Hydrogen Spectrum

The frequency of radiation emitted when electron falls from $\mathrm{n}=4$ to $\mathrm{n}=1$ in a hydrogen atom will be

(Given: Ionization energy of $\mathrm{H}=2.18\times {10}^{-18} \mathrm{J} {\mathrm{atom}}^{-1}$ and $\mathrm{h}=6.625\times {10}^{-34} \mathrm{J} \mathrm{s}$)

What transition in the hydrogen spectrum would have the same wavelength as the transition $\mathrm{n}=4$ to $\mathrm{n}=2$ of ${\mathrm{He}}^{+}$ spectrum?

The wave number of the first emission line in the Balmer series of $\mathrm{H}$-Spectrum is:

($\mathrm{R}=$ Rydberg's constant)

Which of the following transitions of electrons in the hydrogen atom will emit the maximum energy?

In Bohr series of lines of hydrogen spectrum, the third line from the red-end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen?

For Balmer series in the spectrum of atomic hydrogen, the wave number of each line is given by: $\overline{\mathrm{v}}={\mathrm{R}}_{\mathrm{H}}\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$, where, ${\mathrm{R}}_{\mathrm{H}}$ is Rydberg constant and ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$ are integers. Which of the following statement(s) is(are) correct?

I. As wavelength decreases, the lines in the series converge.

II. The integer, ${\mathrm{n}}_1$ is equal to $2.$

III. The ionization energy of hydrogen can be calculated from the wave number of these lines.

IV. The line of the longest wavelength corresponds to ${\mathrm{n}}_2=3.$

What would be the wavelength of the radiation emitted when in a hydrogen atom, an electron falls from infinity to the stationary state $1$? (Rydberg's constant $=1.097\times {10}^7 {\mathrm{m}}^{-1})$