$\sqrt{d_{1}}$ and $\sqrt{d_{2}}$ are the impact parameters corresponding to scattering angles $60^{\circ}$ and $90^{\circ}$ respectively, when an $\alpha$ particle is approaching a gold nucleus. For $d_{1}=x d_{2}$, the value of $x$ will be ________

What is the atomic number of gold ? 

Explain the Rutherford atomic model and its limitation.

Hydrogen $(H)$, deuterium $(D)$, singly ionized helium $(H{e^ + })$ and doubly ionized lithium $(Li)$ all have one electron around the nucleus. Consider $n =2$ to $n = 1 $ transition. The wavelengths of emitted radiations are ${\lambda _1},\;{\lambda _2},\;{\lambda _3}$ and ${\lambda _4}$ respectively. Then approximately

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

What is the percentage of $\alpha -$ particles that have more than $1^o$ scattering in Geiger-Marsden experiment?