# The Physics of the Manhattan Project

**By B. Cameron Reed**, Second edition (Springer-Verlag, Heidelberg, 2011), 170 pp., hardcover, $69.95, ISBN 978-3-642-14708-1.

**Reviewed by Bernard L. Cohen**

This book describes, in complete detail, a course for advanced undergraduate physics majors, on the various physics problems involved in the World War II Manhattan Project that initiated the Nuclear Age. After an introductory chapter on basic nuclear physics and the fission process, some of the principal topics treated are critical mass for a bomb, effects of tamper, bomb efficiency, reactor physics, uranium isotope separation, problems with trace element impurities, and problems with bomb pre-detonation. The author has no access to classified information, and most of the treatments were developed independently by him, using the physics and mathematics appropriate for the targeted students. His treatments involve many calculational simplifications, such as assuming spherical geometry for obviously non-spherical situations (e.g. gun type bombs), but he gives careful consideration to problems from these simplifications, ultimately using information from unclassified literature to evaluate conclusions. He demonstrates extensive familiarity with this unclassified literature, giving abundant references; his collection of these references is a very valuable feature of the book.

The course described includes homework problems, many using Excel spreadsheets available at www.manhattanphysics.com. Some of the results from these spreadsheet calculations are plotted in the book; for example, in the simulation of the Hiroshima bomb based on a 64 kg core of radius 9.35 cm plus a 311 kg tungsten carbide tamper of outer radius 18 cm (these numbers are from unclassified sources), he calculates that nearly all the energy is generated between 0.83 and 0.89 microseconds after initiation, giving a pressure vs time peaking at 50 billion atmospheres, a final core expansion rate of 270 km/sec, and a yield of 11.9 kiloton of TNT, with 1.1% of the U-235 undergoing fission. The U-235 in the core was 3.5 times the critical mass with this tamper. The dependence of yield on tamper is dramatic, increasing by a factor of 8 between 50 kg and 350 kg of tamper mass.

In his treatment of thermal reactors, he calculates the mean free path for scattering in graphite to be 2.6 cm and the number of scatterings required for thermalization to be 50-100; combining these gives a neutron displacement of 19-26 cm which determines the graphite lattice spacing, consistent with the 21 cm lattice spacing in Fermi’s original graphite reactor. In other sections he shows that one boron atom impurity per 17,000 carbon atoms in the graphite would cause a serious loss of neutrons, and that the plutonium production is 593 grams/day in a 1000 MW nuclear power reactor and 190 grams/day in the Hanford production reactors, to be compared with the 6200 grams in the core of the Trinity and Nagasaki bombs.

In treating uranium isotope separation by gaseous diffusion, he calculates the number of stages required for 90% enrichment to be 1665. One thousand stages gives only 34% enrichment. In treating the predetonation probability for the Trinity and Nagasaki bombs, he takes the implosion to double the density of the Pu-239 core (including 1.2% Pu-240) in 4.7 microseconds, and derives a non-predetonation probability of about 88%, citing an unclassified source to show that this estimate is realistic. In other separate sections he calculates that the ambient temperature of the Nagasaki and Trinity bombs approached 79 deg-C, and that these explosions viewed from the Moon would have appeared 30 times brighter than Venus.

If one is interested in how such results (and many more like them) were derived by an academic physicist without any information from classified sources, this book would be an enlightening read for anyone with a physics degree or with equivalent knowledge. To go through the mathematical derivations can be time consuming and tedious unless one is driven by intense interest, but it is easy to get the sense of the treatments with a much smaller effort. Although I have taught courses (albeit on a lower level) involving much of the material covered in this book, I learned a great deal from the treatments presented, including many improved physical insights, and lots of quantitative results.

From the teaching viewpoint, if one wants to provide an advanced undergraduate course on applications involving a great deal of interesting physics, this would be an ideal textbook. At first sight, this material might not seem attractive to most students, but for students with an interest in nuclear bombs and nuclear reactors, this course would be not only satisfying but exciting.

*Bernard L. Cohen*

*Physics Dept., University of Pittsburgh*

*Pittsburgh, PA 15260*

These contributions have not been peer-refereed. They represent solely the view(s) of the author(s) and not necessarily the view of APS.