Two series of spectral lines of atomic hydrogen which do not belong to the infrared spectral region are

In a hydrogen atom,if $9 \, eV$ of energy is supplied,how many spectral lines will be emitted?

In the Bohr model of an atom, the radius of a hydrogen atom in the ground state is $r_1$ and the radius of a $He^{+}$ ion in the ground state is $r_2$. Which of the following is correct?

When the electron passes from the energy state nearest to the nucleus to the third energy level,it will:

The wave number of the first emission line in the Balmer series of the $H$ atom spectrum will be .......

For the Balmer series in the spectrum of $H$ atom,$\bar{v}=R_{H}\left\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\}$,the correct statements among $(I)$ to $(IV)$ are:
$(I)$ As wavelength decreases,the lines in the series converge.
$(II)$ The integer $n_{1}$ is equal to $2$.
$(III)$ The lines of longest wavelength corresponds to $n_{2}=3$.
$(IV)$ The ionization energy of hydrogen can be calculated from wave number of these lines.