What is the name by which Thomson's atomic model is known?

The wavelength and frequency of a photon with energy $2 \ eV$ are respectively:

Heat treatment of muscular pain involves radiation of wavelength of about $900 \ nm$. Which spectral line of $H$ atom is suitable for this? Given: Rydberg constant $R_{H}=10^5 \ cm^{-1}, h=6.6 \times 10^{-34} \ J \ s, c=3 \times 10^8 \ m / s$.

The work function of a metal is $4.2 \, eV$. If radiation of $2000 \, \mathring{A}$ falls on the metal,then the kinetic energy of the fastest photoelectron is:

An electron revolves in an orbit around a stationary nucleus with atomic number $Z = 5$. The energy required to excite the electron from the $3^{rd}$ orbit to the $4^{th}$ orbit is .......... $eV$.

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.