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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).

Class 12th NCERT - Physics Part-II 13. Nuclei

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,

N_A = 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 = m_p + m_n-m_Fe

And Binding energy is given by E_B = 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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