I asked a slightly different question before, but how common are one color frequency items? Many things can reflect many colors of light, but predominantly show one under white light. If they are exposed to different colored light, they produce different colors, but this happens to many things, even black items. Are there any one frequency items that only reflect that color and become black with different colored light? How common are these items?
$\begingroup$ I can say with absolute confidence that there are no one color frequency items in the whole universe. More importantly, if there were, they would be pitch black (or invisible if transparent at other colors), because the total integrated power with which they would be illuminated would be zero. The closest you can get are probably optical interference bandpass filters. A narrowband filter looks like this: edmundoptics.com/optics/optical-filters/bandpass-filters/…. Because the bandwidth is so narrow, the filter looks rather dull. $\endgroup$– CuriousOneDec 30, 2014 at 2:26
I'm going to agree with CuriousOne, but for a slightly different reason. If you want a single frequency - like, 400.000000..... nm (infinite precision, whatever that means), you must be talking about an atomic transition. Such transitions have "single wavelengths" because when an electron jumps from one state to another, that's a well-defined energy. That single (quantized) energy corresponds to a single wavelength of light.
So, why not make an object out of an element with 1 such transition, to make an object with a single color? Two major problems:
a) You will never observe an exactly 400.00000.... nm photon. Not only experimental errors, but the uncertainly principle ensures that even the photon itself has some spread over the wavelength. Maybe you can define "single color" as "wavelength +/- 0.001%", so that would be fine, but you'll never get "exactly" one color.
b) Any element with a "single wavelength" as I've defined it in (a) would necessarily have others. Even the simplest atom (Hydrogen) has many many energy levels between 3.5 eV and 13.6 eV - any real object will have many, many discrete colors, even if we are only talking about atomic transitions.
So, No, there are no single-frequency objects.
$\begingroup$ So am I correct in assuming that even single element items, such as bromine, which is red, is not a single frequency item because of the formation of atoms? $\endgroup$ Dec 30, 2014 at 3:05
1$\begingroup$ Yes. Bromine is red in visible wavelengths (at least, when I go to Wikipedia and look up Bromine, it's a red liquid). It has 35 electrons (just as many protons). When it's a gas (so we are not talking about molecular bonds), if one of those electrons is missing, another can take it's place, releasing a photon. This photon will have a specific energy based on how much energy it lost. The gaseous bromine will therefore emit at that wavelength. It might not be visible light, but there will be many, many different "colors" based on which transitions we are talking about. $\endgroup$ Dec 30, 2014 at 4:15
1$\begingroup$ Atomic transitions don't have a single frequency, either. They all have a lifetime, i.e. they are smeared out in frequency space. That atomic transitions SEEM to have a well defined energy eigenvalue is an artifact of using the Schroedinger equation, which does not include the photon states in the description of radiating atoms. That, of course, is a poor model. $\endgroup$ Dec 30, 2014 at 6:57
1$\begingroup$ What CuriousOne is referring to is because there is a natural rate at which transitions occur (this is a time interval), there is a natural uncertainty related to that time interval (Heisenberg, $\Delta E \Delta t \leq \hbar /2$). This uncertainty creates an uncertainty in the energy of the photon. So in a single sample, there is a natural distribution of photon wavelengths. I was going for a simple model which gave us the same answer - there are no single-color objects. $\endgroup$ Dec 30, 2014 at 14:13
1$\begingroup$ Yes - 13.6 eV is the ionization energy for atomic Hydrogen, so that's the largest energy that a photon can have which is emitted from it as a result of the absorption of an electron. 3.5 eV was from memory (it's closer to 3.4 eV), and is the second excited state. So, there are many states between 3.4 eV and 0 eV, so you could also say there are many possible photon energies between 10.2 eV (13.6-3.4, the n=2 to n=1 transition) and 13.6 eV (which would be n=large to n=1 transition). $\endgroup$ Dec 31, 2014 at 15:04