Mass defect (Δm): It is found that the mass of a nucleus is always less than the sum of masses of it's constituent nucleons in free state. This difference in volumes is known as mass defect. Hence mass defect
Δm = Sum of masses of nucleons - Mass of nucleus
![1648_Mass defect and binding energy.png](https://www.expertsmind.com/../CMSImages/1648_Mass defect and binding energy.png)
where mp = Mass of proton, mn = Mass of each neutron, me = Mass of each electron
M = Mass of nucleus, Z = Atomic number, A = Mass number, M¢ = Mass of atom as a whole.
Packing fraction: Mass defect per nucleon is called packing fraction
Packing fraction (f) = Δm/A = M-A/A where M = Mass of nucleus, A = Mass number
Packing fraction measures the stability of a nucleus. Smaller the number of packing part, bigger is the stability of the nucleus.
(i) Packing fraction can be of negative, positive or zero value.
(ii) At A = 16, f → Zero
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![143_Mass defect and binding energy1.png](https://www.expertsmind.com/../CMSImages/143_Mass defect and binding energy1.png)
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Binding energy (B.E.): The neutrons and protons in a stable nucleus are held together by nuclear forces and energy is needed to pull them infinitely apart (or the same energy is released during the formation of the nucleus). This energy is known as the binding power of the nucleus.
If Dm is mass defect then according to Einstein's mass energy relation
Binding energy = Δm.mc2 = [{mpZ + mn(A - Z)} - M] .c2
(This binding energy is expressed in joule, because Δm is measured in kg)
If Δm is measured in amu then binding energy = Δm.amu = [{mpZ + mn(A - Z)} - M] amu = Δm * 931 MeV
Binding energy per nucleon: The average energy required to release a nucleon from the nucleus is called binding energy per nucleon.
Binding energy per nucleon
![680_Mass defect and binding energy2.png](https://www.expertsmind.com/CMSImages/680_Mass%20defect%20and%20binding%20energy2.png)
Binding energy per nucleon ∝ Stability of nucleus
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