Ratio of centripetal acceleration for an electron revolving in $3^{\text{rd}}$ and $5^{\text{th}}$ Bohr orbit of hydrogen atom is

The electron in a hydrogen atom makes a transition from the $M$ shell to the $L$ shell. The ratio of the magnitudes of the initial to the final centripetal acceleration of the electron is:

The energy of a hydrogen atom in the ground state is $-13.6 \, eV$. The energy of the $He^+$ ion in the first excited state will be .... $eV$.

In $(i)$ a hydrogen atom and $(ii)$ a singly ionized helium atom,an electron makes a transition from the same excited state $n$ to the ground state. The ratio of the wavelengths of the emitted photons in the two cases will be:

Identify the incorrect relationship.

The angular momentum of an electron in the $2^{nd}$ excited state of a Helium ion $(He^+)$ is