# Introduction to Nucleus

Nucleus is the central core of an atom with positive charge where all the mass of the atom is concentrated. The branch of physics dealing with the study of nucleus is known as nuclear physics. When nucleus is involved in a reaction, it is known as nuclear reaction. Nucleus was discovered by E. Rutherford in his alpha particle experiment.

**Nuclear radius: **The nucleus of an atom is spherical in shape. Its radius increases with the increase in atomic number which is given by:

R ∝ A^{1/3}

or, R = r_{o} A^{1/3}

Where r_{o} is a constant and its value is 1.2×10^{-5} m.

**Nuclear density (ρ _{N}): **The mass per unit volume of a nucleus is called nuclear density. We must assume that the nucleus is spherical in shape to find out the nuclear density.

$$\text{Nuclear Density}(\rho_N) = \frac{\text{Nuclear mass}}{\text{Nuclear Volume}}i.e., $$

$$\rho_N = \frac{m_n}{v_n}$$

$$or, \rho_N = \frac{AM_p}{\frac{4}{3}\pi R^3}$$

where, A = atomic mass and M_{p} is the mass of proton. Now, putting the value of R = r_{o} A^{1/3} we get:

$$o \rho_N = \frac{3AM_p}{4\pi (r_oa^\frac{1}{3})^3}$$

$$or, \rho_N = \frac{3AM_p}{4\pi r_o^3 A}$$

$$or, \rho_N = \frac{3AM_p}{4\pi (r_oa^\frac{1}{3})^3}$$

$$or, \rho_N = \frac{3\times 1.66\times 10^-27}{4 \pi(1.2\times 10^{-15})^3}Kgm^{-3}$$

$$\therefore \rho_N = 2.3\times 10^{17} kgm^{-3}$$

Hence, we conclude that the mass of nucleus is very high and is independent with atomic mass.

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