Atomic: number, 177 volume weights

Here Pyj is the structure factor for the (hkl) diffiaction peak and is related to the atomic arrangements in the material. Specifically, Fjjj is the Fourier transform of the positions of the atoms in one unit cell. Each atom is weighted by its form factor, which is equal to its atomic number Z for small 26, but which decreases as 2d increases. Thus, XRD is more sensitive to high-Z materials, and for low-Z materials, neutron or electron diffraction may be more suitable. The faaor e (called the Debye-Waller factor) accounts for the reduction in intensity due to the disorder in the crystal, and the diffracting volume V depends on p and on the film thickness. For epitaxial thin films and films with preferred orientations, the integrated intensity depends on the orientation of the specimen. 

Atomic number Atomic volume Atomic weight Valency... 

A mole of a substance is the number of elementary particles (atoms, molecules) found in the mass (in grams) of that substance that corresponds to its atomic or molecular weight. In molar volumes, which amount to 22.4 L for gases and are different from solid to solid, there are always the same number of atoms or molecules. This "magic number", Avogadro s number, is 6.022xl023 mol-1. 

Symbol B atomic number 5 atomic weight 10.811 a Group III A (Group 13) metalloid element atomic volume 4.70 cc/g-atom electron affinity 0.277 eV electronic configuration Is22s22pi valence state +3 naturally occurring stable isotopes are B-10 and B-11 and their abundance 19.57% and 80.43%, respectively. 

Symbol Ce atomic number 58 atomic weight 140.115 a rare-earth metal a lanthanide series inner-transition /-block element metaUic radius (alpha form) 1.8247A(CN=12) atomic volume 20.696 cm /mol electronic configuration [Xe]4fi5di6s2 common valence states -i-3 and +4 four stable isotopes Ce-140 and Ce-142 are the two major ones, their percent abundances 88.48% and 11.07%, respectively. Ce—138 (0.25%) and Ce—136(0.193%) are minor isotopes several artificial radioactive isotopes including Ce-144, a major fission product (ti 284.5 days), are known. 

Symbol Dy atomic number 66 atomic weight 162.50 a lanthanide series, inner transition, rare earth metal electron configuration [Xe]4 5di6s2 atomic volume 19.032 cm /g. atom atomic radius 1.773A ionic radius 0.908A most common valence state +3. 

Symbol Ho atomic number 67 atomic weight 164.93 a lanthanide series rare earth element electron configuration [Xe]4/ii6s2 valence state +3 metallic radius (coordination number 12) 1.767A atomic volume 18.78 cc/mol ionic radius Ho3+ 0.894A one naturally occurring isotope. Ho-165. 

Symbol Mg atomic number 12 atomic weight 24.305 a Group II A (Group 2) alkaline-earth metal atomic radius 1.60A ionic radius (Mg2+) 0.72A atomic volume 14.0 cm /mol electron configuration [Ne]3s2 valence +2 ionization potential 7.646 and 15.035eV for Mg+ and Mg2+, respectively three natural isotopes Mg-24(78.99%), Mg-25(10.00%), Mg-26(11.01%). 

Symbol Nd atomic number 60 atomic weight 144.24 a rare earth lanthanide element a hght rare earth metal of cerium group an inner transition metal characterized by partially filled 4/ subshell electron configuration [Xe]4/35di6s2 most common valence state -i-3 other oxidation state +2 standard electrode potential, Nd + -i- 3e -2.323 V atomic radius 1.821 A (for CN 12) ionic radius, Nd + 0.995A atomic volume 20.60 cc/mol ionization potential 6.31 eV seven stable isotopes Nd-142 (27.13%), Nd-143 (12.20%), Nd-144 (23.87%), Nd-145 (8.29%), Nd-146 (17.18%), Nd-148 (5.72%), Nd-150 (5.60%) twenty-three radioisotopes are known in the mass range 127-141, 147, 149, 151-156. 

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. 

Many physical properties of metals display an approximate correlation with the number of valence electrons of the periodic sequences of the elements. Lothar Meyer was the first to publish, in 1870, a graph of atomic volume as a function of atomic weight [49]. Rather than atomic volume as a function of atomic weight, it is interesting to consider the reciprocal of the atomic volume as a function of atomic number. With appropriate units, the reciprocal of the atomic volume is, in fact, the atomic density, or molarity, of the element in its pure state. In Figure 4 the molarity of the principal allotropes of the elements is shown plotted as a function of the atomic number z at STP [50]. 

The properties of elements change in a systematic way through a period this is indicated in Figure 5-1, which shows the atomic volume (the atomic weight divided by the density that is, the volume in cm of 1 g-atom of the element) of the elements at 0° C and 1 4tm, as a function of the atomic number. 

What helped make Mendeleev s system seem more plausible was the coincidental publication of Lothar Meyer s periodic table. Meyer had attended the 1860 Karlsruhe conference just as Mendeleev had, and, like Mendeleev, he had gone away convinced that there was some pattern that united the elements through atomic weights. He had sketched out an incomplete table of elements in his book Die modernen Theorien der Chemie (1864), and in 1868 he worked out a much more complete table. He did not publish this until 1870, by which time he was fully aware of Mendeleev s work. In addition to providing independent confirmation of Mendeleev s system, Meyer also added a supporting observation, showing that there was a periodic relationship between atomic number and atomic volume. Atomic volume represents the volume occupied by one mole of an element in its solid state. Meyer showed that atomic volume equaled atomic weight divided by the density of the solid. 

A generalization of the Burden matrix was proposed in DRAGON descriptors where instead of the atomic numbers Z, atomic masses (m), van der Waals volumes (v), Sanderson electronegativities (e), and polarizabilities (p) are used as the weighting schemes for graph vertices. Thus, a general definition of the Burden matrix in terms of a vertex weighting scheme W is... 

A modern (and more complete) version of Julius Lothar Meyer s plot of atomic volume of the elements. He plotted the values against atomic weight here we have plotted them against atomic number, which is a more fundamental property. Note the periodic rise and fall of the values. 

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