Question

What is the mass defect and binding energy of ${{}_{27}{C{o^{59}}}}$ which has a nucleus of mass $58.9334,\,({M_p}\, = \,1.00784,\,{M_n} = \,1.00874) \\\ Number\,of\,n\, = \,59 - 27 = 32 \\\$
(A) 517.914 MeV
(B) 617.914 MeV
(c) 17.914 MeV
(d) 717.914 MeV

Answer 1

Mass defect of a nucleus represents the amount of mass equivalent to the binding energy of the nucleus, which is the difference between the mass of a nucleus and some of the individual masses of the nucleons of which it is composed.

Complete step by step solution:
$Mass\,of\,Nucleus\, = \,(27 \times 1.0078 + 32 \times 1.0087) \\\ = \,27.2106\, + \,32.2784 \\\ = \,59.489 \\\ Mass\,defect\, = Mass\,of\,Nucleus\,(calculated) - mass\,of\,Nucleus \\\$
$= \,59.489 - 58.933 \\\ = \,0.5564 \\\ BE\,of\,nucleus\, = \\\ \Delta {E_b} = \,931.5 \times \Delta m\,\,MeV \\\ = \,931.5 \times \,0.556 \\\ = \,517.914\,MeV \\\$

The option (A) is correct.

Additional Information: According to Einstein’s theory of relativity mass is a measure of the total energy of a system. Thus the total energy of the nucleus is less than the sum of energies of its constituent nucleons. The formation of a nucleus from a system of isolated protons and neutrons is therefore an exothermic reaction – meaning that it releases energy. The energy emitted, or radiated, in this process is $(\Delta m){c^2}$.

Note: The binding energy of the nucleus is the energy needed to separate it into individual protons and neutrons in terms of atomic masses. It is especially applicable to subatomic particles in atomic nuclei, to electrons bound to nuclei in atoms, and to atoms and ions bound together in crystal. According to nuclear particle experiments, the total mass of the nucleus is less than the sum of the masses of its constituent nucleons (protons and neutrons).