what was the name of the program that researched and built the first atomic weapons in the united states
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Step 1: Identify the historical context of atomic weapons development in the United States during World War II. Show more…
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Investigate the history of the Manhattan Project.
What was the Manhattan Project? Briefly describe its development and culmination.
Review. The first nuclear bomb was a fissioning mass of plutonium- 239 that exploded in the Trinity test before dawn on July $16,1945,$ at Alamogordo, New Mexico. Enrico Fermi was 14 $\mathrm{km}$ away, lying on the ground facing away from the bomb. After the whole sky had flashed with unbelievable brightness, Fermi stood up and began dropping bits of paper to the ground. They first fell at his feet in the calm and silent air. As the shock wave passed, about 40 $\mathrm{s}$ after the explosion, the paper then in flight jumped approximately 2.5 $\mathrm{m}$ away from ground zero. (a) Equation 17.10 describes the relationship between the pressure amplitude $\Delta P_{\max }$ of a sinusoidal air compression wave and its displacement amplitude $s_{\max }$ . The compression pulse produced by the bomb explosion was not a sinusoidal wave, but let's use the same equation to compute an estimate for the pressure amplitude, taking $\omega \sim 1 \mathrm{s}^{-1}$ as an estimate for the angular frequency at which the pulse ramps up and down. (b) Find the change in volume $\Delta V$ of a sphere of radius 14 $\mathrm{km}$ when its radius increases by $2.5 \mathrm{m} .$ (c) The energy carried by the blast wave is the work done by one layer of air on the next as the wave crest passes. An extension of the logic used to derive Equation 20.8 shows that this work is given by $\left(\Delta P_{\max }\right)(\Delta V) .$ Compute an estimate for this energy. (d) Assume the blast wave carried on the order of one-tenth of the explosion's energy. Make an order-of-magnitude estimate of the bomb yield. (e) One ton of exploding TNT releases 4.2 $\mathrm{G} \mathrm{J}$ of energy. What was the order of magnitude of the energy of the Trinity test in equivalent tons of TNT? Fermi's immediate knowledge of the bomb yield agreed with that determined days later by analysis of elaborate measurements.
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