# What is the relationship between wavelength, frequency, and energy of a photon?

Oct 19, 2017

The photon model equation relates the frequency and energy of a photon together by a constant of proportionality, where $E \setminus \propto f \implies E = h f$, where:

• $E$ is the energy of the photon ($J$)
• $f$ is the frequency of the photon (${s}^{- 1}$)
• $h$ is Plank's constant ($\approx 6.63 \cdot {10}^{- 34} J s$)

The frequency and wavelength of light are also related by the wave equation where $v = f \setminus l a m \mathrm{da}$, or for EM radiation $c = f \setminus l a m \mathrm{da}$, where:

• $c$ is the speed of light ($\approx 3.00 \cdot {10}^{8} m {s}^{- 1}$)
• $f$ is the frequency of the light (${s}^{- 1}$)
• $\setminus l a m \mathrm{da}$ is the wavelength of the light ($m$)

By rearranging to get $f = \frac{c}{\setminus} l a m \mathrm{da}$, we can rewrite the photon model equation to get $E = \frac{h c}{\setminus} l a m \mathrm{da}$.