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. Cobalt 60 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.

Mass defect: 60.497220 u - 59.933820 u = 0.563400 u

The mass defect is equal to the binding energy of a nucleus.
using the fact that 1 u = 931.5 MeV/c^2

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

Answer 2

The Binding energy of Cobalt - 60 is : 524.8071 MeV

Atomic number of Co = 60

Atomic mass of Co = 27

Nuclear mass = 59.933820u

Number of neutron = 60 - 27 = 33

Number of protons = Atomic number = 27

Recall :

Mass defect = (calculated mass of nucleon - nuclear mass)

Calculated mass of nucleus :

(Number of proton × mass of proton) + (Number of neutron × mass of neutron)

Calculated mass of nucleus :

(27 × 1.007825u) + (33 × 1.008665u)

27.211275u + 33.285945u

= 60.49722u

Mass defect = 60.49722u - 59.933820u

Mass defect = 0.5634u

Binding Energy = 0.5634u × (931.5 MeV / 1u)

1u = 931.5 MeV

Hence, Binding Energy =

0.5634(931.5 MeV) × (931.5 MeV / 931.5MeV)

Binding Energy = 524.8071 MeV

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