joined to other atoms by metallic bonds.

On the periodic table of the elements, atomic radius tends to increase when moving down columns, but decrease when moving across rows (left to right). Consequently, the smallest atom is helium with a radius of 32 pm, while one of the largest is caesium at 225 pm. The atomic radii decrease across the periodic table because as the atomic number increases, the number of protons increases across the period, but the extra electrons are only added to the same quantum shell. Therefore, the effective nuclear charge towards the outermost electrons increases, drawing the outermost electrons closer. As a result, the electron cloud contracts and the atomic radius decreases.

The volume of an atom is about 15 orders of magnitude larger than the volume of a nucleus. For uranium atom, the Van der Waals radius is about 186 pm = 1.86 ×10⁻¹⁰m. The Van der Waals radius, r_w, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. Assuming spherical shape, the uranium atom have volume of about 26.9 ×10⁻³⁰ m³. But this “huge” space is occupied primarily by electrons, because the nucleus occupies only about 1721×10⁻⁴⁵ m³ of space. These electrons together weigh only a fraction (let say 0.05%) of entire atom.

It may seem, that the space and in fact the matter is empty, but it is not. Due to the quantum nature of electrons, the electrons are not point particles, they are smeared out over the whole atom. The classical description cannot be used to describe things on the atomic scale. On the atomic scale, physicists have found that quantum mechanics describes things very well on that scale. Particle locations in quantum mechanics are not at an exact position, they are described by a probability density function. Therefore the space in an atom (between electrons and an atomic nucleus) is not empty, but it is filled by a probability density function of electrons (usually known as “electron cloud“).

Density of Chemical Elements

Typical densities of various substances are at atmospheric pressure.

Density is defined as the mass per unit volume. It is an intensive property, which is mathematically defined as mass divided by volume:

ρ = m/V

In words, the density (ρ) of a substance is the total mass (m) of that substance divided by the total volume (V) occupied by that substance. The standard SI unit is kilograms per cubic meter (kg/m³). The Standard English unit is pounds mass per cubic foot (lbm/ft³).

Density and Atomic Radii

Since the density (ρ) of a substance is the total mass (m) of that substance divided by the total volume (V) occupied by that substance, it is obvious, the density of a substance strongly depends on its atomic mass and also on the atomic number density (N; atoms/cm³),

• Atomic Weight. The atomic mass is carried by the atomic nucleus, which occupies only about 10^-12 of the total volume of the atom or less, but it contains all the positive charge and at least 99.95% of the total mass of the atom. Therefore it is determined by the mass number (number of protons and neutrons).
• Atomic Number Density. The atomic number density (N; atoms/cm³), which is associated with atomic radii, is the number of atoms of a given type per unit volume (V; cm³) of the material. The atomic number density (N; atoms/cm³) of a pure material having atomic or molecular weight (M; grams/mol) and the material density (⍴; gram/cm³) is easily computed from the following equation using Avogadro’s number (N_A = 6.022×10²³ atoms or molecules per mole):

Since nucleons (protons and neutrons) make up most of the mass of ordinary atoms, the density of normal matter tends to be limited by how closely we can pack these nucleons and depends on the internal atomic structure of a substance. The densest material found on earth is the metal osmium, but its density pales by comparison to the densities of exotic astronomical objects such as white dwarf stars and neutron stars.

If we include man made elements, the densest so far is Hassium. Hassium is a chemical element with symbol Hs and atomic number 108. It is a synthetic element (first synthesised at Hasse in Germany) and radioactive. The most stable known isotope, ²⁶⁹Hs, has a half-life of approximately 9.7 seconds. It has an estimated density of 40.7 x 10³ kg/m³. The density of Hassium results from its high atomic weight and from the significant decrease in ionic radii of the elements in the lanthanide series, known as lanthanide and actinide contraction.

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Properties of other elements