Question

What is the energy (in electron volts) of a 50 ghz (1 gigahertz = 109 hz) microwave photon?

Answer 1

The frequency of the microwave photon is:

`f=50 GHz=50 \cdot 10^9 Hz`
and its energy is given by:

`E=hf`
where

`h=6.6 \cdot 10^(-34)Js` is the Planck constant
f is the photon frequency

By substituting the numbers into the formula, we find the photon's energy:

`E=hf=(6.6 \cdot 10^(-34)Js)(50 \cdot 10^9 Hz)=3.3 \cdot 10^(-23)J`

Now we want to convert it into electronvolts (eV). We know that

`1 eV= 1.6 \cdot 10^(-19)J`
Therefore, we should simply divide our energy by this conversion factor, and we get:

`E= (3.3 \cdot 10^(-23) J)/(1.6 \cdot 10^(-19) J/eV)=2.1 \cdot 10^(-4)eV`