Q. 53.9( 16 Votes )

A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of 6329Cu atoms (of mass 62.92960 u).

Answer :

Mass of a copper coin = 3 g


Atomic mass of copper atom, m = 62.92960u


The total number of atoms in the coin = N =


Where,


NA = Avogadro’s number = 6.023 × 1023 atoms /g


Hence, N = = 2.868 × 1022


The number of neutron and Proton both in a 63Cu29 atom is respectively 34 and 29.


The mass defect Δm = mp + mn-mFe


And Binding energy is given by EB = Δmc2


Mass of a proton = 1.007825 u


Mass of a neutron = 1.008665 u


Mass defect = Δm = 29 × 1.007825 + 34 × 1.008665-62.92960 u = 0.591935u


Mass defect of the coin = Δm = 0.591935 × 2.868 × 1022 u = 1.69766958 × 1022 × 931.5 MeV/c2


Binding Energy = 1.581 × 1025MeV = 1.581 × 1025 × 1.6 × 10-13 J = 2.5296 × 1012 J


Hence, 2.5296 × 1012 Joules of energy is required to separate the nucleons of the coin.


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