A small particle of mass m moves in such a way that the
potential energy `U = ar^2`, where a is constant and r is the distance of the
particle from the origin. Assuming Bhor model of quantization of angular
momentum and circular orbits, find the rodius of nth allowed orbit.

Answer

A, B, D

Explanation

The force at a distance r is`
`F =- (dU)/(dr) =- 2ar`
Suppose r be the radius of nth orbit. Then, the necessary centripetal force is porvided by the above force. Thus, `(mv^2)/(r ) =2ar … (i) `
Further, the quantization of angular momentum gives`
`mvr = (nh)/(2pi) ...(ii)`
Solvig Eqs. (i) and (ii) for r, we get`
`r = ((n^2h^2)/(8am pi^2))^(1//4).