We can calculate the energy of electromagnetic radiation two different ways.
We can find out the energy of a photon by using the following equation:

E_photon = hf

E_photon = energy of the photon.

h = Planck’s constant which is 6.63 x 10^-34 j·s
f = frequency

Here is an example of how to use the equation to find the energy of a photon:

Calculate the energy of a photon of red light of a frequency of 4.6 x 10¹⁴ Hz
Calculating the energy of the photon using the equation

E_photon = hf

Energy E = 6.63 x 10^-34 * 4.6 x 10¹⁴
                     =3.0 x 10^-19 J

We can find out the energy from a wavelength by using this equation

E = hc/λ

E = Energy
h = Planck’s constant which is 6.63 x 10^-34 j·s
c = speed of light which is 3 x 10⁸ m/s
λ = wavelength

Watch this video to see a demonstration of how to use the energy equations using Planck’s constant.

Now try out these practice problems. Work the following problems on a scratch sheet of paper. If you get stuck go back and watch the video tutorials again. Once you think you have the correct answer click on the answer box to see the solution.

1. Determine the energy, in joules, of a photon whose frequency is 3.55 x 10¹⁷ s^-1. Interactive popup. Assistance may be required.

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2. What is the energy content of one quantum  (photon) of light with a wavelength of 4.13 x 10^-7 m? Interactive popup. Assistance may be required.

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3. What is the frequency of light if the energy is 2.86 x 10^-19 J ? Interactive popup. Assistance may be required.

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4. What is the wavelength of light if the energy of 1 photon is 3.82 x 10^-18 J? Interactive popup. Assistance may be required.

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