A particle of masss `m` moves along a circular orbiy in cetrosymmetrical potential field `U(r )=kr^(2)//2`. Using the Bohr quantization condition, find the permissible orbital radii and energy levels ot that particle.

Explanation

We have the following equation (we ignore reduce mass effects)
`(mv^(2))/(r)=kr`
so `mvr= nħ`
`m'v=sqrt(mkr)`
and `r=sqrt((nħ)/sqrt(mk))`,
and `v=sqrt(nħsqrt(mk))//m` The energy levels are `E_(n)-(1)/(2)mv^(2)+(1)/(2)kr^(2)`
`=(1)/(2)(n ħsqrt(mk))/(m)+(1)/(2)k(n ħ)/(sqrt(mk))`
`n ħsqrt((k)/(m))`