Prior to the detonation of the first atomic bomb, had the scientist been able to prove by theory that the reaction would stop? I assume they did considering they continued with the test. If not, how was Bethe able to calculate the yield of the explosion?
It stops because the active material is exploding, and separating. The critical mass density is no longer surpassed. Yield was the unknown. Only a slight amount of material is ever converted to energy. THe explosion itself stops the explosion. Bethe was one of the leading people who calculated the critical mass of the uranium bomb, and did the hydrodynamic calculations for the hydrogen implosion device. I don't know, but I suspect the yield of the hydrogen device was a ballpark figure at best then.
It stops because the active material is exploding, and separating. The critical mass density is no longer surpassed. Yield was the unknown. Only a slight amount of material is ever converted to energy. THe explosion itself stops the explosion. Bethe was one of the leading people who calculated the critical mass of the uranium bomb, and did the hydrodynamic calculations for the hydrogen implosion device. I don't know, but I suspect the yield of the hydrogen device was a ballpark figure at best then.
That is not an answer to my question. I know now why it stops. What I need to know is what was known prior to the detonation. Where the scientist working on the Manhattan Project aware of the variables that would prevent the explosion from continuing to react with the surrounding material. As far as when I was referring to Bethe's calculation, he figured in his head immediately that the explosion was 20 kt. He was within .1 of the actual yield.
I apologize for the confusion. To answer your question, prior to the detonation of the first atomic bomb, the scientists involved in the Manhattan Project had developed theoretical calculations and models to understand the behavior of the explosion and potential mechanisms for stopping it. They were aware of the concept of critical mass, which is the minimum amount of fissile material required to sustain a nuclear chain reaction.
Through extensive research, experiments, and calculations, the scientists working on the project had a good understanding of the factors that could prevent the explosion from continuing to react with the surrounding material. They knew that if the density of the fissile material dropped below the critical mass, the chain reaction would cease and the explosion would stop.
With regards to Bethe's calculation of the bomb's yield, it is true that he made a quick estimation of around 20 kilotons (kt) for the first atomic bomb's yield, which was very close to the actual yield of approximately 20-22 kt. Bethe was a highly renowned physicist and mathematician who played a significant role in calculating critical mass for the uranium bomb and conducting hydrodynamic calculations for the hydrogen implosion device. While the exact process behind his calculation is not explicitly known, he likely utilized his extensive knowledge of nuclear physics and his expertise in mathematical modeling to make a reasonably accurate estimate.