A small particle of mass m move in such a way the potential energy `(U = (1)/(2) m^(2) omega^(2) r^(2))` when 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 , show that radius of the nth allowed orbit is proportional to in

Options

A. `sqrt(n)`
B. `sqrt(n^(3))`
C. `(1)/(sqrt(n))`
D. `(1)/(sqrt(n^(3)))`

Answer

A

Explanation

`F=(-dU)/(dr)=-momega^(2)r`.
Since, `mvr=(nh)/(2pi)` or `mr^(2)omega=(nh)/(2pi)`
`implies v=romega implies r^(2)=(nh)/(2pi m omega)`
`implies r=sqrt((nh)/(2pimomega))`
`implies rpropsqrt(n)`.