Question

Show that the density of nucleus is 2.3×1017 kgm- 3

Answer 1

Take sodium for example with mas A=23.

The radius of the nucleus is approximately

$$r=r_0A^{1/3}.$$

The volume is

$$V=\frac{4}{3}\pi r^3.$$

The mass in kilograms can be obtained from A:

$$m=A\cdot1.66\cdot10^{-27}\text{ kg}.$$

The density is

$$\rho=\frac{m}{V}=\frac{3A\cdot1.66\cdot10^{-27}\text{ kg}}{4\pi r_0^3A}=\frac{3\cdot1.66\cdot10^{-27}\text{ kg}}{4\pi r_0^3},\\\space\\ \rho=\frac{3\cdot1.66\cdot10^{-27}\text{ kg}}{4\pi (1.2\cdot10^{-15})^3}=2.29\cdot10^{17}\text{ kg/m}^3.$$

As we see, the density does not depend on the mass number A.