1.) It has been estimated that the Earth contains 1.0 x 10^9 tons of natural uranium that can be mined economically. If all the world's energy needs (7.0 x 10^12 J/s) were supplied by 235(U) fission, how long would this supply last? Assume that the average energy released in a fission event is 208 MeV. (Hint: 235/92(U) has a percent abundance of 0.720)
2.) Two photons are produced when a proton and an antiproton annihilate each other. What is the minimum frequency and corresponding wavelength of each photon?
f = ________Hz
wavelength; = ________fm
3.) When a high-energy proton or pion traveling near the speed of light collides with a nucleus, it travels an average distance of 2.8 x 10^-15 m before interacting with another particle. From this information, estimate the time for the strong interaction to occur.
4.) A K0 particle at rest decays into a pi;+ and a pi;-. What will be the speed of each of the pions? The mass of the K0 particle is 497.7 MeV/c2 and the mass of each pion is 139.6 MeV/c2.
5.) Find the masses of the u and s quarks from the masses of the Σ+ and Ξ0. Assume that binding energies can be neglected. (Give your answers to one decimal place.)
U quark: _______MeV/c2
S quark: _______MeV/c2
6.) The atomic bomb dropped on Hiroshima on August 6, 1945, released 5 x 10^13 J of energy equivalent to that from 12,000 tons of TNT. (Assume that a typical 235U fission releases approximately 200 MeV of energy.)
(a) Estimate the number of 235/92(U) nuclei fissioned.
(b) Estimate the mass of this amount of 235/92(U).
7.) (a) Calculate how much energy would be released by the fusion of the deuterons in 1.0 gal of water. Note that 1 out of every 6500 hydrogen atoms is a deuteron.
(b) The average energy consumption rate of a person living in the United States is about 1.0 104 J/s (an average power of 10 kW). At this rate, how long would the energy needs of one person be supplied by the fusion of the deuterons in 1.0 gal of water? Assume that the energy released per deuteron is 1.64 MeV.
8.) Calculate the mass of 235 U required to provide the total energy requirements of a nuclear submarine during a 101 day patrol, assuming a constant power demand of 150,000 kW, a conversion efficiency of 15%, and an average energy released per fission of 208 MeV.
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This in-depth solution contains step-by-step calculations and explanations by finding the energy released in a fission event, frequency and wavelength of a photon, time for a strong interaction to occur, speed of the pions, masses of the quarks, nuclei fissioned and mass of uranium, energy released in a fission and fusion event, and efficiency of energy in a nuclear submarine. All workings and formulas are shown in a clear manner.