$A$ Hydrogen atom and a $Li^{++}$ ion are both in the second excited state. If $l_H$ and $l_{Li}$ are their respective electronic angular momenta,and $E_H$ and $E_{Li}$ are their respective energies,then:

The electron in a hydrogen atom makes a transition $n_1 \to n_2$,where $n_1$ and $n_2$ are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of $n_1$ and $n_2$ are

In the Auger process,an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive,calculate the kinetic energy of an $n = 4$ Auger electron emitted by Chromium by absorbing the energy from an $n = 2$ to $n = 1$ transition.

The electrostatic potential energy of the electron in an orbit of hydrogen is $-6.8 \ eV$. The speed of the electron in this orbit is ($C$ is the speed of light in vacuum).

Mention the value of the Rydberg constant with its unit.

$(a)$ Using the Bohr model,calculate the speed of the electron in a hydrogen atom in the $n = 1, 2,$ and $3$ levels.
$(b)$ Calculate the orbital period in each of these levels.