Legend has it that because of the wrong estimation of the critical mass of uranium-235, Heisenberg felt that the American atomic bomb could not be used as an actual combat weapon. This article describes estimating using a simple and clear physical image.
Written by | Congjun Wu (New Cornerstone Science Laboratory, Department of Physics, Westlake University)
Source | Selected from Physics, No. 6, 2024
Heisenberg is a famous German physicist, famous for pioneering the first modern form of quantum mechanics - matrix mechanics, and discovering the principle of uncertainty detection. However, there are also some controversial aspects of his life. For example, he once presided over the nuclear program of Nazi Germany. Here's a legend about him.
After Germany's defeat in 1945, Heisenberg and Hahn were captured by the U.S. Army and placed under house arrest together on a British estate. Hahn was a nuclear physicist who discovered the fission of atomic nuclei in 1938. In August 1945, after the atomic bombing of the "Little Boy" in Hiroshima, the United States and Britain deliberately told them the news and then monitored their reactions. Heisenberg and Hahn talked as they walked. Heisenberg said the news was fake unless the United States could drop tons of uranium. He estimated the critical mass of uranium-235 to be in the order of 10 tons. In fact, the "Little Boy" atomic bomb contained only about 60 kilograms of uranium-235. Heisenberg's estimates are far from the real situation, with orders of magnitude of difference.
A week later, Heisenberg realized his mistake. His mistake was to forget that the fission reaction was neutron multiplication. In his estimates, the uranium block would be large enough to hold all the neutrons released in the reaction, but this was unnecessary. In each step of the reaction, the chain reaction can still continue as long as an average of more than one neutron remains in the uranium block, such as 1.1.
The real critical mass value is 52 kg. This estimate is a bit higher than the true value, less than double the difference, and as an order of magnitude estimate, it already works very well.
The calculation of critical mass in nuclear physics books is often complex and requires the solution of the reaction-diffusion equation. The above estimates, the physical images are clear, the calculations are simple and straightforward, and the correct order of magnitude is given. It can be seen that an order of magnitude estimation can solve big problems.
This article is reprinted with permission from the WeChat public account "Chinese Physical Society Journal Network".
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