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

$\sqrt{d_{1}}$ 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 . . . . . .

Choose the correct option from the following options given below.

In the Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of the scattering angle $\theta$. Which of the following options represents the correct plot?

The $\alpha$-particle is the nucleus of an atom of

Calculate the number of atoms in $39.4$ $g$ of gold. The molar mass of gold is $197$ $g$ $mol^{-1}$.