Nuclear Radius - exam practice

Nuclear density...

An alpha particle has an initial kinetic energy of 32 MeV and is directed head-on at a nucleus of gold-197 $\left({}_{\phantom{1}79}^{197}Au\right)$.

What is the distance of closest approach of the alpha particle from the centre of the nucleus?

The diameter of a silver-108 $\left({}_{\phantom{1}47}^{108}Ag\right)$ nucleus is approximately three times that of the diameter of a nucleus of

A neutron of mass m is confined within a nucleus of diameter d.

Ignoring numerical constants what is an approximate expression for the kinetic energy of the neutron?

Element X has a nucleon number A_x_ and a nuclear density ${\rho }_x$. Element Y has a nucleon number of 2A_x_.

What is an estimate of the nuclear density of element Y?

The diameter of a nucleus of a particular nuclide X is 12 fm.

What is the nucleon number of X?