Simple calculation of the critical mass for highly enriched uranium and plutonium-239

Abstract

The correct calculation of and values for the critical mass of uranium or plutonium necessary for a nuclear fission weapon have long been understood and publicly available. The calculation requires solving the radial component in spherical coordinates of a diffusion equation with a source term, so is beyond the reach of most public policy and many first-year college physics students. Yet it is important for the basic physical ideas behind the calculation to be understood by those without calculus who are nonetheless interested in international security, arms control, or nuclear non-proliferation. This article estimates the critical mass in an intuitive way that requires only algebra.