# How do you calculate the energy of a photon of electromagnetic radiation?

You use either the formula ##E = hf## or ##E = (hc)/λ##.

##h## is , ##f## is the frequency, ##c## is the speed of light, and λ is the wavelength of the radiation.

EXAMPLE 1

Calculate the energy of a photon of radiation whose frequency is ##5.00 × 10^14 “Hz”##.

Solution 1

##E = hf = 6.626 × 10^-34 “J”· color(red)(cancel(color(black)(“s”))) × 5.00 × 10^14 color(red)(cancel(color(black)(“s”^-1))) = 3.31 × 10^-19 “J”##

The energy is ##3.31 × 10^-19 “J”##.

EXAMPLE 2

Calculate the energy of a photon of radiation that has a wavelength of 3.3 µm.

Solution 2

##E = (hc)/λ = (6.626 × 10^-34 “J”·color(red)(cancel(color(black)(“s”))) × 2.998 × 10^8 color(red)(cancel(color(black)(“m·s”^-1))))/(3.3 × 10^-6 color(red)(cancel(color(black)(“m”)))) = 6.0 × 10^-20 “J”##

Here’s a video on how to find the energy of a photon with a given wavelength.

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