$(a)$ Explain why did Rutherford select a gold foil in his alpha scattering experiments?
$(b)$ What observations in $\alpha$-scattering experiment led Rutherford to make the following conclusions?
$(i)$ Most of the space in an atom is empty.
$(ii)$ Nucleus is positively charged.
$(c)$ Mention any two drawbacks of Rutherford's model.

(A) Rutherford selected a gold foil because he required a layer that was as thin as possible. This gold foil was approximately $1000$ atoms thick.
$(b)$ $(i)$ Since most of the alpha particles passed through the gold foil without any deviation,it indicates that they did not encounter any obstruction in their path. This implies that most of the space inside an atom is empty.
$(ii)$ $A$ very small fraction of alpha particles were deflected by small angles,and some even rebounded. Since alpha particles are positively charged,this deflection suggests that they were repelled by a concentrated,positively charged center within the atom,which is the nucleus.
$(c)$ The two main drawbacks of Rutherford's model are:
$1$. According to classical electromagnetic theory,any charged particle undergoing acceleration in a circular orbit would continuously radiate energy. Consequently,the revolving electron would lose energy and eventually spiral into the nucleus,making the atom unstable.
$2$. The model could not explain the electronic structure of the atom or how electrons are distributed around the nucleus to maintain stability.