An electron moves in a Bohr orbit. The magnetic field at the centre is proportional to

$A$ particle of mass $m$ moves in circular orbits with potential energy $V(r) = Fr$,where $F$ is a positive constant and $r$ is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by $R$ and its speed and energy are denoted by $v$ and $E$,respectively,then for the $n^{\text{th}}$ orbit (here $h$ is the Planck's constant)-
$(A)$ $R \propto n^{2/3}$ and $v \propto n^{1/3}$
$(B)$ $R \propto n^{2/3}$ and $v \propto n^{1/3}$
$(C)$ $E = \frac{3}{2} \left( \frac{n^2 h^2 F^2}{4 \pi^2 m} \right)^{1/3}$
$(D)$ $E = 2 \left( \frac{n^2 h^2 F^2}{4 \pi^2 m} \right)^{1/3}$

If an electron is revolving in its Bohr orbit having Bohr radius of $0.529 Å$,then the radius of the third orbit is

If $\lambda_{1}$ and $\lambda_{2}$ are the wavelengths of de-Broglie waves for electrons in the first and second Bohr orbits in a hydrogen atom,then the ratio $\left(\frac{\lambda_{1}}{\lambda_{2}}\right)$ is equal to:

The radius of an electron's second stationary orbit in Bohr's atom is $R$. The radius of the $3rd$ orbit will be $.........R$.

If the radius of the first Bohr orbit in a hydrogen atom is $0.53 \, \mathring A$,then the radius of the third Bohr orbit will be ....... $\mathring A$.