Choose the correct option from the following options given below

Energy levels $A, B$ and $C$ of a certain atom correspond to increasing values of energy, i.e. $E_A < E_B < E_C$ . If $\lambda _1, \lambda _2$ and $\lambda _3$ are the wavelengths of radiations corresponding to transitions $C$ to $B, B$ to $A$ and $C$ to $A$ respectively , which of the following relations is correct ?

A proton is fired from very far away towards a nucleus with charge $Q=120 \ e$, where $e$ is the electronic charge. It makes a closest approach of $10 \ fm$ to the nucleus. The de Brogle wavelength (in units of $fm$ ) of the proton at its start is :

(take the proton mass, $m _0=(5 / 3) \times 10^{-27} kg , h / e =4.2 \times 10^{-15} J / s / C ; \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 m / F ; 1 fm =10^{-15} m$ ) 

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.)

In a hydrogen atom, the electron is in $n^{th}$ excited state. It may come down to second excited state by emitting ten different wavelengths. What is the value of $n$ :

In Rutherford's experiment, number of particles scattered at $90^{\circ}$ angle are $x$ per second. Number particles scattered per second at angle $60^{\circ}$ is