# What determines the wavelength of light an object reflects?

1. Aug 2, 2014

### slyrez

Now correct me if I`m wrong please. So the sun shines is light delivering its spectrum across earth and objects absorb certain wavelengths and reflect certain wave lengths. The reflected wavelengths is the color we see that object as. So what is it about the object that determines the wavelength it reflects? Thanks!

2. Aug 2, 2014

### voko

The chemical composition of the object and its physical state, and its electrons ultimately.

3. Nov 5, 2016

4. Nov 6, 2016

### Cutter Ketch

Reflected (or transmitted, the material could be transparent) is that which is not absorbed. The absorption has all the physics / chemistry.

Light is absorbed by electronic transitions. Quantum mechanics requires that the electrons in a material have only certain discrete allowed states. These states have several properties including energy, orbital orientation relative to the crystal structure, spin, and most importantly for this discussion dipole moment.

For a photon of light to be absorbed the material must have an electron in a lower energy state, an allowed higher energy state, with an energy difference exactly equal to the energy of the photon, and a linear combination of the two states must have an oscillating dipole moment. This transition dipole moment means that in the mixed state the charge is an oscillating dipole just like an antenna. From the lower state the system can absorb a photon, while from the upper state a photon can be emitted.

The allowed transitions are a unique characteristic of each material. Looking at the spectrum of absorbed, reflected, or emitted light the material can be determined.

5. Nov 7, 2016

### sophiecentaur

The allowed energy states in a solid or a liquid are not discrete because the interaction between any one electron and all its near neighbours causes the lines (simple quantum behaviour of gas atoms) to spread out into continuous bands. The physics of 'condensed matter' is much harder than the QM we start off with in School and College. A pigment, dye or any coloured substance will absorb pretty broad bands of wavelengths and reflect or transmit what's left over.

There is another cause of coloured surfaces and that can be caused by thin layers (films) on a surface that cause Interference due to multiple reflections. If the layers are very narrow (quarter wavelengths, typically) you can get very strong colours due to the very narrow bandwidth of the reflected or transmitted light. Birds and Butterfly wings have iridescent colours due to this mechanism. (Virtually) no energy is absorbed when this happens.

6. Nov 7, 2016

### Cutter Ketch

I actually typed in the fact that the states become dense and form bands but erased it thinking it confused the description of the fundamental process. However, I agree that the bands immediately dominate the discussion after the basic description, and skipping them was probably doing a disservice to the question. Not that it contradicts your point in any way, but I'll mention that the states are technically still discrete, just very densely packed in energy space.

That's a good point about interference in thin films as there are many things that show color that way (and they all look awesome! Insects in particular, and not just their wings.). While we are at it I should add dispersion in refraction which, for example, makes diamonds (and other things, of course) sparkle with rainbows of color.

7. Nov 7, 2016

### sophiecentaur

It's a bit of a dilemma but I have a lone crusade to discourage beginners from trying to apply 'The Hydrogen" atom to every explanation that involves QM.

8. Nov 8, 2016

### ZapperZ

Staff Emeritus
Are you sure? When you solve the Bloch wavefunction, for example, can you show me where these "densely packed" states are in the solution?

Coming back to the OP, we get this type of question quite often on this forum. I strongly suggest looking up the physics involved in the UV-VIS spectroscopy. This is the technique that measures the spectrum of the reflectance and transmission of light through a material. A lot of information about the molecular vibration and even lattice vibrations can be obtained from this type of experiment.

Zz.

9. Nov 8, 2016

### Cutter Ketch

Yes, quite sure. Here are several arguments.
First, it is required by the Pauli exclusion principle for fermions. Second, you can picture it by construction: bring two atoms together and the outer shells hybridized to make 2 discrete orbitals. Bring another in and the orbitals hybridize further to six orbitals, etc, etc. Third: the approximation of continuity is stated in every band derivation I've ever seen. There is some statement to the effect "if we take the lattice to be infinite the density of states can be treated as continuous" or similar. I'm old and I've lost my old textbooks, so I'm reduced to pointing at Wikipedia articles which aren't quite as trustworthy, but to the degree you can believe it see this article:

https://en.m.wikipedia.org/wiki/Electronic_band_structure

10. Nov 8, 2016

### sophiecentaur

It is a logical conclusion if you approach the situation from a simple gas via increased pressure (line spreading and Pauli Exclusion). So maybe the Bloch and Schroedinger equations are a bit mutually exclusive at some point?

11. Nov 8, 2016

### ZapperZ

Staff Emeritus
I'm sorry, but your starting point is wrong. I asked you to show, starting with the Bloch Hamiltonian, where these discrete levels are in the solution. In fact, the wikipedia link that you cited USED this as a starting point.

I'm a condensed matter physicist by training, and I am very familiar with electronic band structure of materials. I have even directly measured these band structures using ARPES. So you may very-well assumed that I know the physics involved.

So knowing that, I will ask you again. Where, in the solution, do you see this discrete energy levels in the Bloch wavefunction?

Zz.

12. Nov 8, 2016

### Cutter Ketch

Yes. The continuum model is an approximation. However Avagadro's number is big enough to make an approximation of continuity extremely valid as is the case in many things we do in statistical mechanics or calculating the black body spectrum, or other good examples that I would insert here if I had actually come up with them rather than feeling pretty sure they probably exist. (Truth in advertising)

13. Nov 8, 2016

### ZapperZ

Staff Emeritus
First of all, there is a difference between saying "what goes up must come down" versus "when and where it comes down". So far, you've given us a "qualitative" argument on why you think that these bands have discrete energy levels. I am arguing that the quantitative aspect of it, which is the actual calculation from First Principles, actually doesn't show that! And that is what you've been avoiding each time I asked you for it.

