Atomic radius

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An atom is assigned an atomic radius with which its spatial size can be approximated. An absolute radius of an atom - and therefore also an absolute size - cannot be specified, because an atom shows different effective sizes depending on the chemical bond type and, according to the ideas of quantum mechanics, has no defined limit anyway. The atomic radius is determined from the distance between the atomic nuclei in the chemical compounds of the relevant type:

Atomic radii are on the order of 10 −10  m (= 1  Ångström  = 100  pm  = 0.1  nm ). The covalent radius in the hydrogen molecule is z. B. 32  pm , the metal radius of 12-fold coordinated cesium 272 pm.

Relation to the position in the periodic table

Illustration of the proportions of the covalent atomic radii of the elements of the periodic table (to scale).

The atomic radii increase from top to bottom within a group of the periodic table and decrease from left to right within a period. This is explained by the fact that the atomic number and thus the positive charge of the nucleus increase within a period . Thus the negative electrons of the atom are more strongly attracted. The reduction in the atomic radius within the period from halogen to noble gas can be attributed to the particularly stable electron configuration of the noble gases. The increase in radius, from one row to the next within each group, results from the fact that new shells are filled with electrons.

Atomic radii of some chemical elements 1
Atomic number symbol Radius in 10 −12  m
1 H 32
2 Hey 28
3 Li 152
4th Be 112
5 B. 88
6th C. 77
7th N 70
8th O 66
9 F. 64
10 No 58
11 N / A 186
12 Mg 160
13 Al 143
14th Si 117
15th P 110
16 S. 104
17th Cl 99
18th Ar 106
19th K 231
20th Approx 197
1 (Covalent radii; for metals: metal radii)

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 the nearest neighboring atoms) can be calculated by starting from a cube that contains just 10 24 atoms and whose edges are therefore formed by 10 8 atoms. One mole is 6.022 · 10 23 atoms. And that's as many grams as the atomic mass A indicates. A / 0.6022 grams is the weight of a cube with 10 24 atoms. If one divides by the density ρ, then A / (0.6022 · ρ) cm 3 is its volume. The third root thereof gives the length of an edge, and these through 10 8 is dividing the atomic diameter D . For the element polonium ( A = 208.983; ρ = 9.196) the volume of this cube is 37.737 cm 3 and the edge length is 3.354 cm. This implies an atomic radius of 167.7 pm; in data collections are given 167.5 pm.

Pictures 1 and 2. On the left the cubic-primitive grid. In the closest packing of spheres (right), the centers of the atoms in a plane form equilateral triangles and, with one atom from the plane above, tetrahedra

In the case of gold ( A = 196.967 g / mol; ρ = 19.282 g / cm 3 ) this is no longer so accurate, the error is around 12%. The reason for this discrepancy is that gold atoms are not packed primitively, but more densely (face-centered cubic, face centered cubic, fcc, one of the two closest packing of spheres; Figure 2). Are there

  • In one plane the rows of atoms are shifted against each other by half an atomic diameter so that they can be moved closer together, and
  • the atoms on the level above each lie in a hollow between three other atoms. Together they form tetrahedra.

Characterized to an array of atoms by a straight line, the auffädelt the atom center points, the distance between two rows in one plane in the cubic primitive / sc-grid is just D . In the face-centered cubic / fcc lattice 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 one finds: A fictitious gold cube with a cubic primitive crystal structure would have a volume √2 ≈ 1.41421 larger, or its density would be √2 smaller. If one carries out the calculation with the lower density, one obtains D = 288 pm or r = 144 pm, in agreement with the result from the X-ray diffraction.

It is easier if you know the packing densities (the proportion that the atoms assumed to be round make up in the volume). A cubic primitive grid has a packing density of 0.523599, for the face-centered cubic it is 0.740480. The same packing density also has the hexagonal lattice (layer sequence AB, with face-centered cubic ABC). The quotient (0.74… / 0.52…) results in the factor √2. The table lists examples of elements whose crystal structure is face-centered cubic or hexagonal, together with the result of the calculation and the measured atomic radius.

Ordinal
number		 element Crystal
structure		 Atomic mass density r calc [pm] r exp [pm]
4th Be hex 9.012 1,848 112.7 112
12 Mg hex 24.305 1.738 160.1 160
20th Approx fcc 40.078 1.55 196.5 197
22nd Ti hex 47.867 4,506 146.1 147
27 Co hex 58.933 8.86 125.0 125
28 Ni fcc 58.693 8,908 124.6 124
29 Cu fcc 63,546 8,933 127.8 128
40 Zr hex 91.224 6.506 160.3 160
46 Pd fcc 106.42 12.023 137.5 137
47 Ag fcc 107.868 10.501 144.5 144
57 La hex 138.905 6.162 187.7 187
76 Os hex 190.23 22.59 135.2 135
77 Ir fcc 192.217 22.56 135.7 136
78 Pt fcc 195.084 21.45 138.7 138.5
79 Au fcc 196.967 19.282 144.2 144
Fig. 3. The face-centered cubic cell contains six half atoms on the faces and one eighth of the eight atoms at the corners, so together they contain four whole atoms.

For the body-centered unit cell (body centered cubic, bcc; example: sodium) the packing density is 0.68175. Here the density ρ has to be divided by (0.68… / 0.52…). This again corresponds to a volume of a fictitious cube with an sc structure which is larger by this factor. For sodium ( A = 22.9898; ρ = 0.968) the third root of [22.9898 / (0.6022 · 0.968)] · (0.68… / 0.52…) gives a D = 371, 4 pm and r = 185.7 pm; measured 186 pm.

The classic crystallographic method counts how many atoms there are in a unit cell. In the case of face-centered cubic (fcc), this contains parts of four whole atoms (Fig. 3). The volume in which there are four atoms can be determined from the atomic mass, the density and the Avogadro number, i.e. the size of the unit cell (in this case, the shape of a cube). The diameter of an atom is the distance between the centers of two atoms that are closest to each other in the cell. They are arranged along the diagonal of the surface (and not along the edge, since they are further apart). This is four atomic radii long (in Figure 3, the atoms are shown smaller for the sake of clarity). The edge length, the length of the diagonal and thus the atomic radius are obtained from the volume. With the cubic-primitive unit cell, the calculation can also be carried out for polonium.

See also

literature

  • Charles E. Mortimer, Ulrich Müller: Chemistry. The basic knowledge of chemistry. 9th, revised edition. Thieme, Stuttgart 2007, ISBN 978-3-13-484309-5 .
  • Hans Rudolf Christen : Fundamentals of general and inorganic chemistry. 6th edition. Salle et al., Frankfurt am Main et al. 1980, ISBN 3-7935-5394-9 .

Individual evidence

  1. ↑ Polonium . uniterra.de. Retrieved May 28, 2011.
  2. ↑ Frank Rioux: Calculating the Atomic Radius of Polonium (PDF; 114 kB) users.csbsju.edu. Retrieved May 28, 2011.