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?

The ionization potential for the second $He$ electron is ...... $eV$.

Given below are two statements $:$ one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ The Bohr model is applicable to hydrogen and hydrogen$-$like atoms only.
Reason $R :$ The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements,choose the correct answer from the options given below $:$

The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11} \ m$. What is the radius of the $n=4$ state?

The kinetic energy of the electron in an orbit of radius $r$ in a hydrogen atom is proportional to ($e$ = electronic charge).

The ionization potential of a hydrogen-like atom is $122.4 \, V$. Find its atomic number $Z$.