Which energy level transition among the following will have the least wavelength?

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.

If the electron of a hydrogen atom is present in the first orbit,the total energy of the electron is

The energies of an electron in the first orbit of $He^{+}$ and in the third orbit of $Li^{2+}$ in $J$ are respectively:

The ionization energy of an electron in an excited state of a hydrogen atom is $+0.85 \, eV$. What will be the energy of the emitted photon in $eV$ when it returns to the ground state?

The kinetic energy of an electron is $5.65 \times 10^{-25} \ J$. Find the frequency of the electron.