What transition in $He^{+}$ ion shall have the same wave number as the first line in Balmer series of hydrogen atom?

Ionisation energy of $He^{+}$ is $19.6 \times 10^{-18} \, J \, atom^{-1}$. The energy of the first stationary state $(n = 1)$ of $Li^{2+}$ is

In an atom,two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is

Given below are two statements:
Statement $I$: Bohr's theory accounts for the stability and line spectrum of $Li^{+}$ ion.
Statement $II$: Bohr's theory was unable to explain the splitting of spectral lines in the presence of a magnetic field.
In the light of the above statements,choose the most appropriate answer from the options given below:

The energy of an electron in the first Bohr orbit of $H$-atom is $-13.6 \ eV$. The possible energy value of an electron in the first excited state of $Li^{2+}$ is (in $eV$)

When a hydrogen atom in an excited state undergoes electronic transitions to the ground state,$5$ spectral lines are observed in the ultraviolet region. How many spectral lines will be observed in the infrared region due to transitions from the same excited state?