An illustration of Benford's first digit law using alpha decay half lives

Abstract

Benford's law states that the first digits of a large body of naturally occurring numerical data in decimal form are not uniformly distributed but follow a logarithmic probability distribution. The values of radioactive decay half lives, which have been accumulated throughout the present century and vary over many orders of magnitude, afford an excellent opportunity to test the predictions of this law. To this end, we examine the frequency of occurrence of the first digits of both measured and calculated values of the half lives of 477 unhindered alpha decays and compare them with the predictions of Benford's law. Good agreement is found, and a similar distribution law for second digits is also considered.