q-Calculus and the Symmetrized Radioactive Decay Law

The radioactive decay law was first formulated by Ernest Rutherford and Frederick Soddy in 1902. As a well-known law, one of its primary applications is to determine the dates of ancient specimens. The process is known as radiocarbon dating and is subjected to the known properties of radioactive nuclei. In this paper, we implement quantum calculus to express the solution of the radioactive decay equation in symmetrized q-exponential form. Also, we explore a q-analog of the decay constant using Tsallis logarithmic function for various miscellaneous q-values. Furthermore, the factor-label method was applied to our analysis to show that the correct units remained intact under the application of quantum calculus. In conclusion, our work suggests that a variation of the q-parameter was akin to the production of a new isotope for all q in (0,1); the superadditive regime.

6. Physics invades the periodic table

‘Physics invades the periodic table’ assesses the impact of key discoveries in physics on the understanding of the periodic table. Ernest Rutherford provided evidence for the nuclear structure of atoms, and also determined that the charge of an atom is equal to half its atomic weight. Anton van den Broek linked this principle to the number of protons in a nucleus, thus devising the notion of atomic number. Henry Moseley quantified this principle, and used it to show exactly how many elements would fill the gaps in the periodic table. Radioactive experiments created new forms of elements with different weights but the same charge, which Frederick Soddy identified as isotopes.

A stable relationship: isotopes and bioarchaeology are in it for the long haul

Given their ubiquity in dietary reconstruction, it is fitting that the story of isotopes began with a conversation over dinner. Although coined in scientific literature by Frederick Soddy (1913), the word ‘isotope’ was first conceived by Margaret Todd, a medical doctor (also known as the novelist ‘Graham Travers’, and an all-round gender-stereotype-smasher of their age). In 1912, Soddy and Todd were attending a supper in Glasgow. When talk turned to work, Soddy described the then nameless concept of elements of different masses that occupy the same place in the periodic table. Todd suggested the term ‘isotope’, from the Greekisos(‘same’) +topos(‘place’), and the name stuck (Nicol 1957; Nagel 1982).

Apollonius’ Problem: A Study of Solutions and Their Connections

In Tangencies Apollonius of Perga showed how to construct a circle that is tangent to three given circles. More generally, Apollonius' problem asks to construct the circle which is tangent to any three objects that may be any combination of points, lines, and circles. The case when all three objects are circles is the most complicated case since up to eight solution circles are possible depending on the arrangement of the given circles. Within the last two centuries, solutions have been given by J. D. Gergonne in 1816, by Frederick Soddy in 1936, and most recently by David Eppstein in 2001. In this report, we illustrate the solution using the geometry software Cinderella™, survey some connections among the three solutions, and provide a framework for further study.

Two Oxford science professors, F. Soddy and J. S. E. Townsend

A light–hearted account is given of incidents in the lives of Frederick Soddy, Nobel laureate in Chemistry 1921, and Dr Lee's Professor of Chemistry in Oxford, 1919–1936, together with Sir John Townsend, Wykeham Professor of Physics in Oxford, 1900–1941.