Calculate the wave number of a photon emitted during the transition from the orbit $n = 2$ to $n = 1$ in a hydrogen atom $(R_{H} = 109677 \ cm^{-1})$. (in $cm^{-1}$)

When a metal surface is irradiated with light of frequency $x \ Hz$,the kinetic energy of emitted photoelectrons is $z \ J$. When the same metal is irradiated with light of frequency $y \ Hz$,the kinetic energy of emitted electrons is $\frac{z}{3} \ J$. What is the threshold frequency (in $Hz$) of the metal?

What is the wavenumber of the photon emitted during transition from the orbit $n=5$ to that of $n=2$ in hydrogen atom (in $cm^{-1}$)?
$\left[R_{H}=109677 \ cm^{-1}\right]$

In which transition is minimum energy emitted?

The quantity $h \nu / K_{B}$ corresponds to

An electron in a hydrogen atom in its ground state absorbs $2$ times as much energy as the minimum required for it to escape from the atom. The kinetic energy of the emitted electron is ............ $eV$.