The energy of an electron in the ground state of a hydrogen atom is $E$. What is the energy of an electron in the $2^{nd}$ excited state of $Li^{++}$?

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:

In the Bohr model of the hydrogen atom, the electron is pictured to rotate in a circular orbit of radius $5 \times 10^{-11} \, m$, at a speed of $2.2 \times 10^{6} \, m/s$. What is the current associated with the electron's motion (in $ \, mA$)?

The magnetic moment of an electron due to its orbital motion is proportional to (where $n$ is the principal quantum number).

In the Bohr model,an electron moves in a circular orbit around the nucleus. Considering an orbiting electron to be a circular current loop,the magnetic moment of the hydrogen atom,when the electron is in the $n^{th}$ excited state,is ($e=$ electronic charge,$m_{e}=$ mass of the electron,$h=$ Planck's constant).

The magnetic moment of an orbital electron in the first orbit of an $\text{H}$-atom is $\mu_{B}$. What is the magnetic moment of that electron in the second orbit?