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:
$E= \frac{3.3 \cdot 10^{-23} J}{1.6 \cdot 10^{-19} J/eV}=2.1 \cdot 10^{-4}eV$