Atomic radius alkali metals

AHa for the Adsorption of Alkali Metals. If an alkali metal atom is located at an infinite distance from a metal surface at zero potential, then the heat of adsorption comprises the work done in (1) transferring an electron from the atom to the metal, and (2) bringing the positive ion to its equiUbrium distance from the metal surface (127). In the first step, the energy change is (e0 — el), where is the work function of the metal and I is the ionization potential of the alkali metal atom. In the second, the force of attraction on the positive ion at a distance d from the metal surface, i.e., the electrostatic image force, is e /4d hence, the heat Uberated is e /4do, where do is the equilibrium distance of the adsorbed ion from the metal surface. This distance is often assumed to be equal to the ionic radius, which is 1.83 A. for the Na ion. The initial heat of adsorption, therefore, is... 

The ionization potentials (IPs) of ammonia clusters containing alkali metal atoms, such as Li [10], Na [8] and Cs [9], have been reported by Hertel s and Fuke s groups. These clusters have been prepared by pickup sources coupled with a heated oven (Na and Cs) or a laser-vaporization source (Li). The IP(n) values decrease almost linearly with (n-f 1) , which is approximately proportional to the inverse of the cluster radius. Although the IPs of free atoms are different (5.392, 5.139 and 3.894 eV for Li, Na and Cs, respectively), those of the clusters (n > 5) are almost the same irrespective to the metal atoms. The intercept at (n + 1) 0... 

The adsorption geometry of alkali-metal atoms chemisorbed on metal surfaces. The alkali metal to substrate bond length is derived from the determined coordinates. The adatont radius is obtained by subtracting the metallic Tadius of the substrate atom from the determined bond length. The adatom radius is expressed as the ratio of the adatom radius to the mcLallic radius of the adatom. 

The second structure common to a number of T1-B1 systems is that of sodium thallide, sometimes called the Zintlphase. This structure (fig. 13.12) is closely related to that of caesium chloride in that the pattern of sites occupied forms a cubic body-centred lattice. The distribution of the atoms, however, is such that each atom has four neighbours of each kind, and the true cell is therefore the larger unit shown, containing sixteen instead of only two atoms. Some phases in which the sodium thallide structure occurs are LiZn, LiCd, LiAl, LiGa, Liln, Naln and NaTl. It is a characteristic feature of all of these phases that in them the alkali metal atom appears to have a radius considerably smaller than in the structure of the element (even when allowance is made for the change in co-ordination number), suggesting that this atom is present in a partially ionized condition and that forces other than purely metallic bonds are operative in the structure. 

As in gas and liquid hydrates, the formation of Si and Ge clathrates is mostly governed by steric criteria ". Assuming for the alkali-metal atoms a radius close to the covalent radii , the analytical and crystallographic data listed in Table 1 can be explained by means of a diagram such as Fig. 1. 

Figure 1. Comparison of the covalent radii of alkali-metal atoms with the free radius of the available voids in clathrate-type silicon host lattices (from ref. 3).

Potassium, with a covalent radius of 203 pm, is too large to occupy the smallest rn.i voids. The clathrate obtained has a type 1 host lattice with the eight available voids occupied by an alkali-metal atom. 

The following tables contain experimentally-determined commensurate structure parameters for alkali metal adsorption systems (only simple structures are listed). The temperatures quoted are the measurement temperature. The bond length quoted is the chemisorption bond length. Effective r (Eff r) is the chemisorption bond length minus the metalHc radius of the substrate atom. Excess r (Exc. r) is the Effective r minus the ionic radius of the alkali metal atom N is the coordination number of the alkali adatom. A coordination number denoted as indicates that due to surface reconstruction, an unambiguous assigmnent carmot be made. 

This statement above is easily rationalized the farther an electron is from the nucleus, the more easily it can be removed. The decrease in ionization energy that accompanies an increase in atomic radius is evident when we compare the ionization energies and atomic radii of the alkali metal atoms (Table 9.3). 

The hydrogen atom has a high ionization energy (1312kJmol ) and in this it resembles the halogens rather than the alkali metals. Removal of the Is electron leaves a bare proton which, having a radius of only about 1.5 x 10 pm, is not a stable chemical entity in the condensed phase. However, when bonded to other species it is well known in solution and in... 

