In the Rutherford scattering experiment,what will be the correct scattering angle $\theta$ for an $\alpha$-particle with an impact parameter $b = 0$ (in $^o$)?

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:

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.)

According to Richard Feynman,matter is made of which constituent particles? Why is it important? Write the atomic hypothesis.

Calculate the number of atoms in $39.4$ $g$ of gold. The molar mass of gold is $197$ $g$ $mol^{-1}$.

Give the relationship between impact parameter and scattering angle.