# Nuclear Stability

BINDING ENERGY OF NUCLEUS

As pointed out earlier, the particles present in the nucleus (protons and neutrons) are called nucleons. The sum of the individual masses of various particles in the nucleus must be

equal to the nuclear mass. But this is not so in actual practice. The nuclear mass is somewhat less than the sum of the individual masses of various nuclear particles. The difference between the actual nuclear mass and the expected nuclear mass (sum of the individual masses of nuclear particles) is referred to as mass defect. The mass defect can be converted into equivalent energy by means of Einstein equation (E = mc2). The energy equivalent to mass-defect is responsible for holding the nucleons together and is called binding energy of the nucleus.

For example, let us calculate the binding energy of helium nucleus which contains two protons and two neutrons.

Mass of 2 free neutrons (2 x 1.00867 u) = 2.01734 u

Mass of 2 free protons (2 x 1.00728 u) = 2.01456 u

Sum of the masses of 2 free neutrons and 2 free protons

= 4.03190 u

Thus, binding energy of helium nucleus is 28.3 MeV. The binding energy per nuclear particle (nucleon) is a measure of the stability of nucleus. Binding energy may also be considered as the energy required to separate the individual particles of the nucleus.

It may be noted that binding energy in MeV can be directly founded by multiplying the mass defect ( Δm) in u ( amu) with (931.48), a conversion factor as explained below:

1 u = 1.6603 x 10-27 kg

c = 2.9979 x 10s ms1

Using   E=m2

= 1.6603 X 10-27 kg X (2.9979 X 108 ms-1)2

= 1.4924 X 10-10 kg m2 s-2

= 1.4924 x 10-10 1

= 1.4924 x 10-10 / 1.602 x 10-19 ev = 931 .48 x 106 ev

= 931.48 mev.

NCLEAR FORCES

The forces which hold nuclear particles together are referred to as nuclear forces. The exact nature of these forces is still not clear. However, a Japanese physicist Yukawa (1935) has provided theoretical explanation for the origin of these forces. He postulated the presence of a new fundamental particle meson (π-) in the nucleus of the atom. The meson is approximately 273 times heavier than electron. The meson may be positively charged (π+) or negatively charged (π- or neutral (π- Yukawa further postulated that in the nucleus, there is interconversion of proton into neutron and vice versa through the exchange of meson. For example, a proton may change into neutron by losing a positive meson (π+) or by capture of negative meson π-). Similarly neutron may change into proton either by capture of positive meson (n+) or by loss of negative meson (π) The rapid exchange of mesons among the nucleons gives rise to exchange forces which are responsible for holding the nucleons together. Some interesting features about nuclear forces are:

• Nuclear forces are about 1038 times as strong as gravitational forces and 100 times as strong as coulombic forces.

• They are short range forces and are independent of charge.

• They are not governed by inverse square law.