The diagram shows the path of four $\alpha$-particles of the same energy being scattered by the nucleus of an atom. Which of these is/are not physically possible?

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below $14\; K$.) What results do you expect?

An alpha particle colliding with one of the electrons in a gold atom loses

An alpha nucleus of energy $\frac{1}{2}mv^2$ bombards a heavy nuclear target of charge $Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to

Answer the following questions,which help you understand the difference between Thomson's model and Rutherford's model better.
$(a)$ Is the average angle of deflection of $\alpha$-particles by a thin gold foil predicted by Thomson's model much less,about the same,or much greater than that predicted by Rutherford's model?
$(b)$ Is the probability of backward scattering (i.e.,scattering of $\alpha$-particles at angles greater than $90^{\circ}$) predicted by Thomson's model much less,about the same,or much greater than that predicted by Rutherford's model?
$(c)$ Keeping other factors fixed,it is found experimentally that for small thickness $t$,the number of $\alpha$-particles scattered at moderate angles is proportional to $t$. What clue does this linear dependence on $t$ provide?
$(d)$ In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of $\alpha$-particles by a thin foil?

What is the impact parameter?