In the alpha particle scattering experiment,if $v$ is the initial velocity of the particle,then the distance of closest approach is $d$. If the velocity is doubled,then the distance of closest approach changes to:

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.

Explain Rutherford's explanation for scattered $\alpha$-particles.

Using Thomson's model of the atom,consider an atom consisting of two electrons,each of charge $-e$,embedded in a sphere of charge $+2e$ and radius $R$. In equilibrium,each electron is at a distance $d$ from the center of the atom. What is the equilibrium separation between the electrons?

Show the trajectory of $\alpha$-particle for different impact parameters and explain how Rutherford used this to determine the upper limit of the nuclear size.

The Franck-Hertz experiment proves that