At what rate must electrons in a wire vibrate to emit microwaves with a wavelength of 1.00 mm

The equation to use is v=fλ where v is the speed of light, f is the frequency, i. e. the rate at which they vibrate, and λ is the wavelength in meters.

Rearrange the above equation and you get f=v/λ. So the answer is f=300000000/0.001 or 300GHz.