The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11} \ m$. What is the ratio of the radii of the orbits for $n=2$ and $n=3$?

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 $Li^{++}$?

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

The potential energy of an electron in an orbit of a hydrogen atom is $-6.8 \text{ eV}$. The de Broglie wavelength of the electron in this orbit is (where $r_0$ is the Bohr radius).

For $He^{+}$, a transition takes place from the orbit of radius $105.8 \ pm$ to the orbit of radius $26.45 \ pm$. The wavelength (in $nm$) of the emitted photon during the transition is. . . . .
[Use: Bohr radius, $a_0=52.9 \ pm$; Rydberg constant, $R_H=2.2 \times 10^{-18} \ J$; Planck's constant, $h=6.6 \times 10^{-34} \ J \ s$; Speed of light, $c=3 \times 10^8 \ m \ s^{-1}$]

In the Bohr model of the $H$-atom,the kinetic energy of an electron in any orbit depends on the principal quantum number $n$ as: