Question

Show that the density of the nucleus is 2.3×1017 kgm3

Answer 1

The radius of the nucleus can be expressed in terms of mass number:

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

The volume of the nucleus:

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi r_0^3A.$$

The mass in kilograms in terms of A:

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

The nuclear density

$$\rho=\frac{m}{V}=\frac{3A\cdot1.66\cdot10^{-27}\text{ kg}}{4\pi r_0^3A}=\frac{3\cdot1.66\cdot10^{-27}\text{ kg}}{4\pi r_0^3},\\\space\\ \rho=\frac{3\cdot1.66\cdot10^{-27}\text{ kg}}{4\cdot3.14 (1.2\cdot10^{-15})^3}=2.29\cdot10^{17}\text{ kg/m}^3.$$