The mass of a proton is 1.00728 amu and that of a neutron is What is the binding energy per nucleon of a (The mass of a cobalt-59 nucleus is 58.9332 amu.The speed of light is 3.00 × m/s.)

Question

The mass of a proton is 1.00728 amu and that of a neutron is  What is the binding energy per nucleon  of a  (The mass of a cobalt-59 nucleus is 58.9332 amu.The speed of light is 3.00 ×  m/s.)

Quizplus · Accepted Answer

The binding energy per nucleon of a nucleus is given by:
(Binding energy of the nucleus) / (Number of nucleons in the nucleus)

To find the binding energy of a cobalt-59 nucleus, we need to first convert its mass from amu to kg:
mass = 58.9332 u * 1.66 × 10^-27 kg/u = 9.78 × 10^-26 kg

The total energy of a nucleus can be approximated by Einstein's famous equation:
E = mc^2

where m is the mass defect of the nucleus, which is the difference between the total mass of its individual nucleons and the mass of the nucleus. The mass defect can be calculated as follows:
mass defect = [(number of protons * mass of proton) + (number of neutrons * mass of neutron)] - mass of nucleus
mass defect = [(27 * 1.00728 u) + (32 * 1.00867 u)] - 58.9332 u
mass defect = 0.5308 u

Using Einstein's equation, we can find the total energy of the cobalt-59 nucleus:
E = (0.5308 u * 1.66 × 10^-27 kg/u) * (3.00 × 10^8 m/s)^2
E = 4.76 × 10^-11 J

The binding energy of a nucleus is the amount of energy required to completely separate all of its nucleons. This means that the binding energy is a measure of the strength of the nuclear force that holds the nucleons together. To find the binding energy per nucleon, we divide the binding energy by the number of nucleons in the nucleus:
binding energy per nucleon = (total binding energy) / (number of nucleons in the nucleus)
binding energy per nucleon = (4.76 × 10^-11 J) / (59 nucleons)
binding energy per nucleon = 8.07 × 10^-13 J/nucleon

This value is closest to choice A: 1.37 × 10^7 J/kg or 1.37 × 10^-13 J/nucleon, which is the correct answer.

The Mass of a Proton Is 1