Could a nucleus fission into two nuclei? Your answer, which should include some calculations, should be based on the curve of binding energy.
negative sign of energy indicates that the energy is absorbed in the reaction. But in the fission reactions, energy releases. Hence, with the release of energy, cannot undergo fission into two nuclei.
Here, is energy released in the fission reaction.
From the figure , plot binding energy per nucleon verse mass number given in the text book, the binding energy per nucleon for nucleus approximately is and the binding energy per nucleon for nucleus is .
The nucleus has nucleons, so the total binding energy of one nucleus is,
Total binding energy two nucleus is,
The amount of energy released in the nuclear reaction which involves a 56 nucleus fission into two nuclei is
Here, negative sign of energy indicates that the energy is absorbed in the reaction. But in the fission reactions, energy releases. Hence, with the release of energy, cannot undergo fission into two nuclei.
The plutonium isotope 239 Pu has a half-life of 24,000 years and decays by the emission of a 5.2 MeV alpha particle. Plutonium is not especially dangerous if handled because the activity is low and the alpha radiation doesn’t penetrate the skin. However, there are serious health concerns if even the tiniest particles of plutonium are inhaled and lodge deep in the lungs. This could happen following any kind of fire or explosion that disperses plutonium as dust. Let’s determine the level of danger.
Alpha decay occurs when an alpha particle tunnels through the Coulomb barrier. FIGURE CP42.63 shows a simple one-dimensional model of the potential-energy well of an alpha particle in a nucleus with A ≈ 235. The 15 fm width of this one-dimensional potential-energy well is the diameter of the nucleus. Further, to keep the model simple, the Coulomb barrier has been modeled as a 20-fm-wide, 30-MeV-high rectangular potential-energy barrier. The goal of this problem is to calculate the half-life of an alpha particle in the energy level E = 5.0 MeV. a. What is the kinetic energy of the alpha particle while inside the nucleus? What is its kinetic energy after it escapes from the nucleus? b. Consider the alpha particle within the nucleus to be a point particle bouncing back and forth with the kinetic energy you found in part a. What is the particle’s collision rate, the number of times per second it collides with a wall of the potential? c. What is the tunneling probability Ptunnel ?
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