Atomic radius

An atom may be attributed to the prediction of binding ratios varied atomic radii.

An absolute radius of an atom - and therefore also an absolute magnitude - can not be specified as an atom according to the ideas of quantum mechanics has no defined limit.

Depending on the present chemical bond type, one can determine the effective size of an atom. The designated simply put the distance between the nuclei in a given chemical compound of this type:

• In predominantly ionic structured systems the atoms ionic radii are attributed.
• For atoms in molecular, covalent compounds characterized as covalent radii are given.
• In metals the atoms get metal atom radii.
• Between the molecules of covalent compounds have Van der Waals forces; Accordingly, there is to the van der Waals radii.

Atomic radii are of the order of 10-10 m ( 1 Angstrom = 100 = pm = 0.1 nm, covalent radius in the hydrogen molecule 32 pm, the metal radius of 12 -fold coordinated cesium 272 pm ).

Relationship between atomic radius and position in the periodic system

In addition, the atomic radii within a group ( Periodic Table) from top to bottom to take and within a period from left to right. This state of affairs based on the fact that within a period, the nuclear charge increases. Therefore, the positive charge of the core and thus increases the negative electrons of the atom to be more attracted. The increase in the atomic radius within the period from halogen to the noble gas can be attributed to the particularly stable electron configuration of the noble gases. The increase of the radius within the groups due to the fact that new shells are filled with electrons.

Metal atom radius, sphere packing and Bravais lattice

In the simplest case, an element crystallizes as shown in Figure 1 (simple cubic, cubic simple or primitive ). The diameter D of an atom (distance between the centers of nearest neighboring atoms ) can be calculated by starting from a cube that contains just 1024 atoms and whose edges are thus formed by 108 atoms. One mole of atoms are 0.6022 ∙ 1024. And these are also so many grams as the atomic mass A indicates. A / 0.6022 grams is the weight of a cube with 1024 atoms. Dividing by the density ρ even, then A / ( 0.6022 ∙ ρ ) is cm3 in volume. The third root of it gives the length of an edge, and this divided by 108, the atomic diameter D. When element polonium (A = 208.983; ρ = 9.196 ), the volume of this cube 37.737 cm3 and the edge length of 3.354 cm. It follows an atomic radius of 167.7 pm; be specified in data collections 167.5 pm.

In gold (A = 196.967 g / mol; ρ = 19.282 g/cm3 ) fits the not so accurate, the error is about 12%. The reason for this discrepancy is that gold atoms are not packed cubic primitive, but dense ( face-centered cubic, face centered cubic, fcc, one of the densest sphere packings; Fig. 2). Here are

• The rows of atoms relative to each other in a plane by one-half atomic diameter, so that they can be moved closer to each other, and
• The atoms of the layer above it lie in a hollow between three other atoms, respectively. Together, they form the tetrahedron.

Characterized you a number of atoms by a straight line, the auffädelt the atomic centers, then the distance between two rows is in a plane kubisch-primitiven/sc-Gitter just D. In kubisch-flächenzentrierten/fcc-Gitter it is smaller, namely D ∙ ( √ 3 /2) ( = height of an equilateral triangle ) and the distance between two planes is equal to the height of a tetrahedron [D ∙ √ (2/ 3)]. From the product of the two factors can be found: A fictitious gold cube with cubic primitive crystal structure would have a larger order √ 2 ≈ 1.41421 volume, and its density would be smaller by √ 2. Does you the invoice with the lower density by, one obtains D = 288pm or r = 144pm, in accordance with the result of X-ray diffraction. It is easier if you know the packing density ( the proportion which the atoms around as adopted on account volume ). A primitive cubic lattice has a density of 0.523599, the face-centered cubic she is 0.740480. The same packing density also has the hexagonal lattice ( the layer sequence AB in ABC face-centered cubic ). The quotient (0.74 .. / .. 0.52 ) again yields a factor of √ 2 The table shows examples of elements, face-centered cubic crystal structure which is hexagonal or, together with the result of the calculation and the measured atomic radius.

For the body-centered cubic unit cell (body centered cubic, bcc, for example: sodium) is the packing density 0.68175. Here the density ρ must be divided by (0.68 .. / .. 0.52 ). This is also again a larger by this factor volume of a cube with fictitious sc structure. When sodium (A = 22,9898; ρ = 0.968 ) is obtained from the cube root of [ 22,9898 / ( 0.6022 ∙ 0.968 ) ] ∙ (0.68 .. / .. 0.52 ) a D = 371.4 pm and r = 185.7 pm; were measured 186pm.

The classical crystallographic method counts how many atoms comprising a unit cell. This includes, in the case of face-centered cubic (fcc ), the shares of all four atoms ( Fig. 3). From the atomic mass, the density and Avogadro's number, the volume can be determined, which contains four atoms, so the size of the unit cell (in this case the shape of a cube ). The diameter of the atom, the distance between the center points of two atoms which have the smallest spacing found in the cell. They are disposed along the diagonal surface (and not along the edge, as they are further apart ). This is four atomic radii long (in Figure 3 are the atoms of clarity smaller shown). From the obtained volume of the edge length, the length of the diagonal and so the atomic radius. With the cubic primitive unit cell can also perform the calculation for polonium.