Question

What is the binding energy of a mole of nuclei with a mass defect of 0.00084 kg/mol?

Answer 1

7.55×10^10 KJmol-1

Step-by-step explanation:

The actual mass of a nucleus is usually less than the sum of the masses of the constituent neutrons and protons that make up the nucleus. This difference is called the mass defect.

The mass defect is related to the binding energy holding the neutrons and protons together in the nucleus. Since energy and mass are related by Einstein's equation;

E=∆mc^2 where;

E = binding energy of the nucleus

∆m= mass defect of the nucleus

c= speed of light

The larger the mass defect, the larger the binding energy of the nucleus and the more stable the nucleus.

From the data provided;

Mass defect= 0.00084 kg/mol or 0.84g/mol

Since 1 g/mol= 1 amu

0.84g/mol= 0.84 amu

The conversion factor from atomic mass units to MeV is 931

Binding energy = 0.84 × 931= 782.04 MeV

Since 1eV= 96.49KJmol-1

782.04×10^6eV= 7.55×10^10 KJmol-1

Answer 2

The binding energy of a mole of the nuclei is 252KJ

Step-by-step explanation:

The binding energy is the amount of energy required to separate an atom into its nuclei.

From Einstein's relations,

E = Δm
`c^(2)`

where E is the energy, Δm is the mass defect and c is the speed.

The mole of nuclei moves with the speed of light, so that;

c = 3.0 ×
`10^(8)` m/s

Given that Δm = 0.00084Kg/mol, the binding energy is calculated as;

E = 0.00084 × 3.0 ×
`10^(8)`

= 252000

= 252KJ

The binding energy of a mole of the nuclei is 252KJ.