How much energy is needed to release the electron from the second excited state in the hydrogen atom (in $eV$)?

$A$ hydrogen atom is bombarded with electrons accelerated through a potential difference of $V$, which causes excitation of hydrogen atoms. If the experiment is performed at $T = 0 \,K$, the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be $\frac{\alpha}{10} \,V$, where $\alpha = $ . . . . . . .

When a hydrogen atom transitions from $n=2$ to $n=1$, it emits a photon. The recoil speed of the atom is $\frac{x}{5} \,m/s$. Find the value of $x$. (Use: mass of hydrogen atom $= 1.6 \times 10^{-27} \,kg$)

$A$ difference of $5.4 \ eV$ separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level? (Take $1 \ eV = 1.6 \times 10^{-19} \ J$,$h = 6.625 \times 10^{-34} \ Js$)

The binding energy of the electron in a hydrogen atom is $13.6\, eV$. The energy required to remove the electron from the first excited state of $Li^{++}$ is ......... $eV$.

The minimum excitation energy of an electron revolving in the first orbit of hydrogen is (in $eV$)