Is radioactive decay really exponential?

Department of Mathematics, University of Surrey - Guildford, Surrey GU2 7XH, UK

^a P.Aston@surrey.ac.uk

Received: 30 November 2011
Accepted: 25 January 2012

Abstract

Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of ¹⁴C can be calibrated over a period of 12550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3000 years are in error, which is generally attributed to past variation in atmospheric levels of ¹⁴C. We note that predicted atmospheric variation (assuming exponential decay) does not agree with results from modelling, and that theoretical quantum mechanics does not predict exact exponential decay. We give mathematical arguments that non-exponential decay should be expected for slowly decaying isotopes and explore the consequences of non-exponential decay. We propose an experimental test of this prediction of non-exponential decay for ¹⁴C. If confirmed, a foundation stone of current dating methods will have been removed, requiring a radical reappraisal both of radioisotope dating methods and of currently predicted dates obtained using these methods.