q-Calculus and the Symmetrized Radioactive Decay Law

Abstract

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.

A q-Analysis of Stable Daughter Nuclide

“…That is, λ ≈ λ q , since the half-lives are attainable-see ref. [18]. But for stable daughter nuclide the mean lifetime τ , which is given by τ = ∞ 0 t exp(−λt) ∞ 0 exp(−λt) is infinite.…”

“…N d (t) =N p (0)( [1] q − e q (−λ p t)) (2.4) However, a redefinition of the q-integer (see ref. [18]), where…”