In which transition of the hydrogen atom will the emitted radiation have the lowest frequency?

For $Li^{2+}$ ion,the ratio of radii $r_2 : r_5$ will be

The wavelength of the spectral line obtained in the spectrum of $Li^{2+}$ ion, when the transition takes place between two levels whose sum is $4$ and difference is $2$, is

When a certain metal was irradiated with light of frequency $4.0 \times 10^{16} \ s^{-1}$,the photoelectrons emitted had four times the kinetic energy as the kinetic energy of photoelectrons emitted when the same metal was irradiated with light of frequency $2.0 \times 10^{16} \ s^{-1}$. The threshold frequency $(v_0)$ of the metal in $s^{-1}$ is

Threshold frequency,$v_0$ is the minimum frequency which a photon must possess to eject an electron from a metal. It is different for different metals. When a photon of frequency $1.0 \times 10^{15} \ s^{-1}$ was allowed to hit a metal surface,an electron having $1.988 \times 10^{-19} \ J$ of kinetic energy was emitted. Calculate the threshold frequency of this metal. Show that an electron will not be emitted if a photon with a wavelength equal to $600 \ nm$ hits the metal surface.

Ratio of velocities of electrons of hydrogen atom in $1^{st}$,$2^{nd}$,$3^{rd}$ orbit is