State how the magnitude and nature (repulsive or attractive) of the strong nuclear force between two nucleons varies as their separation distance, $r$, increases from $0$ to values greater than $4fm$.

Identify the only baryon that is stable when free (not bound within a nucleus), and state its quark structure.

Write a decay equation representing beta-minus (${\beta }^{-}$) decay in terms of the fundamental quarks and leptons involved.

A nucleus with nucleon number $A$ can be modeled as a sphere of radius $R=r_0{A}^{1/3}$, where $r_0$ is a constant.

By first expressing the volume $V$ of the nucleus in terms of $A$, show that the nuclear density ${\rho }_0$ is constant (independent of $A$) and is given by:

${\rho }_0=\frac{3m_n}{4\pi r_0^3}$

where $m_n$ is the average mass of an individual nucleon.