Angular Frequency

Some dude in physics was like let’s make a new, transformed version of frequency called angular frequency ω\omega! (Not to be confused with angular momentum, which is a different physical quantity.)

Let

ω=2πf\begin{gather*} \omega=2\pi f \end{gather*}

Because of this, we can say that

E=hf=hω2π\begin{gather*} E=hf\\ =h\frac{\omega}{2\pi} \end{gather*}

From Reduced Planck constant, we can also say

E=ℏω\begin{gather*} E=\hbar \omega \end{gather*}

Bohr, a person, hypothesized that atoms absorb light at discrete frequencies.

This means that atoms (photons too) have discrete (non-continuous) energy levels.