The electron in a hydrogen atom makes a transition $n_1\to n_{\mathrm{2 }}$where $n_1$and $n_2$ are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is $8$ times that in the final state. The possible values of $n_1$ and $n_2$ are

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,