A small particle of mass `m` moves in such a way that the potential energy `U=ar^(2)` where `a` is a constant and `r` is the distance of the particle from the origin. Assuming Bohr's model of quantization of angular momentum and circular orbits, find the radius of `n^(th)` allowed orbit.

Answer

`r = [(n^(2)h^(2))/(8 am pi^(2))]^(1//4)`