In the Bohr model,an electron of mass $m$ moves in a circular orbit around the proton. Considering the orbiting electron as a circular current loop,find the magnetic moment of the hydrogen atom when the electron is in the $n$th orbit. (Assume $h$ is Planck's constant)

In a hydrogen atom,the electron and proton are bound at a distance of about $0.53 \; \mathring{A}$.
$(a)$ Estimate the potential energy of the system in $eV$,taking the zero of the potential energy at infinite separation of the electron from the proton.
$(b)$ What is the minimum work required to free the electron,given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)$?
$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06 \; \mathring{A}$ separation?

In a hydrogen atom,an electron excites from the ground state to a higher energy state,and its orbital velocity is reduced to $\frac{1}{3}$ of its initial value. The radius of the orbit in the ground state is $R$. The radius of the orbit in that higher energy state is: (in $R$)

The ratio of angular momentum of an electron in $n^{\text{th}}$ orbit of a hydrogen atom to the velocity of the electron in the $n^{\text{th}}$ orbit is proportional to

Instead of angular momentum quantisation,a student predicts that energy is quantised as $E = \frac{-E_{0}}{n}$,$(E_{0} > 0)$ and $n$ is a positive integer. Which of the following options is correct?

What is the ratio of the area of the orbit of an electron in the first excited state to that in the ground state of a hydrogen atom (in $: 1$)?