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

Answer

A

Explanation

`F = (dU)/(dr) = - m^2 omega^2 r`
Now, (mv^2)/(r ) = |F| m^2 omega^2 r`
or `v prop r`
or `v = alpha r`
Now, m vr = n(h)/(2pi)`
or `m (alphar)r = n(h)/(2pi)`
`:. r prop sqrtn.`