An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius $r$. The Coulomb force $\vec{F}$ between the two is
$k\,\,\frac{{{e^2}}}{{{r^2}}}\,\,\hat r$
$ - k\,\,\frac{{{e^2}}}{{{r^3}}}\,\,\hat r$
$k\,\,\frac{{{e^2}}}{{{r^3}}}\,\,\hat r$
$ - k\,\,\frac{{{e^2}}}{{{r^3}}}\,_r^ \to $
Explain Rutherford's explanation for scattered $\alpha $ -particles.
In third orbit of hydrogen atom, de Broglie wavelength of electron is $\lambda $ then radius of third orbit is
$\sqrt{d_{1}}$ 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 ________