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(C) The angular velocity $\omega$ is given by the relation $\omega = \frac{v}{r}$.According to Bohr's theory for a hydrogen atom:$1$. The orbital velo

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$\omega_n \propto 1/n^3$

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(C) The angular velocity $\omega$ is given by the relation $\omega = \frac{v}{r}$.According to Bohr's theory for a hydrogen atom:$1$. The orbital velocity of an electron in the $n^{th}$ orbit is $v_n \propto \frac{1}{n}$.$2$. The radius of the $n^{th}$ orbit is $r_n \propto n^2$.Substituting these proportionalities into the angular velocity formula:$\omega_n = \frac{v_n}{r_n} \propto \frac{1/n}{n^2} = \frac{1}{n^3}$.Therefore,$\omega_n \propto \frac{1}{n^3}$.

In the Bohr model of the hydrogen atom,the angular velocity $\omega_n$ of the electron depends on the principal quantum number $n$ as:

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