Question

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

Answer 1

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.

Answer 2

f = 3×10¹¹ Hz

Step-by-step explanation:

Relation ship between frequency and wavelength

"The wave speed (v) is defined as the distance traveled by a wave per unit time. If considered that the wave travels a distance of one wavelength in one period,

ν=λ/T

As we know that T = 1/f, hence we can express the above equation as,

V = f λ

The wave speed is equal to the product of its frequency and wavelength, and this implies the relationship between frequency and wavelength."

The relation between frequency and wavelength is

λ×f = c

c = speed of light = 3×10⁸ m/s

λ = 1.00 mm = 10⁻³ m

f=c/λ

f=(3×10⁸ m/s)/ 10⁻³ m

f = 3×10¹¹ Hz