Question

$\sqrt{ d _{1}}$ 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______

Answer 1

$\sqrt{ d } \propto \cot \frac{\theta}{2}$
$\cot ^{2} 30^{\circ}=x \cot ^{2} 45^{\circ}$
$3=x$