Energy of an electromagnetic wave

[PreposterousUniverse]

The energy of an electromagnetic wave does not depend on the frequency of the wave, only on the amplitude. Then why is light with higher frequency more energetic than light with lower frequency?

 

[hmmm27]

cite ?

 

[malawi_glenn]

Then why is light with higher frequency more energetic than light with lower frequency?

I think you are confusing this with photons vs. electromagnetic waves.

 

[Ibix]

Then why is light with higher frequency more energetic than light with lower frequency?

It isn't. A single photon has an energy that depends on frequency, yes. But by the time you've got enough photons that you can talk about light as a classical electromagnetic wave you have two variables: frequency and number of photons. You can vary the energy being carried at a given frequency by varying the number of photons. That's why classical electromagnetism has no defined relationship between energy carried and frequency.

 

[vanhees71]

A classical electromagnetic wave is not a photon state but a coherent state. It has not even a well-defined "photon number". Forget about photons at this stage and first study thoroughly classical electrodynamics. The energy density of the electromagnetic field in the vacuum is (in SI units)
$$u=\frac{\epsilon_0}{2} \vec{E}^2 + \frac{1}{2 \mu_0} \vec{B}^2.$$
The total energy is given by the integral over all space.

 

[PreposterousUniverse]

Then why are infrared light, visible light and microwaves less energetic than gamma rays, X-rays, and ultraviolet light?

 

[Ibix]

Then why are infrared light, visible light and microwaves less energetic than gamma rays, X-rays, and ultraviolet light?

They aren't if you are talking about electromagnetic waves. Photons of higher frequency do have higher energy, but that's not the same thing as "all gamma radiation carries more energy than all X ray radiation", which would be wrong.

 

[Ibix]

Uranium atoms are heavier than iron atoms. That does not mean that it's impossible to make a chunk of iron heavier than a chunk of uranium. The number of atoms matters as well as their individual masses!

There are complexities with photons that aren't present in this analogy, to which @vanhees71 alludes. But the basic problem is that you are taking statements that are true about individual photons and assuming that they apply to arbitrary EM waves that are not single photons.

 

[gleem]

In free space, the energy density of an EM wave moving in the z direction has a time dependent amplitude that can be given by

If you average over one period S_ave becomes

This is independent of frequency but allows the energy of the wave to contain or be composed of a number of individual quanta whose energy does depend on the frequency ( hf)

 

[vanhees71]

Sigh. Why is everybody so obsessed in using a kind of pseudo-photons in classical electrodynamics? A classical electromagnetic wave is, seen from the QED perspective, a coherent state of the electromagnetic (quantum) field. For not too low intensities the quantum fluctuations can be neglected and you can work with classical electrodynamics.

 

[gleem]

@vanhees71 Sigh. Sorry about that, I figured I might get a negative reaction. However, the OP suggested that he/she might not be able to look at a classical EM wave from a QED perspective.

 

[malawi_glenn]

Then why are infrared light, visible light and microwaves less energetic than gamma rays, X-rays, and ultraviolet light?

Are they? My microwave oven is 800 W. My gamma ray emitting samples in the physics lab does not come close to that (would be kinda disasterous if they did)

Radiowave transmitters also have some substantial power

 

[gleem]

Comparing energy and power?

 

[malawi_glenn]

Comparing energy and power?

How do you measure energy in a wave? How can I have just one single radio wave?

If OP @PreposterousUniverse could mention the sources for his claims, I think we can help him/her better

 

[Vanadium 50]

I am really confused. Two years ago, the OP ws discussing gauge transformation. Now he seems to be mixing together classical EM, classical waves, photons, wavelength, frequency, energy and power. What is going on?

 

[vanhees71]

Some retardation effect? ;-) SCNR.