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

Question

Natalie Anton · Accepted Answer

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

#h# is Planck's Constant, #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.

Jeremiah Adams · Answer

undefined The formula for calculating the energy of an electromagnetic radiation photon is E = h * f, where h is Planck's constant (6.62607015 × 10^-34 m^2 kg / s), f is the radiation frequency in hertz (Hz), and E is the photon's energy. Alternatively, you can use the formula E = hc / λ, where λ is the radiation's wavelength in meters and c is the speed of light (roughly 3.00 × 10^8 m/s).