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# 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 atoms (of mass 62.92960 u).

## 2 Answers

8 years ago

Mass of a copper coin, mâ€™ = 3 g
Atomic mass of atom, m = 62.92960 u
The total number of atoms in the coin Where,
N
A = Avogadroâ€™s number = 6.023 Ã— 1023 atoms /g
Mass number = 63 g  nucleus has 29 protons and (63 âˆ’ 29) 34 neutrons
âˆ´Mass defect of this nucleus, Î”m'' = 29 Ã— m
H + 34 Ã— m
n âˆ’ m
Where,
Mass of a proton, m
H = 1.007825 u
Mass of a neutron, m
n = 1.008665 u
âˆ´Î”m'' = 29 Ã— 1.007825 + 34 Ã— 1.008665 âˆ’ 62.9296
= 0.591935 u
Mass defect of all the atoms present in the coin, Î”m = 0.591935 Ã— 2.868 Ã— 1022

= 1.69766958 Ã— 1022 u
But 1 u = 931.5 MeV/c2

âˆ´Î”m = 1.69766958 Ã— 1022 Ã— 931.5 MeV/c2
Hence, the binding energy of the nuclei of the coin is given as:
E
b= Î”mc2

= 1.69766958 Ã— 1022 Ã— 931.5 = 1.581 Ã— 1025 MeV
But 1 MeV = 1.6 Ã— 10âˆ’13 J
E
b = 1.581 Ã— 1025 Ã— 1.6 Ã— 10âˆ’13

= 2.5296 Ã— 1012 J
This much energy is required to separate all the neutrons and protons from the given coin.

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