# B Is electromagnetic radiation a form of kinetic energy?

Tags:
1. Oct 7, 2016

### Green dwarf

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?

2. Oct 7, 2016

3. Oct 7, 2016

### PeroK

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

$E = pc$

4. Oct 7, 2016

### Green dwarf

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.

5. Oct 7, 2016

### ZapperZ

Staff Emeritus
"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.

6. Oct 7, 2016

### 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, $T \approx \frac{1}{2}mv^2$

7. Oct 8, 2016

### Green dwarf

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?

8. Oct 11, 2016

### Khashishi

Potential. Rest mass is potential energy.

9. Oct 12, 2016

### Green dwarf

Thanks Khashishi.