Photons are quanta of light, or elementary particles that transmit the electromagnetic waves of light. Visible light represents an excellent example of photons. Several physical values, including the wavelength and the frequency (measured in hertz, or Hz), characterize photons. You can calculate the photon energy, based on the frequency or the wavelength, with the aid of certain fundamental physical constants.

Record the physical constant values needed for the calculation of the energy calculations. In this case, they are:

Speed of light (c) = 299,792,458 m/s

Planck constant (h) = 4.13566733E-15 eV s (1E-15 represents "ten in power -15").

Note that an electron volt (eV) is a unit commonly used to express photon energy.

Multiply the speed of light and the Planck constant, and divide the product by the wavelength to calculate the photon energy. For example, yellow visible light photons have a wavelength of about 580 nm or 5.8E-7 m. Thus, their energy is 299,792,458 m/s x 4.13566733E-15 eV s/5.8E-7 m = 2.14 eV.

Note that the prefix "nano" (n) denotes the magnitude 1E-9.

Another approach is to multiply the photon frequency and the Planck constant to calculate photon energy. For example, the frequency of photons corresponding to ultraviolet (UV) light is 7.8E14 Hz or 780 Thz; the photon energy is 7.8E14 Hz x 4.13566733E-15 eV s = 3.23 eV.

Note that the prefix “tera" (T) means the magnitude 1E12.

Multiply the energy in eV by the factor 1.6021765E-19 to calculate it in joules (J), if necessary. For instance, the energy of 3.23 eV will convert to 5.18E-19 J.

#### References

- Algebralab.org: Electromagnetic Radiation - Wavelength, Frequency, and Photon Energy
- Physics;” John D. Cutnell and Kenneth W. Johnson; 2006

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