Based on which experiment did the Rutherford nuclear model come from?

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

Choose the correct alternative from the clues given at the end of each statement:
$(a)$ The size of the atom in Thomson's model is .......... the atomic size in Rutherford's model. (much greater than/no different from/much less than.)
$(b)$ In the ground state of .......... electrons are in stable equilibrium,while in .......... electrons always experience a net force. (Thomson's model/Rutherford's model.)
$(c)$ $A$ classical atom based on .......... is doomed to collapse. (Thomson's model/Rutherford's model.)
$(d)$ An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in .......... (Thomson's model/Rutherford's model.)
$(e)$ The positively charged part of the atom possesses most of the mass in .......... (Rutherford's model/both the models.)

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:

In the Rutherford's nuclear model of the atom,the nucleus (radius about $10^{-15} \; m$) is analogous to the sun about which the electron moves in an orbit (radius $\approx 10^{-10} \; m$) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom,would the earth be closer to or farther away from the sun than it actually is? The radius of the earth's orbit is about $1.5 \times 10^{11} \; m$. The radius of the sun is taken as $7 \times 10^{8} \; m$.

In the Rutherford experiment,$\alpha$-particles are scattered as shown in the figure. Which of the four paths is not possible?