13.5 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 up of 6329Cu atoms (mass of each atom = 62.92960 u).
Hint: The required energy will be equal to the total bindding energy of the nucleons. Step 1: Fidn the number of atoms in the coin.
Mass of a copper coin, m = 3 gm
Atomic mass of Cu6329 atomis in the coin, m = 62.92960 u
The total number of Cu6329 atomis in the coin, N=NA×m'massNumber
where,
NA= Avogadro's number =6.023×1023 atoms/g and mass number = 63 g
N=6.022×1023×363=2.868×1022 atoms Step 2: Find the mass defect in 6329Cu nucleus.
Cu6329 nucleus has 29 protons and (63-29) 34 neutrons.
∴ Mass defect of this nucleus, ∆m=29×mH+34×mn-m
where, Mass of a proton, ∆m= 1.007825u
Mass of a neutron, mn=1.008665 u ∆m= 29x1.007825+34x 1.008665-62.9296 = 0.591935 u Step 3: Find the mass defect of the coin.
Mass defect of all the atoms present in the coin, ∆M=0.591935×2.868×102=1.69766958×1022u
But1u=931.5MeV/c2 ∴∆M=1.69766958×1022×931.5MeV/c2
Step 4: Find the binding energy of the coin.
Hence, the binding energy of the nuclei of the coin is given as: