# Nuclear Size & Nuclear Density ?

### Size of the Nucleus:

The number density of nuclear matter is approximately constant. This implies that the Volume of the nucleus is directly proportional to its mass number :

$\large \frac{4}{3} \pi R^3 \propto A$

The size of the nucleus depends on the number of nucleons present in it. The statistical radius of a nucleus is therefore given by the expression:

$\large R^3 \propto A$

R = R0 A1/3

where, R0 = 1.2 × 10-15 m.

A = mass number of the nucleus

### Density of Nuclear matter

Density of Nuclear matter = Mass of nucleus/Volume of Nucleus

If m = Average mass of a Nucleon , then mass of the nucleus = m A ; Where A = mass number

$\large \rho = \frac{m A}{\frac{4}{3} \pi R^3 }$

$\large \rho = \frac{m A}{\frac{4}{3} \pi (R_0 A^{1/3})^3 }$

$\large \rho = \frac{3 m }{4 \pi R_0^3}$

Using m = 1.67 x 10-27 kg , R0 = 1.2 × 10-15 m

$\large \rho = \frac{3 \times 1.66 \times 10^{-27} }{4 \times 3.14 \times (1.2 \times 10^{-15})^3}$

= 2.29 × 1017 kg/m3 ; which is very large as compared to ordinary matter . Hence matter in the nucleus is very densely packed .