The frequency of the $1^{st}$ line of the Balmer series in the ${H_2}$ atom is ${\nu _0}$. What is the frequency of the corresponding line emitted by a singly ionized ${He^+}$ atom?

When an electron in a hydrogen atom makes a transition from the $2^{nd}$ excited state to the ground state,it emits a photon of frequency $f$. The frequency of the photon emitted when an electron of $Li^{++}$ makes a transition from the $1^{st}$ excited state to the ground state is:

In a hydrogen atom,when an electron transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit,the wave number is $20,397 \, cm^{-1}$. What will be the wave number when an electron in a $He^+$ ion transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit?

$A$ diatomic molecule has moment of inertia $I$. By applying Bohr's quantization condition,its rotational energy in the $n^{\text{th}}$ level is $[n \geq 1]$ $(h = \text{Planck's constant})$

The following parameter is the same for all hydrogen-like atoms and ions in their ground state.

The energy required to remove the electron from a singly ionized Helium atom is $2.2$ times the energy required to remove an electron from a Helium atom. The total energy required to ionize the Helium atom completely is......$eV$