What is the plum pudding model of the atom?

In an alpha particle scattering experiment,the distance of closest approach for the $\alpha$-particle is $4.5 \times 10^{-14} \ m$. If the target nucleus has an atomic number $Z = 80$,then the maximum velocity of the $\alpha$-particle is approximately $... \times 10^5 \ m/s$.
$\left(\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ SI \ unit, \text{mass of } \alpha \text{-particle } m = 6.72 \times 10^{-27} \ kg, e = 1.6 \times 10^{-19} \ C\right)$

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.

$A$ proton is fired from very far away towards a nucleus with charge $Q=120 \ e$,where $e$ is the electronic charge. It makes a closest approach of $10 \ fm$ to the nucleus. The de Broglie wavelength (in units of $fm$) of the proton at its start is: (take the proton mass,$m_0 = (5/3) \times 10^{-27} \ kg$,$h/e = 4.2 \times 10^{-15} \ J \cdot s/C$,$\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ N \cdot m^2/C^2$,$1 \ fm = 10^{-15} \ m$)

State the atomic hypothesis regarding the structure of matter.

In the Rutherford experiment,$\alpha -$ particles are scattered from a nucleus as shown. Out of the four paths,which path is not possible?