$A$ beam of fast-moving alpha particles was directed towards a thin gold foil. The parts $A, B$,and $C$ of the incident beam and their corresponding transmitted or reflected parts $A^{\prime}, B^{\prime}$,and $C^{\prime}$ are shown in the adjoining diagram. The number of alpha particles in:

An alpha particle is accelerated through a potential difference of $10^6 \ V$. Its kinetic energy will be $MeV$.

$A$ fundamental particle of mass $m$ and charge $+e$ is projected towards a much heavier charged particle of charge $+Ze$,where $Z > 0$. The distance of closest approach of the incident particle is ........

When an $\alpha$-particle of mass $m$ moving with velocity $v$ bombards a heavy nucleus of charge $Ze$,its distance of closest approach from the nucleus depends on $m$ as

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?

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