Question

A given coin has a mass of 3.0 g. Calculate the nuclear energy thatwould be required to separate all the neutrons and protons fromeach other. For simplicity assume that the coin is entirely made of6329Cu atoms (of mass 62.92960 u).

Answer 1

Given: The mass of a copper coin 3 g, the atomic mass of copper 29 63 Cu is 62.92960 u

The total numbers of atoms in the coin are given as,

N= N A ×m A

Where, Avogadro number is N A , the number of atoms are N, the mass number of copper A and the mass of a copper coin is m.

By substituting the given values in the above equation, we get

N= 6.022× 10 23 ×3 63 =2.868× 10 22  atoms

The number of protons in the nucleus of 29 63 Cuis 29 and the number of neutrons in the nucleus of 29 63 Cuis 34.

The mass defect of the nucleus of copper atom is given as,

Δ m ′ =29 m p +34 m n −m

Where, the mass of proton is m p , the mass of neutron is m n and the mass defect of the nucleus is Δ m ′ .

By substituting the given values in the above equation, we get

Δ m ′ =29×1.007825+34×1.008665−62.9296 =29.226925+34.29461−62.9296 =0.591935 u

The mass defect of all the atoms present in the coin is given as,

Δm=Δ m ′ ( N )

By substituting the given values in the above equation, we get

Δm=0.591935×2.868× 10 22 =1.69766958× 10 22  u

The binding energy of the nucleus of iron is given as,

E=Δm c 2

Where, the speed of light is c and the binding energy is E.

By substituting the given values in the above equation, we get

E=1.69766958× 10 22 c 2 ×931.5  MeV/ c 2 =1.584× 10 25 ×1.6× 10 −13  J =2.535× 10 12  J

Thus, the amount of energy required to separate all the neutrons and protons from the given coin is 2.535× 10 12  J.