Math Connection: Let’s Put it Together

We can describe the relationship between these three factors in the following ways:

Energy and frequency are directly related – as one goes up, so does the other.
Wavelength and frequency are inversely related – as one goes up, the other goes down.
Using the information above, find a partner and discuss the relationship between energy and wavelength.

Here are the mathematical equations and constants used to describe these relationships.

c = λν

E = hν

E = hc/λ

If a radio wave has a wavelength of 10 meters, how much energy (in joules) does it carry?

E = hc/λ
E = (6.626 x 10^-34 J s)(3.0 x 10⁸m/s)/10 meters
E = 1.9878 x 10^-26

λ is wavelength in meters

ν is frequency in hertz, 1/s or s^-1

E is Energy in Joules (J)

c = 3.0 x 10⁸m/s (the speed of light in a vacuum)

h = 6.626 x 10^-34 J s (Planck’s constant)