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 $$n^{th}$$ orbit (here h is the Planck’s constant)

A

$$R \propto n^{1/3}$$ and $$V \propto n^{2/3}$$

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

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