- 2019: The angular velocity of the electron is given by
$$\omega = \frac{2\pi}{T}$$
where $T$ is the period of revolution. The period of revolution is given by
$$T = \frac{2\pi r}{v}$$
where $r$ is the radius of the orbit and $v$ is the speed of the electron. Substituting this into the equation for angular velocity, we get
$$\omega = \frac{2\pi r}{v} \frac{v}{2\pi r} = \frac{v}{r}$$
The speed of the electron is given by
$$v = \frac{2\pi e^2}{nh}$$
where $e$ is the charge of the electron, $h$ is Planck’s constant, and $n$ is the principal quantum number. Substituting this into the equation for angular velocity, we get
$$\omega = \frac{2\pi e^2}{nh} \frac{nh}{2\pi r} = \frac{e^2}{2r}$$
Substituting the values for
