Otto Hahn und die Kaiser-Wilhelm-Gesellschaft im Zerrspiegel neuerer Kritik

In recent publications Otto Hahn, last president of the Kaiser-Wilhelm-Gesellschaft, is charged with having favoured the Nazi regime, before World War II by politically purging institutes and suppressing Lise Meitner’s contribution to the discovery of nuclear fission, and during the war by contributing to the German war efforts, mainly to the development of nuclear weapons. These charges, however, which partly concern also the Kaiser-Wilhelm-Gesellschaft and some of their institutes are based on ignorance or disregard of the historical sources

Kann Fermats so genannter letzter Satz auf Grund einfacher Überlegungen verstanden werden?

It is considered whether Fermat’s so called Last Theorem can be understood by substituting variables by polynomials and discussing their properties. The same substitution yields a survey of the Pythagorean Triples

Simple considerations on Fermat's last theorem

Die Bedingung für die Aufspaltung einer Potenz in zwei Potenzen mit gleichem Exponenten ist eine Gleichung, die nur zwei Lösungen hat. Das ist unvereinbar mit Exponenten grösser als 2.The condition of splitting a power into two powers with the same exponent is an equation which has two solutions only. This is incompatible with exponents greater than 2

Atomic volume, atomic distances and chemical bonding in solid metallic elements

Relationships between bond lengths and bond numbers and also between atomic volumes and valencies are derived and parameters for their calculation are given for the s-block, p-block, and d-block metals. From the atomic volumes under pressure, the valencies of three solid lanthanoids have been confirmed or redetermined: La 3; Ce 2. 3. and 4; Yb 2 and 3

Atomic volume, packing density and chemical bonding in solid iodine under pressure

The volume changes of solid iodine under pressure are discussed with respect to the packing density of the atoms and to valence. The packing density of solid iodine which is 0.805 under ambient pressure increases to 0.976 in monoatomic iodine-II, 0.993 in iodine-III, and 1 in fcc iodine-IV. Simultaneously, the valence increases from 1 in the free molecule to 1.78 in the crystal structure under ambient pressure, 2.72 – 2.81 in iodine-II, 2.86 – 2.96 in iodine-III, and 3 in fcc iodine-IV. The valence then remains constant up to about 180 GPa and rises moderately to 3.15 at the highest investigated pressure of 276 GPa. Parameters for calculating bond numbers, valences and atomic volumes of densely packed halogens, hydrogen, oxygen, and nitrogen are given

Metallic radii, ionic radii, and valences of solid metallic elements

Metallic radii rm are correlated with the ionic radii ri by linear relationships. For groups 1 up to 7 as well as for Al, Ga, In, Tl, Sn, and Pb the ionic radii refer to the maximum valences (oxidation states) as known from compounds according to rm ~ 1.16 x (ri + 0.64) [A° ]. For groups 8 up to 12, rm ~ 0.48 x (ri + 2.26) [°A] with valences W = 14 - G (G = group number). These valences are considered regular (Wr). For groups 1 up to 12, they obey the equation Wr = 7 - |G - 7|. According to this equation all outer s electrons and the unpaired d electrons should be involved in chemical bonding, i.e. in the cohesion of the element in the solid state. From the melting temperatures and the atomic volumes it is concluded, however, that only 19 out of the 30 d-block elements have regular valences, namely the elements of groups 3, 5, 6, 10, 11 as well as Os, Ir, Zn, Cd, and possibly Ru. All of the non-regular valences are lower than the regular ones. Four of them are integers: Mn 3; Fe, Co 4; Re 6

Atomic volume and packing density of atoms in metallic elements

In the body-centered cubic structure and in closest sphere-packings the atoms are arranged to give structures with equal densities. A measure of the packing density of atoms is derived. Several crystal structures of elements, including the bcc structure and the closest sphere packings, represent a state of maximum density in which the atomic volume is characteristic of each element. From any crystal structure of an element its atomic volume in this state can be calculated to a good approximation