The radius of the orbit of an electron in a hydrogen atom is $0.5 \ \mathring{A}$. The speed of the electron is $2 \times 10^6 \ m/s$. The current in the loop due to the motion of the electron is ............. $mA$.

According to de-Broglie, the de-Broglie wavelength for an electron in an orbit of a hydrogen atom is $10^{-9} \, m$. The principal quantum number for this electron is:

In a muonic atom,a muon of mass $200$ times that of an electron and the same charge is bound to a proton. The wavelengths of its Balmer series are in the range of

In a hydrogen atom in its ground state,the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is (in $r_1$)

Using Bohr's atomic model,derive an equation for the radius of the $n^{th}$ orbit of an electron.

$A$ particle of mass $m$ moves around the origin in a potential $\frac{1}{2} m \omega^{2} r^{2}$,where $r$ is the distance from the origin. Applying the Bohr's model in this case,the radius of the particle in its $n$th orbit in terms of $a=\sqrt{\frac{h}{2 \pi m \omega}}$ is