It is possible to explain these trends in terms of the electron configurations of the corresponding atoms. Consider first the increase in radius observed as we move down the table, let us say among the alkali metals (Group 1). All these elements have a single s electron outside a filled level or filled p sublevel. Electrons in these inner levels are much closer to the nucleus than the outer s electron and hence effectively shield it from the positive charge of the nucleus. To a first approximation, each inner electron cancels the charge of one pro-... 

These three structures are the predominant structures of metals, the exceptions being found mainly in such heavy metals as plutonium. Table 6.1 shows the structure in a sequence of the Periodic Groups, and gives a value of the distance of closest approach of two atoms in the metal. This latter may be viewed as representing the atomic size if the atoms are treated as hard spheres. Alternatively it may be treated as an inter-nuclear distance which is determined by the electronic structure of the metal atoms. In the free-electron model of metals, the structure is described as an ordered array of metallic ions immersed in a continuum of free or unbound electrons. A comparison of the ionic radius with the inter-nuclear distance shows that some metals, such as the alkali metals are empty i.e. the ions are small compared with the hard sphere model, while some such as copper are full with the ionic radius being close to the inter-nuclear distance in the metal. A consideration of ionic radii will be made later in the ionic structures of oxides. 

The rather complex structure of the compound NaZn13 was studied by Ketelaar (1937) and by Zintl and Haucke (1938). Every Na atoms is surrounded by 24 Zn atoms at the same distance. The lattice parameters of several MeZn13 compounds pertaining to this structural type are, in a first approximation, independent of the size of the alkali (or alkaline earth) metal atom. Similar consideration may be made for the MeCd13 compounds. Zintl, therefore, considered the fundamental component of this crystal structure to be a framework of Zn (or Cd) atoms with the alkali (or alkaline earth) metal atoms occupying the holes of the framework. However notice (Nevitt 1967) that in compounds MeX13 radius ratios (rMe/rx) deviating by more than about 15% from the mean value 1.54 are unfavourable for the occurrence of the structure. 

Symbol Cs atomic number 55 atomic weight 132.905 a Group lA (Group 1) alkali metal element electron configuration [Xe]6si atomic radius 2.65 A ionic radius (Cs ) 1.84 A ionization potential 3.89 eV valence +1 natural isotope Cs-133 37 artificial isotopes ranging in mass numbers from 112 to 148 and half-lives 17 microseconds (Cs-113) to 2.3x10 years (Cs-135). 

Symbol Rb atomic number 37 atomic weight 85.468 a Group I (Group 1) alkali metal element electron configuration [Kr] 5si valence -i-l atomic radius 2.43A ionic radius, Rb+ 1.48A atomic volume 55.9 cc/g-atom at 20°C ionization potential 4.177 V standard electrode potential Rb+ + e Rb, E° = -2.98V two naturally-occurring isotopes, Rb-85 (72.165%) and Rb-87 (27.835%) Rb-87 radioactive, a beta emitter with a half-bfe 4.88xl0i° year twenty-seven artificial radioactive isotopes in the mass range 74—84, 86, 88-102. 

Symbol Na atomic number 11 atomic weight 22.9898 a Group lA (Group 1) alkali metal element electron configuration [NejSs valence +1 atomic radius 1.85A ionic radius, Na" in crystals 1.02A (for a coordination number 6) ionization potential 5.139 eV standard electrode potential, E°(Na+ + e Na) -2.71 V one naturally-occurring stable isotope, Na-23 (100%) sixteen artificial radioactive isotopes in the mass range 19-22, 24—35 longest-lived radioisotope, Na-22, ti/2 2.605 year shortest-lived isotope Na-35, ti/2 1.5 ms. 

The jellium model of the free-electron gas can account for the increased abundance of alkali metal clusters of a certain size which are observed in mass spectroscopy experiments. This occurrence of so-called magic numbers is related directly to the electronic shell structure of the atomic clusters. Rather than solving the Schrodinger equation self-consistently for jellium clusters, we first consider the two simpler problems of a free-electron gas that is confined either within a sphere of radius, R, or within a cubic box of edge length, L (cf. problem 28 of Sutton (1993)). This corresponds to imposing hard-wall boundary conditions on the electrons, namely... 

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