Nuclear Stability

The nucleus of an atom is extremely small.  The radius of the nucleus is about 10^-15  m. In such a small place protons and neutrons are held together. Protons are positively charged so they should get repelled however the majority of the nuclei are stable hence there must be certain factors which affect nuclear stability. Some of the factors that affect nuclear stability are

• Nuclear forces.
• Mass defect and binding energy.
• The neutron to proton ratio (N/Z ratio).
• Odd and even number of nucleons.

Stability of Nucleus Due to Nuclear Forces:

The forces which hold the nucleons together within the nucleus are called nuclear forces. These are short-range forces. They are different from gravitation forces.

Explanation :

The nucleus of an atom, except in the case of radioactive elements is extremely stable. The nucleus on account of its stability does not take part in the chemical reaction.

There are forces between proton and proton (P-P), neutron (N-N) and even between proton and neutron (P-N). There are repulsive forces between proton and proton. In presence of such forces, the nucleons are kept together within the nucleus by such strong forces that very high energy is required to break the nucleus.

The nature of nuclear binding forces is totally different from that of gravitational and electrostatic forces. Nuclear forces are stronger than gravitational and electrostatic forces. These nuclear binding forces are independent of charge and operate over only a very short distance of range 10-15  m. Hence they are short-range forces.

Concept:

According to particle exchange theory proposed by Japanese scientist Yukawa, the nuclear forces arises from a constant exchange of particles called mesons between the nearby nucleons.

As two atoms are held together by sharing of electrons, two nucleons or nuclear particles are held together by sharing of mesons(π). According to charge carried by them, Mesons are classified into three type viz. Positive charge meson (π⁺), Negative charge meson (π^–), Zero charge meson (π⁰)

Exchange of positive charge meson (π⁺), negative charge meson (π^–) accounts for the nuclear force between protons and neutrons. Transfer of charged meson converts a proton to neutron and neutron to proton.

p        →    n   + π⁺

n      →   p   +    π^–

Mesons are exchanged between like particles such as p-p or n-n

p₁      →   p₂   +  π⁰

n₁      →   n₂   +  π⁰

Due to the constant interaction between nucleons, an exchange force is developed called nuclear force which holds nucleons together inside the nucleus of an atom with minimum potential energy. The greater the exchange force (nuclear force) the greater is the stability of the nucleus.

Mass of π⁺  and π^– is 273 times that of the electron. While that of π⁰ is 264 times that of the electron. Mesons are unstable outside the nucleus.

Stability of Nucleus Due to Nuclear Binding Energy:

Mass Defect:

The difference between the calculated mass due to nucleons and the actual observed isotopic mass of the nucleus is called the mass defect. Mass defect is denoted by ‘Δm’.

Explanation: 

Considered _Z X^A isotope.  Let A be the mass number and Z be the atomic number of the element. If m_p, me and mn be the masses of a proton. electron and neutron respectively, M_i be isotopic mass then,

Thus calculated mass, M_cal     = Z ×  m_p +  ( A  –  Z  ) × m_n

Now mass defect (Δm) =   Calculated mass   –   observed mass

Δm   =   [ Z  × m_p +   ( A  -Z  ) × m_n]  –   M_i

mass of an electron is negligible. Hence it is not considered for calculation of mass defect.

The mass equivalent of mass defect is converted into energy which is given by Einstein’s energy equation.

E   = Δm ×  C²

Where C = speed of light in free space.

This energy holds the nucleons together in the nucleus called nuclear binding energy. Hence nuclear stability is proportional to the mass defect.

Nuclear Binding Energy:

The energy equivalent to mass defect, which is required to break the nucleus into its isolated nucleons is called nuclear binding energy. It is denoted by E and is measured in MeV (million electron volts) or J (joule). It is obtained by multiplying mass defect in a.m.u. by 931.Therefore,

Nuclear binding energy  = mass defect in a.m.u.  x  931

Nuclear Binding Energy Per Nucleon or Average Binding Energy:

It is the ratio of total nuclear binding energy to the total number of nucleus present in that isotope.

Nuclear Stability on the Basis of Nuclear Binding Energy:

Since binding energy is responsible for holding the nucleons in the nucleus.  Nuclear stability is proportional to the nuclear binding energy.  The more the binding energy the greater is the nuclear stability. If we plot binding energy per nucleon in MeV against mass numbers (A) for different nuclei, a curve is obtained. The curve is called binding energy curve. This curve represents the relative stability of the nuclei of the elements.

• The curve shows that the average binding energy rises sharply and then it is constant for a broad range and then it decreases slowly.
• It is observed that higher the binding energy per nucleon, greater is the stability of the nucleus.
• It is found that the stable nuclei have binding energy per nucleon between 8 and 8.8 MeV. Binding energy per nucleon for the majority of the elements lies between 8 – 8.85 Mev.
• Elements having a mass number less than 25 have low binding energy per nucleon. They show the tendency of nuclear fusion. Elements  ₂He⁴,  ₆C¹² and  ₈O¹⁶ lie above the curve, it indicates there greater stability.
• For elements having the mass number in the range, 25 to 65 binding energy per nucleon smoothly increases from 7.5 MeV to 8.8 MeV. It attains maximum value for iron. Due to extra stability iron, cobalt and Nickel form the core of the earth.
• For nuclei having the mass number in the range, 65 to 160 binding energy per nucleon is almost constant at 8.5 MeV.
• For nuclei having mass number beyond 160, the binding energy per nucleon decreases steadily and it becomes 8 MeV for ₈₃Bi209 and it reaches to 7.6 MeV for Uranium.
• Nuclei with the mass number more than 220 and having binding energy per nucleon less than 8 are highly unstable and have a tendency of fission or natural radioactivity.
• Thus the nuclei having B.E. per nucleon in a range of 8 to 8.5 MeV are stable while those having B.E. per nucleons less than 8 MeV are unstable or less stable.