The radii of the first four Bohr orbits of the hydrogen atom are related as:

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

The magnetic moment of an electron due to its orbital motion is proportional to (where $n$ is the principal quantum number).

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

The electron in a hydrogen atom makes a transition $n_1 \rightarrow n_2$,where $n_1$ and $n_2$ are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of the electron in the initial state is $1/27$ of that in the final state. The possible values of $n_1$ and $n_2$ are

In any Bohr orbit of a hydrogen atom,the ratio of $K.E.$ to $P.E.$ of a revolving electron at a distance $r$ from the nucleus is: