The radius of a nucleus is given by $r_0 A^{1 / 3}$, where $r_0=1.3 \times 10^{-15} \,m$ and $A$ is the mass number of the nucleus. The lead nucleus has $A=206$. The electrostatic force between two protons in this nucleus is approximately ……………. $N$

Choose the correct alternative from the clues given at the end of the 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.)

Given below are two statements :

$Statement$ $I$ : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model.

$Statement$ $II$ : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.

In the light of the above statements, choose the most appropriate from the options given below.

The energy of hydrogen atom in $n^{th}$ orbit is $E_n$, then the energy in $n^{th}$ orbit of singly ionised helium atom will be

An electron makes a transition from orbit $n = 4$ to the orbit $n = 2$ of tha hydrogen atom. The wave number of the emitted radiations ($R =$ Rydberg's constant) will be