# Is electromagnetic radiation a form of kinetic energy?

• B
Hi, I'm a high school science teacher. Most textbooks classify EM radiation as kinetic energy. But this doesn't seem right to me. As a photon is massless it's hard to see how it can have kinetic energy which is 1/2 mv^2.
It could be said that it has energy hf and therefore mass hf/c^2. Then its kinetic energy would be 1/2 hf/c^2 x c^2, which is 1/2 hf. If its energy is kinetic, then it seems hf = 1/2 hf . . . disproof by contradiction? Or is half of its energy kinetic and half something else?
A Higgs boson has an energy/mass of about 127 GeV. This is the case even if it's not moving, so it's not kinetic energy. Is it a separate type of energy (not kinetic or potential) - maybe mass energy or rest-mass energy. If it is, then can a photon (which is also a boson) be energy of the same type?

PeroK
Homework Helper
Gold Member
2020 Award
In the middle of your calculations you assumed ##E = mc^2## to get the mass of a photon. This equation is for the rest energy of a particle. In fact. It is sometimes written as ##E_0 = mc^2##.

As a photon is never at rest this equation does not apply.

The equation relating the mass and total energy of a particle is

##E = \gamma mc^2##

As the photon travels at ##c## its gamma factor is undefined, so this equation doesn't apply either.

Another useful equation is

##E^2 = p^2c^2 + m^2c^4##

This applies to all particles, including massless photons, in which case it reduces to

##E = pc##

Thanks DrClaude and PeroK for your responses pointing out the errors in my thinking. I still don't know the answer to my question though - whether EM radiation is kinetic energy. Just a yes/no answer would be ok.

ZapperZ
Staff Emeritus
Thanks DrClaude and PeroK for your responses pointing out the errors in my thinking. I still don't know the answer to my question though - whether EM radiation is kinetic energy. Just a yes/no answer would be ok.
"Yes"

Please note that the people who responded made an effort to not just say "Yes" or "No", but rather tried to explain the answer.

Zz.

• PeroK
Khashishi
EM radiation is unique in that it is all kinetic energy.

The equation for kinetic energy that you quoted above ##T = \frac{1}{2} mv^2## is a nonrelativistic approximation which cannot be used for light.
The more correct form for the kinetic energy is:
##T = E - mc^2##
where ##E = \sqrt{m^2c^4 + p^2c^2}##
For light, ##m=0##, so you get
##T = pc##

For your benefit, let's approximate T when v<<c.
##p=\gamma m v \approx m v##
##E \approx mc^2 \sqrt{1 + v^2/c^2} \approx mc^2 + \frac{1}{2} m v^2##
Therefore, ##T \approx \frac{1}{2}mv^2##

Thanks ZapperZ and Khashishi. I am now happy that EM radiation is kinetic energy.
I am still wondering though, what type of energy is the 127 GeV of a Higgs boson. Is it kinetic or potential or something else?

Khashishi