The frequency of the microwave photon is:
[tex]f=50 GHz=50 \cdot 10^9 Hz[/tex]
and its energy is given by:
[tex]E=hf[/tex]
where
[tex]h=6.6 \cdot 10^{-34}Js[/tex] is the Planck constant
f is the photon frequency
By substituting the numbers into the formula, we find the photon's energy:
[tex]E=hf=(6.6 \cdot 10^{-34}Js)(50 \cdot 10^9 Hz)=3.3 \cdot 10^{-23}J[/tex]
Now we want to convert it into electronvolts (eV). We know that
[tex]1 eV= 1.6 \cdot 10^{-19}J[/tex]
Therefore, we should simply divide our energy by this conversion factor, and we get:
[tex]E= \frac{3.3 \cdot 10^{-23} J}{1.6 \cdot 10^{-19} J/eV}=2.1 \cdot 10^{-4}eV [/tex]
