When an electron in the ground state of a hydrogen atom is given $12.4 \, eV$ of energy,to which orbit will it transition?

When a hydrogen atom emits a photon during a transition from $n=4$ to $n=2$,its recoil speed is about (in $m \ s^{-1}$)

If the binding energy of a ground state electron in a hydrogen atom is $13.6\,eV$,then the energy required to remove the electron from the second excited state of $Li^{2+}$ will be $x \times 10^{-1}\,eV$. The value of $x$ is $...........$

An electron collides elastically with an $H$-like atom and excites it from the ground state to $n = 3$. Find the energy transferred to the $H$-like atom in $eV$.

Which of the transitions in a hydrogen atom emits a photon of the lowest frequency? ($n =$ quantum number)

$A$ photon is emitted in transition from $n = 4$ to $n = 1$ level in a hydrogen atom. The corresponding wavelength for this transition is $......... \, nm$ (given,$h = 4 \times 10^{-15} \, eV \cdot s$ and $c = 3 \times 10^8 \, m/s$):