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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).
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orey laveti iam nagesh
Mass of a copper coin, m’ = 3 gAtomic mass of atom, m = 62.92960 uThe total number of atoms in the coinWhere,NA = Avogadro’s number = 6.023 × 1023 atoms /gMass number = 63 gnucleus has 29 protons and (63 − 29) 34 neutrons∴Mass defect of this nucleus, Δm'' = 29 × mH + 34 × mn − mWhere,Mass of a proton, mH = 1.007825 uMass of a neutron, mn = 1.008665 u∴Δm'' = 29 × 1.007825 + 34 × 1.008665 − 62.9296= 0.591935 uMass defect of all the atoms present in the coin, Δm = 0.591935 × 2.868 × 1022= 1.69766958 × 1022 uBut 1 u = 931.5 MeV/c2∴Δm = 1.69766958 × 1022 × 931.5 MeV/c2Hence, the binding energy of the nuclei of the coin is given as:Eb= Δmc2= 1.69766958 × 1022 × 931.5 = 1.581 × 1025 MeVBut 1 MeV = 1.6 × 10−13 JEb = 1.581 × 1025 × 1.6 × 10−13 = 2.5296 × 1012 JThis much energy is required to separate all the neutrons and protons from the given coin.
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