Some Series and Mathematic Constants Arising in Radioactive Decay

  •  Xun Zhou    


In this paper we show the construction of 32 infinite series based on the law of decay of radioactive isotopes, which indicates that a radioactive parent isotope is reduced by 1/2 and 1/e of its initial value during each half-life and mean life, respectively. We found that the ratios among the values of the radioactive parent isotope and the radiogenic daughter isotope for each half-life’s and mean life’s decay can be used to construct 16 half-life related (or 2-related) and 16 mean life related (or e-related) infinite series. There are 8 divergent series, 4 previously known convergent series and 2 series converging to the Erdös-Borwein constant. The remaining 18 series are found to converge to 18 mathematical constants and the divergent and alternating mean life related series leads to another 2 mathematical constants. A few interesting mathematical relations exist among these convergent series and 5 sequences are also attained from the convergent half-life related series.

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