The ratio of centripetal acceleration for an electron revolving in the $3^{\text{rd}}$ orbit to the $5^{\text{th}}$ Bohr orbit of a hydrogen atom is:

The kinetic energy of the electron in an orbit of radius $r$ in a hydrogen atom is ($e =$ electronic charge).

Explain the limitations of the Bohr atomic model.

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: $[\mu_0 \rightarrow \text{permeability of free space, } m \rightarrow \text{mass of electron, } \varepsilon_0 \rightarrow \text{permittivity of free space, } h \rightarrow \text{Planck's constant}]$

$A$ sample of hydrogen-like atoms produces an emission spectrum consisting of $10$ wavelengths arising from all possible transitions. During this process,the maximum angular momentum change for an electron transitioning from a higher energy level to a lower energy level is:

In the Bohr model of the hydrogen atom,the electrostatic force on the electron depends on the principal quantum number $n$ as: