Inner shell electrons in atoms moving from one energy level to another lower energy level produce

$A$ stationary hydrogen atom has an electron that transitions from the fifth energy level to the ground level. The velocity that the atom acquires as a result of photon emission will be: ($m$ is the mass of the atom,$R$ is Rydberg constant,and $h$ is Planck's constant).

$A$ free electron of $2.6 \, eV$ energy collides with a $H^+$ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. $(h = 6.6 \times 10^{-34} \, J \cdot s)$

The following diagram indicates the energy levels of a certain atom. When the system moves from the $2E$ level to the $E$ level,a photon of wavelength $\lambda$ is emitted. The wavelength of the photon produced during its transition from the $\frac{4E}{3}$ level to the $E$ level is

What is the total energy of an electron at an infinite distance from the nucleus in an atom?

The ratio of the energies of the hydrogen atom in its first to second excited state is