Using Thomson's model of the atom,consider an atom consisting of two electrons,each of charge $-e$,embedded in a sphere of charge $+2e$ and radius $R$. In equilibrium,each electron is at a distance $d$ from the center of the atom. What is the equilibrium separation between the electrons?

$A$ nucleus with energy $\frac{1}{2}mv^2$ is fired at a target nucleus of charge $Ze$. The distance of closest approach to the $Ze$ nucleus is proportional to which of the following?

Which scientist proposed the plum pudding model of the atom?

Who discovered the spin quantum number?

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.)

The distance of closest approach of an alpha particle to a nucleus when the alpha particle moves towards the nucleus with linear momentum $P$ is $d$. What is the distance of closest approach of the alpha particle to the nucleus if the linear momentum of the alpha particle is $1.5 P$?