What is the angular momentum of an electron in the $n=5$ orbit of a $Be^{+3}$ ion?

$A$ hydrogen-like atom of atomic number $Z$ is in an excited state of quantum number $2n$. It can emit a maximum energy photon of $204 \ eV$. If it makes a transition to quantum state $n$,a photon of energy $40.8 \ eV$ is emitted. The value of $n$ will be

For $He^{+}$, a transition takes place from the orbit of radius $105.8 \ pm$ to the orbit of radius $26.45 \ pm$. The wavelength (in $nm$) of the emitted photon during the transition is. . . . .
[Use: Bohr radius, $a_0=52.9 \ pm$; Rydberg constant, $R_H=2.2 \times 10^{-18} \ J$; Planck's constant, $h=6.6 \times 10^{-34} \ J \ s$; Speed of light, $c=3 \times 10^8 \ m \ s^{-1}$]

Consider an electron in the $n^{th}$ orbit of a hydrogen atom in the Bohr model. The circumference of the orbit can be expressed in terms of the de Broglie wavelength $\lambda$ of that electron as

The ionization potential of a hydrogen atom is $13.6 \ eV$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 \ eV$. According to Bohr's theory,the number of spectral lines emitted by the hydrogen atoms will be:

When a hydrogen atom,initially at rest,emits a photon resulting in a transition $n = 5 \rightarrow n = 1$,its recoil speed is about