# Is the Electromagnetic Spectrum non-continuous?

1. Mar 20, 2013

### Eriance

From what I've learned in physics, electrons falling from higher energy levels to a lower energy level emits an photon equal to that of the difference in energy between the two levels. Each atom has a set number of energy levels for the electrons, and thus each element can only emit a set number of photon wavelengths.

Given there are limited numbers of elements, and a limited number of energy levels for each electron, does that mean the number of wavelengths for photons is limited also? Meaning, there isn't a continuous spectrum for EM radiation, rather quantized wavelengths, while some wavelengths don't exist? (i.e. say if no electron in any element have levels have the energy correlated to a photon of 345 nm, then such a photon doesn't exist in nature).

Or am I misinterpreting something?

2. Mar 20, 2013

### Staff: Mentor

Transitions between atomic energy levels are not the only way to generate EM radiation.

3. Mar 21, 2013

### Jano L.

It depends on how you describe the EM field. If you expand it in Fourier series, only components with certain preferred wave vectors $\mathbf k$ are used. The spectrum as a function of frequency will then be discrete and look like comb, hence it will be discontinuous.

On the other hand, if you decide to describe the field by the Fourier integral, it may happen that the Fourier transform is continuous (but it is not necessary). The spectrum then may be continuous.

Both descriptions are sometimes possible for the same field, which seems to imply that the distinction is in the description, not the actual state of the field.

4. Mar 21, 2013

### cabrera

When Plank was trying to explain the origin of the black body radiation was using oscillators as sources of EM radiation. What he found was that he had to the amount of oscillators in volume of space was limited. He had to assume that spectral density of the sources of EM radiation (oscillators) was not continuous. What that meas is that you cannot fit a continuous number of oscillators in a volume of space, they must be quantified. That doesn't means that the EM spectrum is discontonous

5. Mar 21, 2013

### Staff: Mentor

Don't forget also that what you said there is only valid for an isolated atom. In a gas, you have to take into account atom-atom interactions, which will shift the position of the levels. There is also the Doppler effect. And molecules do not have the same spectrum as their constituant atoms. And we're not even talking here about solids...

6. Mar 25, 2013

### TheNutyProfesr

I agree with DrClaude, (Doppler shift part specifically). Lets take the highest known energy photon with frequency f, now as the universe expands and the rate accelerates the frequency will slowly decrease. Hence a single photon can exhibit infinite energies as it morphs with time.
This assumes that time is also continuous.

...However our model of light may not be the best one yet!!!

7. Mar 25, 2013

### Eriance

Ah ok. Thank you all for the explanation.

8. Mar 26, 2013

### AkInfinity

Very good observation Eriance! Another way to creat EM waves is through a spark, which can produce all of them provided the spark had enough energy.

However if you take planks constant, you will see that it the EM field is not continuous and goes up by small steps known as "planks constant".