Atoms and Nuclei Part 3

According to Bohr's model, for the $n$-th orbit:The speed of the electron is $v_n = \dfrac{v_0}{n}$, where $v_0$ is the speed in the first orbit.The radius of the orbit is $r_n = r_0 n^2$, where $r_0$ is the radius of the first orbit.The frequency of revolution is the number of revolutions per second, i.e. $f_n = \dfrac{v_n}{2\pi r_n}$.Substituting the $n$-dependences:$f_n = \dfrac{v_0/n}{2\pi r_0 n^2}$$f_n = \dfrac{v_0}{2\pi r_0}\cdot \dfrac{1}{n^3}$Since $\dfrac{v_0}{2\pi r_0} = f_0$ is the frequency in the first orbit,$f_n = \dfrac{f_0}{n^3}$Therefore $f \propto \dfrac{1}{n^3}$.Hence the correct option is $\dfrac{1}{n^3}$ (option with option B).