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- by Pritisha Malla 3 months ago

**Introduction**

The branch of physics dealing with the study of atomic nucleus is called nuclear physics.

**Properties of Nucleus**

1.Charge: The nuclei consists of protons and neutrons. Since neutrons are neutral, the nuclei is positively charged.

Z(+e) = +Z(e)

2. Mass of nucleus: The mass of the nucleus is the sum of masses of nucleons.

Mass of nucleus = Z m _{p }+ Nm _{n}

_{3.Size: }_{Rutherford's work on the scattering of }_{α-}_{particle showed that mean radius of atomic nucleus is of the order }10^{-14} m to 10^{-15 }m while that of the atom is about 10^{-10}m.Thus, the nucleus is about 10,000 times smaller than the atom. The empirical formula for the nuclear radius is R=r_{o}A^{1/3}

where A is the mass number and r _{o} = 1.2 * 10-^{15}m = 1.2 F m

4. Nuclear density: The mass per unit volume of a nucleus is called nuclear density.

\Nuclear density, ρ = Nuclear Mass/ Nuclear Volume =A m _{N}/(4/3)*π*r_{o}R3_{=} A m _{N}/(4/3)*π*(r_{o}A^{1/3} )^{3}= 3m_{N}A/ 4π r _{o }A

where m _{N }is mass of a nucleon.

5. Nuclear spin and magnetic moment : Protons and neutrons are in continuous motion in discrete quantized orbits. This orbital motion produces the nucleons with mechanical angular momentum. In addition to orbital motion, nucleons have internal angular momentum called spin. As a result, they possess magnetic moment associated with their orbital motion and spin.

**Einstein's Mass Energy Relation**

From Einstein's Mass Energy Relation,

E = mc^{2}

^{ } =1.66*10^{-24}g =931.5*10^{-6}*10^{-19}

^{ = 931.5 MeV}

^{M }p^{ = 1.672622*}^{10}^{-27 kg = 1.007276=938.279MeV}

^{M }n=1.674927*10^{-27 }kg = 1.008665u = 939.573 MeV

M_{e = 9.10938* 10}^{-31}_{kg = 0.000548580u = 0.511 MeV}

_{If we give} _{Δ }_{E energy to some matter, then by above relation, its mass will increase by }_{Δ}_{m given by}

_{ }_{Δ m = } _{Δ }_{E/c}2

In view of the mass energy relation, the law of energy conservation and mass conservation are no more independent laws but single law called law of mass - energy conservation.

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