The radius of the first Bohr orbit is $r$. What is the radius of the $2^{nd}$ Bohr orbit?

The frequency of the light emitted when an electron transitions from the $n=4$ to $n=2$ level in a hydrogen atom is $\frac{3}{7}$ times the frequency of a transition in a $Li^{2+}$ ion. Which transition in the $Li^{2+}$ ion corresponds to this?

The ratio of the total energy of the $2^{\text{nd}}$ orbit electron for the hydrogen atom $(_1H^1)$ to that of the helium ion $(He^+)$ $(_2^4He)$ is:

The magnetic moment $(m_{orb})$ of a revolving electron around the nucleus varies with the principal quantum number $(n)$ as

An electron in the ground state of a hydrogen atom is revolving in a circular orbit of radius $R$. The orbital magnetic moment of the electron is ($m =$ mass of electron,$h =$ Planck's constant,$e =$ electronic charge).

The time period of revolution of an electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16} \; s$. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is: