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

The ratio of speed of an electron in ground state in Bohrs first orbit of hydrogen atom to velocity of light in air is

The graph which depicts the results of Rutherform gold foil experiment with $\alpha$ -particales is

$\theta:$ Scattering angle

$\mathrm{Y}:$ Number of scattered $\alpha$ -particles detected

(Plots are schematic and not to scale)

When an $\alpha -$particle of mass $m$ moving with velocity $v$ bombards on a heavy nucleus of charge $Z_e$ , its distance of closest approach from the nucleus depends on $m$ as

Discuss the experimental results of Geiger-Marsden's $\alpha $ -particle scattering. 

What was the thickness of the gold foil kept in the Geiger-Marsden scattering experiment?