The product of angular speed and tangential speed of an electron in the $n^{\text{th}}$ orbit of a hydrogen atom is:

$A$ particle of mass $200 \, MeV/c^2$ collides with a hydrogen atom at rest. Soon after the collision,the particle comes to rest,and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in $eV$) is $\frac{N}{4}$. The value of $N$ is: (Given the mass of the hydrogen atom to be $1 \, GeV/c^2$)

Mention the value of the Rydberg constant with its unit.

What is the ratio of the wavelengths emitted during the $2 \to 1$ transition in $Li^{++}$,$He^+$,and $H$?

The energy of $He^{+}$ ion in its first excited state is $......eV$ (The ground state energy for the Hydrogen atom is $-13.6\,eV$).

Find the radius of $Be^{3+}$ ions in its ground state assuming Bohr's model to be valid $(a_0 = 53 \ pm)$. (in $pm$)