Nuclear forces: The strong attractive forces acting between the neutrons and the protons which keep them bound together inside the tiny nucleus are called nuclear forces.

Important – properties:

(1) Nuclear forces are the strongest-attractive forces known is nature.

F_G        :           F_E        :           F_N        =          1          :           10³⁶    :           10³⁸     

(2) They are short range forces effective up to 2.3 fermi from a nucleon.

(3) They have changes, independent in nature

(4) They show saturation effect i.e. a nucleon can interact only with neighbors nucleus (nucleon).

(5) They are non-central forces i.e. they do not  act-along the line joining the centre of the 2 nucleus.

Nuclear Binding Energy:- The binding energy of a nucleus may be defined as the energy required to break up to nucleus into its constituent protons and neutrons and separate them to such a large distance that they may not increase with each other.

Mass Defect of a Nucleus

The difference between the rest mass of a nucleus and the sum of the rest masses of its constituent nucleons is called mass defect.

Consider the nucleus

it has Z protons and A – Z neutrons. Therefore the mass defect will be

Δm = Z m_p + (A – Z) m_n - m_N

Where m_p, m_n, m_N, are the rest masses of protons, neutrons and the nucleus of   respectively .
Expression for Binding energy

Let

be any element of mass number A, and atomic number Z, then mass of

Z protons = m_p. Z

Mass of Z electrons  = m_e. Z.

Mass of neutrons: (A – Z) m_n

Its mass defect is given by

Δ m = Z. mp + (A – Z) m_n - m_N                — (1)

Where m_N is the nuclear mass

 the binding energy of the nucleus given by

Δ E_b = B.E = (Δ m) c²

Δ E_b = [{Z m_p + (A – Z) m_n – m_N}] c² — (2)

Now adding and subtracting

Z m_e

In equation number (2) we have,

Δ E_b =B.E = [Z m_p + Z m_e + (A – Z) m_n – m_N –Z m_e] c²   — (3)

= B.E = [Z(m_p + m_e) + (A – Z) m_n – (m_N + Z m_e] c²       — (4)

Δ E_b =B.E = [Z (m_H) + (A – Z) m_n –m ( )].c²        — (5)

Where m_p + m_e = m_H = (mass of H-atom)

Or m_N = m( )  - m_eZ

 Where m ( ) is called the atomic mass.

Binding Energy per nucleon:

ΔE_bn = ΔE_b/A = [Z (m_H) + (A – Z) m_N m( )] c²

 

-->  The amount of energy required to separate are one nucleon from the nucleus is called binding energy per nucleon.

-->  It is obtained by dividing the binding energy of the nucleus by its mass number

-->  The binding energy per nucleon of a nucleus gives a measure of stability of a nucleus. Greater is the binding energy per nucleon of a nucleus more stable is the nucleus.