How to Calculate the Momentum of a Photon of Yellow Light in a Wavelength

Einstein's equation E = mc^2 is important in deriving the expression for a photon's momentum.
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Photons exhibit what's known as "wave-particle duality," meaning that in some ways light behaves as a wave (in that it refracts and can be superimposed on other light) and in other ways as a particle (in that it carries and can transfer momentum). Even though a photon has no mass (a property of waves), early physicists found that photons hitting metal could displace electrons (a property of particles) in what's known as the photoelectric effect.

    Determine the light's frequency from its wavelength. The frequency (f) and wavelength (d) are related by the equation f = c/d, where c is the speed of light (approximately 2.99 x 10^8 meters per second). A specific yellow light might be 570 nanometers in wavelength, therefore, (2.99 x 10^8)/(570 x 10^-9) = 5.24 x 10^14. The yellow light's frequency is 5.24 x 10^14 Hertz.

    Determine the light's energy using Planck's constant (h) and the particle's frequency. The energy (E) of a photon is related to Planck's constant and the photon's frequency (f) by the equation E = hf. Planck's constant is approximately 6.626 x 10^-34 m^2 kilograms per second. In the example, (6.626 x 10^-34) x (5.24 x 10^14) = 3.47 x 10^-19. The energy of this yellow light is 3.47 x 10^-19 Joules.

    Divide the photon's energy by the speed of light. In the example, (3.47 x 10^-19)/(2.99 x 10^8 ) = 1.16 x 10^-27. The momentum of the photon is 1.16 x 10^-27 kilogram meters per second.

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