Calculate the mass defect and nuclear binding energy per nucleon of each nuclide. a. O-16 (atomic mass = 15.994915 amu) b. Ni-58 (atomic mass = 57.935346 amu) c. Xe-129 (atomic mass = 128.904780 amu)

검증된 단계별 안내

Identify the number of protons, neutrons, and electrons in each nuclide. For example, O-16 has 8 protons, 8 neutrons, and 8 electrons.

Calculate the total mass of the protons, neutrons, and electrons if they were free particles. Use the approximate masses: proton = 1.007276 amu, neutron = 1.008665 amu, and electron = 0.0005486 amu.

Determine the mass defect by subtracting the actual atomic mass of the nuclide from the calculated total mass of the free particles.

Convert the mass defect from atomic mass units (amu) to energy using Einstein's equation, E = mc², where c is the speed of light (approximately 3.00 x 10^8 m/s). Use the conversion factor 1 amu = 931.5 MeV.

Calculate the nuclear binding energy per nucleon by dividing the total nuclear binding energy by the number of nucleons (protons + neutrons) in the nuclide.

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주요 개념

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Mass Defect

Mass defect refers to the difference between the mass of an atomic nucleus and the sum of the masses of its individual protons and neutrons. This discrepancy arises because some mass is converted into energy when nucleons bind together, according to Einstein's equation E=mc². The mass defect is crucial for calculating the binding energy of a nucleus.

Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is directly related to the mass defect; the greater the mass defect, the higher the binding energy. This energy is a measure of the stability of a nucleus, with higher binding energies indicating more stable nuclei.

Binding Energy per Nucleon

Binding energy per nucleon is the total binding energy of a nucleus divided by the number of nucleons (protons and neutrons) it contains. This value provides insight into the stability of different nuclei and allows for comparisons between them. A higher binding energy per nucleon generally indicates a more stable nucleus.