The radius of a hydrogen atom in its ground state is $5.3\times {10}^{-11} \mathrm{m}$. After collision with an electron, it is found to have a radius of $21.2\times {10}^{-11} \mathrm{m}$. What is the principal quantum number $n$of the final state of the atom?

Consider third orbit of ${\mathrm{He}}^{+}$ (helium), using non-relativistic approach, the speed of electron in this orbit will be given constant $K{\text{=9×10}}^{\text{9}}$, $Z=2$ and $h$ (Planck's Constant)$\text{= 6}\text{.6 }\times {\text{ 10}}^{-34}\text{ J s}$

The magnitude of acceleration of the electron in the $n^{\text{th}}$ orbit of hydrogen atom is $a_{\mathrm{H}}$ and that of singly ionised helium atom is $a_{\mathrm{He}}$. The ratio $a_{\mathrm{H}}:a_{\mathrm{He}}$ is,