What is the relationship between wavelength and the amount of energy the wave carries?

Energy is inversely proportional to wavelength.

Explanation:

The amount of energy, E, a wave carries is given as:

E = hf

where h = Planck's constant and f = frequency of the wave

Frequency and wavelength are related by the equation:

c = λf

=> f = c/λ

where λ = wavelength

Therefore, energy is:

E = hc/λ

This shows that energy is inversely proportional to wavelength. As wavelength increase, energy decreases and vice versa.