Go back and look at the Wikipedia link that you gave me and see how the band dispersions were derived mathematically. The "approximation" being done here, and in the Bloch wavefunction is not that these are "large" number, but rather in the nature of the periodic potential (and, if you want to be more technical, in the many-body renormalization). This is why I asked you where, in the actual physics itself rather than in the handwaving argument, are these discrete energy levels, or even the approximation that wiped them out.

So far, I have not received any clear explanation from you on this issue.

Zz.

14. Nov 8, 2016

### Cutter Ketch

Read the text. The Wikipedia article describes the approximation of the continuum and then states it's assumptions including infinite size as the starting point for its derivation.

"Eventually, the collection of atoms form a giant molecule, or in other words, a solid. For this giant molecule, the energy levels are so close that they can be considered to form a continuum"

And later under "Assumptions and limits of band structure theory" item number 1 is "infinite-size system: For the bands to be continuous, we must consider a large piece of material." I know they said large, but the label is infinite and the reason is that continuity is a large number approximation the same as we see throughout statistical mechanics. Of course Avagadro's number is huge and any tiny piece is approximately infinite (at least until you start making computer chips with 14nm features.)

15. Nov 8, 2016

### Cutter Ketch

You seem to not know the meaning of the word approximation. A theory is derived from a more complete theory. It states in the derivation that it is an approximation of the more complete theory. It indicates what the approximation is and somehow because it is a good approximation you take that to mean that the more complete theory from which it was derived is therefore not valid?!?! That's ludicrous. You can't derive the band theories without starting with the discrete states and stating an approximation. The name "Density of States" isn't random. It is literally true. There are that many discrete states in that energy interval. The numbers are huge and the spacing is irrelevantly tiny, but that's the way it is.

16. Nov 8, 2016

### ZapperZ

Staff Emeritus
The infinite-size assumption is not a stretch. Practically almost every theory that we have make use of that type boundary conditions. It isn't an "approximation" to not consider the gravitational field from Alpha Centauri when we do our mechanics calculation. To me, that is not the source of the continuous spectrum.

Secondly, the DOS is actually less fundamental than, say, the single-particle spectral function A(k,w). It is this spectral function that produces not only the DOS, but also many other basic properties of a material. You get the DOS upon an integration over k. So it is this function that you need to show to have "discrete" states, even small. The DOS is given a name that, as in many other parts of physics, leads to a misleading impression that these are discrete states.

This appears to bring up the fundamental issue of Phil Anderson's "More Is Different". The reductionism argument these many-body systems are, fundamentally, just simply added complexities of each of the individual components have been addressed many times. They are not. The many-body wavefunction did not start out (and in fact, many argued, could NOT start out) from simply piling up the properties of each individual components of the system.

Zz.

17. Nov 10, 2016

### sophiecentaur

Yes. We don't have that problem when we derive the gas laws from simple ideas on Kinetic Theory.

18. Nov 14, 2016

### Saw

ZapperZ, you may be right but what is clear is that you are in contradiction with the Wikipedia. I don't know if the math that gives a continuous result makes the assumtpion of the object in question being of infinite size or large enough, but what is undeniable is (as mike.albert99 points out) that the words used in Wiki do make such assumption in the site discussed so far (https://en.m.wikipedia.org/wiki/Electronic_band_structure).

And if you look at the text of this other site (https://en.wikipedia.org/wiki/Energy_level), Wiki's position cannot be clearer:

"Crystalline solids are found to have energy bands, instead of or in addition to energy levels. Electrons can take on any energy within an unfilled band. At first this appears to be an exception to the requirement for energy levels. However, as shown in band theory, energy bands are actually made up of many discrete energy levels which are too close together to resolve. Within a band the number of levels is of the order of the number of atoms in the crystal, so although electrons are actually restricted to these energies, they appear to be able to take on a continuum of values."

19. Nov 14, 2016

### sophiecentaur

Whether you predict Energy Bands or very fine Line Structure will probably depend on how you model the system. Is there much point in arguing about which one is the 'correct' model? Is there any fundamental truth in Science?

20. Nov 14, 2016

### ZapperZ

Staff Emeritus
First of all, if you live by Wikipedia, you die by Wikipedia as well.

Secondly, re-read again my ORIGINAL objection in Post #8. Let me rephrase what I asked: Where exactly is the discrete energy level from these atoms in the physics when you solve for the Hamiltonian of the Bloch wavefunction?

My objection was the notion that there are many of these discrete energy states, so much so that they form a continuous band, AND, that these can be seen from the physics that we used to arrive at the band structure. This is what I want to see.

When you make such a claim, you have to show the physics, rather than expect someone else to debunk it. I have stated why this is not how we do the physics (i.e. summing up the energy states of each atom by infinite amount to get these bands). I've also stated why, from Anderson's "More Is Different" (P. Anderson, Science v.177,p.4 (1972)), that this is an example of an emergent phenomenon that simply can't be solved by considering the individual components separately. One just has to look at Laughlin's Nobel Prize speech (R.B. Laughlin, Rev. Mod. Phys., v.71, p.863 (1999)) and what he said about the derivation of phenomena such as Superconductivity. None of those started from an assumption that we can simply add up all the properties of the individual atoms and molecules.

One would think that we have all learned by now that there are many things in science that are NOT intuitive, at least not at first. While you may think that it is "obvious" that we can simply sum up all the discrete states to get the band dispersion in solids, it still doesn't change the fact that that is NOT how we do it to get these bands. To dismiss the missing evidence and simply sweep it under the rug as simply being part of the approximation means that (i) you do not understand the concept of emergent phenomenon and (ii) you've accepted the validity of the missing step in the process. If you are happy to live with that, then there's nothing I can do anymore.

Solid State Physics is NOT Many-Atomic Physics.

Zz.