In a hydrogen atom,let $R$,$v$,and $E$ denote the radius,velocity,and total energy of the electron,respectively. Then,the principal quantum number $n$ is proportional to which of the following?

Using the Bohr model,calculate the electric current created by the electron when the $H$-atom is in the ground state.

$A$ particular hydrogen-like ion emits radiation of frequency $3 \times 10^{15} \,Hz$ when it makes a transition from $n=2$ to $n=1$. The frequency of radiation emitted in a transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15} \,Hz$, where $X = \text{ . . . . . . }$.

Excitation energy of a hydrogen-like ion in its first excitation state is $40.8 \, eV$. Energy needed to remove the electron from the ion in the ground state is ........ $eV$.

The total energy of an electron in the $n^{th}$ orbit of a hydrogen atom is $E_n$. The total energy of an electron in the $n^{th}$ orbit of a $He^+$ ion is .........

If an electron is moving in the $4^{\text{th}}$ orbit of the hydrogen atom,then the angular momentum of the electron in $SI$ units is