Comparison Between Historic Nuclear Explosion Yield Formulas

During the Manhattan Project, a simple formula was developed by Bethe and Feynman in 1943 to estimate the yield of a fission-only nuclear explosion of a uniformly dense bare sphere of supercritical fissile material. We have not found any evidence that Bethe and Feynman knew of the first yield formula obtained by Frisch and Peierls contained within their famous March 1940 memorandum. Similarly, we have not found any technical documents that compare the Bethe-Feynman formula to the earlier works of Frisch and Peierls or Serber. After adjusting for differences in the labeling of critical radii, we find that earlier formulas only differ by a scaling factor.