An $\alpha$-particle of energy $4 \text{ MeV}$ is scattered through $180^\circ$ by a fixed uranium nucleus. The distance of the closest approach is of the order of

The size of an atom is of the order of:

Calculate the number of atoms in $39.4$ $g$ of gold. The molar mass of gold is $197$ $g$ $mol^{-1}$.

$A$ nucleus with energy $\frac{1}{2}mv^2$ is fired at a target nucleus of charge $Ze$. The distance of closest approach to the $Ze$ nucleus is proportional to which of the following?

An $\alpha$ particle is accelerated through a potential difference of $10^6 \ V$. Then the kinetic energy $(K.E.)$ of the particle will be .......... $MeV$.

Given below are two statements:
$Statement$ $I$: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it,is Rutherford's model.
$Statement$ $II$: An atom is a spherical cloud of positive charges with electrons embedded in it,is a special case of Rutherford's model.
In the light of the above statements,choose the most appropriate from the options given below.