### How do photons have momentum?

Posted:

**Thu Oct 06, 2016 9:25 pm**Since momentum is mass times velocity, how do photons have momentum if they have no mass?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=18&t=15692

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Posted: **Thu Oct 06, 2016 9:25 pm**

Since momentum is mass times velocity, how do photons have momentum if they have no mass?

Posted: **Thu Oct 06, 2016 9:50 pm**

Well photons don't have momentum because they don't have mass. Like you said, momentum is mass x velocity and since photons have no mass, they have no momentum.

Posted: **Thu Oct 06, 2016 10:02 pm**

Photons can however, with enough energy, eject electrons. These electrons have mass and velocity and therefore, have momentum. So even though photons themselves don't have any momentum, their energy can create momentum on electrons.

Posted: **Thu Oct 06, 2016 10:16 pm**

Einstein's equation E= mc^2 is really just a shortened version of the real equation: E²=(mc²)²+(pc)². E=mc^2 is used for bodies with mass but are not moving while the other equation is used for bodies that are moving such as a photon.

So when a photon is massless we can simplify the equation to E=pc.

Thus a photon can still have energy and momentum without needing to have mass.

If there was some value for m (mass of a photon), then we would find a photon could never reach the speed of light.

In fact, any matter with mass cannot attain the speed of light.

So when a photon is massless we can simplify the equation to E=pc.

Thus a photon can still have energy and momentum without needing to have mass.

If there was some value for m (mass of a photon), then we would find a photon could never reach the speed of light.

In fact, any matter with mass cannot attain the speed of light.

Posted: **Sat Oct 08, 2016 1:53 pm**

Photons themselves don't have momentum due to no mass. If you want to determine the wavelength of a photon, the E= wavelength * frequency equation is what you need to use.