Is the electromagnetic spectrum continuous or discrete? It is my understanding that when an electron falls to a lower orbit and emits a photon, it emits a photon with a frequency that is proportional to the energy required to make the electron jump back to the orbit it was in before the emission. Furthermore, I understand that the jumps are additive such that the energy emitted jumping from orbital high (I don’t remember orbital names anymore) to orbital low equals the energy emitted by jumping from high to middle plus the energy from jumping from middle to low.
It should follow that each atom can only emit some particular set of frequencies and that the sum of all these comprise the spectrum. It would seem to me therefore the spectrum would be discrete.
Do other frequencies arise from combining out-of-phase photons?
Also, what does photon amplitude equate to? Power?
The spectrum for any one element is discrete (well, for low energies at least). What’s your question?
Try other energies from other atoms.
Power would be ludicrous, since power is a rate and you’re asking about single photons.
So, the answer is sort of twofold. The amplitude you’re likely thinking of is essentially the number of photons making up the signal. More photons -> bigger amplitude -> brighter light. There’s something else that’s called amplitude, though, which is a sort of probability distribution that varies from place to place and time to time. Where it’s big the photon is likely to be seen, while where it’s small the photon is unlikely to be seen.
Atomic spectra are discrete, yes, but radiation from other sources (such as black-body radiation) can form a continuous spectrum. For example, the spectrum of light from the sun consists of a continuous black-body spectrum (at 5780 K) with discrete absorbtion lines from the various atoms in the solar atmosphere.
Yes, if they interact in a suitably non-linear medium. I don’t know off-hand of any media that are non-linear in the visual part of the spectrum, but I’m sure they exist.
Wait, I thought the big flaw in the Newtonian description of blackbody radiation was that it claimed that it was continuous. Something about infinite energy being released and all that.
To horrendously over-simplify it, the problem with the classical picture of black-body radiation (Maxwell, rather than Newton - Newton’s theory of optics did use discrete “corpuscles” of light, but didn’t equate light with electromagnetism) was that it assumed the radiation came out as one “lump”, rather than as individual photons.
The energy of an individual photon can take an arbitary value - however, light leaving a body has to leave as individual photons, not in a continuous stream.
Note that when a photon is emitted, a lot of factors can change the wavelength slightly. The motion of the atom, a strong magnetic field, etc. When a photon interacts with a free electron, then you get Compton scattering which can shift the wavelength (continuously).
Ergo, a line in an emission spectra has width.
Also, relativistically speaking, if you can get the atom moving at the desired speed with respect to you (the observer), then the photon can take on any wavelength you desire.
There really isn’t an “amplitude”. The energy of each photon is determined by wavelength; a single 500 nm visible-light photon has half the energy of a 250 nm UV photon.
The intensity of light is determined by the number of photons. Twice as many photons = twice as bright.
But if you’re looking at radio waves, I suppose it looks like it has amplitude. But it’s the same story here - a wave with “larger amplitude” is simply made up of a larger number of photons.
I hear that recent work suggests time and length are quantized, though in quanta too small to show up in real physical experiments. Maybe that means the EM spectrum is quantized. But earlier posts are right - while transition lines in atomic spectra are (sort of) discrete, other kinds of radiation (and Doppler-shifted atomic spectra) are not discrete in that sense.
Basically, what’s going on behind the quantization of frequency for EM is that while classically the frequency of light is a function, quantum-mechanically it’s a linear operator on the space of states of the photon. The possible values we can observe are in the spectrum of that operator[1], which is a generalization of the set of eigenvalues. A number x is in the spectrum of L if (L-xI) is not invertible. For the atomic system we’re considering, the low energy part of the spectrum is discrete and only takes certain specific values. However, a system can be constructed to have any real x show up in its spectrum somewhere, so the set of all possible frequencies is not discrete.
Now, for quantization of spacetime, we do the same thing. What we’ve thought were functions – the area of a triangle or the volume of a tetrahedron, for instance – may really be linear operators with the observable values being the eigenvalues of the operators. Similarly, while a given system may have a discrete part of its spectrum, the set of all possible values is not discrete.
[1] The spectrum of a linear operator is called this exactly because of this fact. It’s not a coincidence.
According to classical theory the amount of energy radiated by a black body at a specific frequency is proportional to the frequency; hence huge amounts of energy should be radiated in the ultraviolet and beyond. This is, of course, the ultraviolet catastrophe.
Max Planck proposed that energy could only be radiated in chunks equal to Planck’s constant times the frequency (E = hf). For high frequencies the chunks of energy are very large and only a few atoms in the black body will have that much energy thus solving the UV catastrophe.
So the EM spectrum is continuous but the amount of energy that can be radiated at a specific frequency is quantized. However this is only true for a bound system. In general energy is a continuous variable.
I didn’t mean for the above to sound so snarky. QM is, after all, a mathematical theory and about the only thing we know for sure is that the math correctly predicts experimental results. (Who the hell knows what an electron really is?)
In 1925 P.M. Dirac reformulated QM in terms of Operator Theory /Linear Algebra (sort of) and this is where all the eigenvalues, eigenvectors, state spaces etc. come from. If you’re curious as to what these things are, pick up Elementary Linear Algebra by Anton-Rorres probably the simplest text on this stuff I’ve ever seen.
Well, my first post was more directly on-point. That last one was in response to Napier raising the spectre of quantum gravity. If a reader doesn’t understand my post beyond the first line (“it doesn’t change the answer already given”) then some handwaving about an oversimplified version of a theory that nobody knows how to make work yet will be over his head as well.
Quick simple answer for those who want it:
[ul]
[li] In quantum mechanics, “energy” and “frequency” are essentially the same thing.[/li][li] The “spectrum” of a system is the list of all possible energies or frequencies that you might see when you look at it.[/li][li] For any quantum system, a given energy may or may not be in the spectrum. The spectrum will in general have some areas where only certain energies show up (the “discrete spectrum”) and others where any energy can show up (the “continuous spectrum”).[/li][li] However, for every value of energy, some quantum system will have that energy in its spectrum.[/li][li] So “the electromagnetic spectrum”, as the set of all frequencies (energies) that a photon can be seen in is continuous, while the spectrum for photons emitted by a given atom is discrete.[/li][/ul]
may I throw in my chemists hat. The spectra from individual atoms is very sharp. However the emission from molecules is usually very broad and continuous. The reason is that the energy levels are now not so well defined, but consist of a whole series of vibrational and rotational sublevels. This means that instead of just one energy jump, there is a whole series of them very closely spaced. Throw in the uncertainty principle and you have a continuous spectra.