Calculate the binding energy a uranium-235 nucleus in units of MeV/nucleon. The mass of an 235U atom is 235.043 929, the mass of a proton is 1.007 28, the mass of a neutron is 1.008 67, and the mass of an electron is 5.486 x 10^-4. (1 MeV = 1.60 x 10^-13 J)(a) 2.84 MeV/nucleon(b) 1.70 x 10^3 MeV/nucleon (c) 11.3 MeV/nucleon (d) 7.62 MeV/nucleon
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Calculate the number of protons (Z) and neutrons (N) in the uranium-235 nucleus. Uranium-235 has 92 protons, so the number of neutrons is 235 - 92 = 143.
Calculate the total mass of the protons and neutrons if they were free particles: Total mass = (Z * mass of proton) + (N * mass of neutron).
Calculate the mass defect (Δm) by subtracting the actual mass of the uranium-235 nucleus from the total mass of the protons and neutrons: Δm = (Total mass of protons and neutrons) - (mass of 235U atom).
Convert the mass defect from atomic mass units (amu) to energy using Einstein's equation, E = Δm * c^2, where c is the speed of light. Note that 1 amu = 931.5 MeV/c^2.
Calculate the binding energy per nucleon by dividing the total binding energy by the number of nucleons (A = 235) in the uranium-235 nucleus.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Binding Energy
Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It reflects the stability of the nucleus; a higher binding energy indicates a more stable nucleus. This energy can be calculated using the mass defect, which is the difference between the mass of the individual nucleons and the actual mass of the nucleus.
The mass defect is the difference between the total mass of the separate nucleons (protons and neutrons) and the mass of the nucleus itself. This mass loss, due to the conversion of mass into energy according to Einstein's equation E=mc², is crucial for calculating the binding energy. It highlights how energy is released when nucleons bind together to form a nucleus.
In nuclear physics, energy is often expressed in different units, such as joules and MeV (mega-electronvolts). To convert the binding energy from joules to MeV, one must use the conversion factor where 1 MeV equals 1.60 x 10^-13 joules. Understanding this conversion is essential for accurately reporting binding energy in the context of nuclear reactions and stability.
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