# E = Mc^2 and the Energy of Light

*Most recent answer: 04/03/2015*

- Gokul (age 11)

Fort St. John,B.C.,Canada

Good for you for wondering why your answer doesn't make sense! The reason is that E = mc^{2} is only part of the story. (Here we are using the notation that "m" stands for the invariant rest mass, not the inertial mass.) It's an incomplete equation that usually only applies to objects that aren't moving. Light is always moving at speed c (the speed of light), so we can't use E = mc^{2}.

Here's the extra piece of physics you need to get the right answer: the full equation is E^{2} = (pc)^{2} + (mc^{2})^{2}. Light has no mass, but it does have momentum, which is called p.

Here's a which explains more about this equation. The math may be confusing if you haven't studied trigonometry yet, but the pictures might help.

If we use m = 0 in the full equation and calculate E, we get E = pc. So, the energy of light depends on its momentum. The momentum of a photon (an individual particle of light) depends on its wavelength, which is related to its color for visible light. Shorter-wavelength light (blue and violet) has more momentum and more energy per photon than longer-wavelength red light.

Rebecca Holmes

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*(published on 04/03/2015)*