(a) Explain briefly how Rutherford scattering of -particle by a target nucleus can provide information on the size of the nucleus.

(b) Show that density of nucleus is independent of its mass number A.

a)In Rutherford famous gold foil experiment most of the -particle pass through the foil undeflected signifying most of the space inside the atom should be empty, and many of them get deflected by a very small angle implying that the nature of the charge inside the atom (nucleus) that is located at the centre of the atom should be the same as the -particles i.e. positive. Out of 10000 -particle, one of them gets deflected for almost 180⁰ that means the particles retraces its path telling something very dense is situated at the centre of the atom.

b)Let the volume of the nucleus be V the mass of the nucleus be M and the mass of nucleous be m

we know the volume of the sphere is

and density ()

As we know where r₀ lies in between 1.2 fermis to 1.5 fermi

(mass of nucleus)

As we know the mass of the nucleus is A times mass of nucleons (m)

Equating mass of nucleus we get

We can see that nuclear density is independent of mass number (A)