A particle of mass $m$ moves in circular orbits with potential energy $U\left(r\right)=Fr$, 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 $n^{\mathrm{th}}$ orbit (here $h$ is the Planck's constant)

• A

  $R\propto n^{1/3}$ and $v\propto n^{2/3}$
• Correct answer
  B

  $R\propto n^{2/3}$ and $v\propto n^{1/3}$
• Correct answer
  C

  $E=\frac{3}{2}{\left(\frac{n^2{h}^2{F}^2}{4{\pi }^{2}m}\right)}^{1/3}$
• D

  $E=2{\left(\frac{n^2{h}^2{F}^2}{4{\pi }^{2}m}\right)}^{1/3}$

Hence, the correct answer is options: 'B', 'C'.