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 $= 1.6 \times 10^{-27} \,kg$)

If energy of $15 \ eV$ is given to an electron in the $4^{th}$ orbit,find its final energy when it comes out of the $H$-atom. (in $eV$)

$A$ hydrogen atom makes a transition from $n = 2$ to $n = 1$ and emits a photon. This photon strikes a doubly ionized lithium atom $(Z = 3)$ in an excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for this process is:

The binding energy of a hydrogen atom in the ground state is $13.6 \ eV$. The energies required to remove an electron from the first three energy levels of the hydrogen atom are,respectively,(in $eV$):

If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of the $n = \infty$ state is,

In hydrogen and hydrogen-like atoms,the ratio of the difference of energies $E_{4n}-E_{2n}$ and $E_{2n}-E_{n}$ varies with its atomic number $Z$ and $n$ as: