Question

The isotope Cobalt-60 has a nuclear mass of 59.933820 u Calculate the Binding Energy of Cobalt-60 using the following information. Mass of Proton: 1.007825 u. Mass of Neutron: 1.008665 u. 1 u = 931.5 MeV

Answer 1

Cobalt has an atomic number (Z) of 27, which means the nuclei of all its isotopes have 27 protons. 60-Co has an atomic mass of 60, so it has 60-27 = 33 neutrons.

The mass of 27 isolated protons plus the mass of 33 isolated neutrons would be:

27*(1.007825 u) + 33*(1.008665 u) = 60.497220 u

The actual mass of the nucleus of 60-Co is 59.933820 u. The mass defect of a nucleus is the difference between the mass of the collection of isolated protons and neutrons that compose the nucleus and the actual experimental mass of the nucleus. In this case, the mass defect is:

60.497220 u - 59.933820 u = 0.563400 u

The mass defect is equal to the binding energy of a nucleus. Changing the energy of a system results in a change in mass of the system, as implied by Einstein's famolus formula, E = m*c^2. The conversion factor you are given for converting between atomic mass units and energy in MeV comes directly from this formula.

Using the conversion factor, the binding energy of the 60-Co nucleus is:

(0.563400 u)*(931.5 MeV/u) = 524.807 MeV

Answer 2

@asmagul nice writeup. Sometimes the binding energy will be given in terms of MeV/nucleon which in the case of Co-60 would be 524.807 MeV/60 nucleons or 8.747 MeV/nucleon