If the total energy of an electron in an orbit is positive,then

Using the formula for the radius of the $n^{th}$ orbit $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$,derive an expression for the total energy of an electron in the $n^{th}$ Bohr orbit.

Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2, \lambda_3$ are the wavelengths of radiations corresponding to the transitions $C$ to $B$,$B$ to $A$,and $C$ to $A$ respectively,which of the following statements is correct?

Assuming the atom is in the ground state, the expression for the magnetic field at the nucleus in a hydrogen atom due to the circular motion of the electron is [$\mu_0 =$ permeability of free space, $m =$ mass of electron, $\epsilon_0 =$ permittivity of free space, $h =$ Planck's constant].

The ionisation energy of $Li^{2+}$ is equal to

The time of revolution of an electron around a nucleus of charge $Ze$ in the $n^{th}$ Bohr orbit is directly proportional to