NUCLEAR PROPERTIES
An atomic nucleus is a bound quantum state which is capable to exist in variable quantum states characterized by their different properties. It constitutes two different elementary particles known as protons and neutrons. These elementary particles are jointly known as nucleons. The atomic nucleus generally exists in the lowest energy state also known as ground state. The properties corresponding to these ground states are known as static properties whereas the dynamic properties are those which are characterized during nuclear reactions, nuclear decay and nuclear excitation.
In this article we will discuss the static properties of nuclei.
Static properties of nuclei

Electric charge
A proton is nothing but the nucleus of Hydrogen atom. It carries one electronic unit of positive charge. The neutron on the other hand is electrically neutral.

Mass
The mass of a proton is about 1836 times the mass of an electron. The mass of neutrons is slightly greater than that of protons. The sum of the numbers of neutrons and numbers of protons is the mass number of an atom.

Binding energy
The minimum amount of energy required to break a nucleus completely in order to separate all the elementary particles from one another is known as Binding energy of the nucleus. As per the Special theory of relativity given by Albert Einstein, mass and energy are equivalent. Thus, if we wish to transform 1g into energy we will get 9 × 10^{13 }joules of energy. It implies the mass of an object can be completely transformed into energy.
i.e. E = mc^{2 }
where, c is the velocity of light
The Binding energy of a nucleus can be calculated using the below stated formula.
E_{B }= {ZM_{H }+ NM_{n} – M} c^{2}
In the above equation,


E_{B }– Binding Energy

Z – Number of protons

M_{H }– Mass of hydrogen atom

N – Number of neutrons

M_{n }– Mass of a neutron

M – Mass of the atom

c – Velocity of light

Binding energy per nucleon in the nucleus is known as Binding Fraction. It is given by
f_{B }= E_{B }/ A = (ZM_{H }+ NM_{n} – M)/ A

Size and shape
The mass of a nucleus is directly proportional to the mass number which implies the nuclear density, i.e. mass per unit volume is a constant quantity. This reveals that nuclear volume V ∝ Mass of nucleus A.
Considering the shape of the nucleus to spherical having radius R, we get
V = 4/3 π R^{3} ∝ A
Hence, R ∝ A^{1/3}
Or, R = r_{o} A^{1/3}
Here, r_{o} is a proportionality constant known as nuclear radius parameter.
The nuclear radius is generally expressed in femtometer which is equivalent to 10^{15} m. The femtometer is also known as Fermi (fm).

Nuclear spin
The nucleons have intrinsic spin angular momentum, i.e. ћ/2. Moreover, the nucleons also possess quantized angular momenta about the centre of mass of the nucleus similar to the electrons in an atom. Hence, it is clearly understood that the resultant angular momentum of the nucleus (I) is the vector sum of the orbital angular momentum (L) and spin angular momentum of the nucleus (S).
i.e. I = L + S
As per the quantum mechanical considerations, the total orbital and spin angular momenta of a nucleus are given by
P^{2}_{I }= I (I + 1) ћ^{2}
P^{2}_{L} = L (L + 1) ћ^{2}
P^{2}_{S} = S (S + 1) ћ^{2}

Magnetic dipole moment
The protons and neutrons also possess some measured values of magnetic dipole moments like that of electrons. The values are as follow:
µ_{p} = 2.7927 µ_{N}
µ_{n }= 1.9131 µ_{N}
Here,

 µ_{N} is termed as nuclear magneton
 e is mass of proton
 M is charge of proton
µ_{N} is given by, µ_{N }= eћ/2M_{p}
Substituting the respective values we get, µ_{N} = 5.0571 × 10^{27} J/T

Electric quadrupole moment
The electric quadrupole moment of a nucleus describes the effective shape of the ellipsoid of nuclear charge distribution. A nonzero quadrupole moment Q indicates that the charge distribution is not spherically symmetric. It was first discovered in the deuteron while observing the hyperfine structure of the atomic spectral lines. The interaction of the nuclear electric quadrupole moment with the homogeneous electric field due to the atomic electron distribution produces additional hyperfine splitting, which departs from the interval rule followed by the normal hyperfine splitting due to the interaction between the nuclear magnetic moment and the atomic magnetic moment.

Statistics of nuclei
All the fundamental particles can be categorised into two groups. The class of particles that constitutes spin 0 or integral obeys BoseEinstein statistics and are known as bosons. The second class comprises of particles that have half – integral spins (1/2,1/3,…..) obey FermiDirac statistics and are called fermions. Fermions obey Pauli’s exclusion principle which means no two particles can occupy the same quantum state.