A small particle of mass moves such that its potential energy is

PHYSICS · Subjective · CBSE · Physics · Atoms · Atoms

Problem

A small particle of mass

m

moves such that its potential energy is

U=\frac{1}{2}m^2\omega^2r^2

, where

\omega

is a constant and

r

is the distance of the particle from the origin. Assuming Bohr quantization of angular momentum and circular orbits, show that the radius of the

n

th allowed orbit is proportional to

\sqrt{n}