Binding Energy, Mass Detect, Packing Fraction, Binding Energy of Nucleus and per Nucleon

Mass Defect

The nucleus is formed by bringing protons and neutrons together. The mass of nucleus so formed is less than the sum of masses of constituent protons and neutrons. The mass difference is called mass defect and denoted byΔm.

If Z is the number of protons in the nucleus(Atomic number Z), then the number of neutrons in the nucleus is (A - Z) (A is atomic mass). If m_pthat of the neutron, then

Sum of the masses of the protons and neutrons

= Zm_p+ (A - Z) m_n

If M_Nis the actual mass of the nucleus, then

Mass defect Δm = Zm_p + (A - Z ) m_n

Therefore, mass defect is defined as the difference between the sum of the rest masses of the nucleons forming the nucleus and the actual rest mass of the nucleus.

For example in the case of deuteron which contains one proton and one neutron the combined mass is {1.0073 + 1.0087} = 2.1060 a.m.u., whereas the actual mass of deuteron is 2.0136 a.m.u.

∴ Mass defect Δm = 2.1060 - 2.0136 = 0.0024 a.m.u.

Packing Fraction

It has been found that atomic mass through very close to whole number values invariably differs from the integral value by a small amount. For example, the atomic mass of H¹and Li⁶are H¹ = 1.007825, He⁴= 4.002603, Li⁶ = 6.015126.

The deviation of atomic mass fro whole number value is express in the form of a quantity known as packing fraction. Packing fraction defined as the ratio of the difference between the atomic mass of the atom M and its mass number A, i.e. (M - A) to its mass number A.

Therefore, packing fraction f= \(\frac{M-A}{A}\)

Variation of Packing Fraction with mass number

A graph between packing fraction f (multiplied by a factor 10⁴) and mass number A is shown in fig. It is known as packing fraction curve .