What decides the colour of light?

[jack476]

It's very rare to encounter light that is only a single frequency, light from most sources in the real world is actually a mixture of light at a number of different frequencies. What happens when light passes through a filter is that some of those frequencies are absorbed and some are not.

To give an example, think about the greenhouse effect. You know that it's due to certain gases having a really good ability to absorb radiation that's been reflected from the Earth, the energy of that radiation is absorbed by the gas (technically, at the molecular scale the radiation is actually being scattered, but the net result is that the gas as a whole absorbs energy) causing the atmosphere to warm. A common misconception is that climate change will "balance out" because the understanding is that it's reflecting radiation, therefore reflecting the solar radiation that would warm the Earth in the first place, but the reason that's not true is down to that frequency-dependent absorption: Carbon dioxide is a filter for light in some ranges of the IR spectrum, not a reflector.

Frequency can be directly changed in some cases, for instance in Doppler shifting, but that's very different from what's happening in a color filter.

 

[evan-e-cent]

When the cis isomer gets hit by a photon the added energy causes it to flip back into the trans form.

I don't think this mechanism of light detection corresponds with the excited state of electrons. It is more like a chemical reaction which requires a certain thermal activation energy to get over the energy hump and then drop into a lower energy state. This mechanism would not depend so precisely on the quantum of energy in the photon and may respond to a broad range of light energies.

In fact it may respond to light of a wide range of frequencies. The fact that some species of insect use a colored oil droplet in front of the light sensor suggests that different types of color filters are used in the various cones and rods that detect different colors. The literature talks about different color pigments in the different types of cones and I think these act as color filters. The rods probably use the same chemical mechanism without filters, making them more sensitive to light but unable to distinguish colors (they are also more compact and there are more sensors packed into a small space giving greater sensitivity.)

For those unfamiliar with cis / trans isomers may find these diagrams from Wikipedia useful. In the model you can see how the two large CH3 groups can interact with each other causing a higher energy state than the trans configuration of the same molecule where the CH3 groups are on opposite sides of the double bond. If the CH3 groups were replaced with long chains as in retinal, the interactions are more severe.

The graph below shows the concept of activation energy Ea. Although the cis isomer is in a higher energy state than the trans, it requires additional energy to distort the double bond and transition from one state to the other. During the transition a temporary high energy transitional state exists where it is neither cis nor trans. So the cis isomer can exist for long periods of time before that extra energy becomes available. In the eye the extra energy is provided by a photon. Photons providing excessive energy would also cause the transition so it may not be particularly color sensitive unless filters are used.

The fact that cis-retinal can get used up faster than its rate of production causes the after-image if you stare at a bright image for a long time and then look into the dark.

https://en.wikipedia.org/wiki/Cis–trans_isomerism

CIS ISOMER (higher energy state)

TRANS ISOMER (Lower energy state)

https://en.wikipedia.org/wiki/Activation_energy

 

[evan-e-cent]

Further reading of Wikipedia on opsin proteins revealed:

https://en.wikipedia.org/wiki/Photopsin

In humans there are 3 different iodopsins (rhodopsin analogs) that contain the protein-pigment complexes photopsin I, II, and III.
The 3 types of iodopsins are called erythrolabe(photopsin I + retinal), chlorolabe(photopsin II + retinal), and cyanolabe(photopsin III + retinal).[3]
These photopsins have absorption maxima for red ["erythr"-red] (photopsin I), green ["chlor"-green] (photopsin II), and bluish-violet light ["cyan"-bluish violet] (photopsin III).

This indicates that the "color filter properties" are built into the proteins that contain the retinal light sensing molecule. The Greek roots refer to the colors; erythro means red, cholera means green and cyano refers to blue or cyan.

 

[sophiecentaur]

I have actually been banned from one of these discussions for saying that. There is a "perception is all that counts" mind set here.

Which "here" were you referring to, at the time? The 'here' of this thread or the 'here' of the PF site in general?

 

[FactChecker]

Which "here" were you referring to, at the time? The 'here' of this thread or the 'here' of the PF site in general?

About a year ago on another similar thread (definition of color) on PF.

 

[sophiecentaur]

About a year ago on another similar thread (definition of color) on PF.

I skimmed through that thread and it is almost a re-run of this one. The same misconceptions and mis-used words are there and the continued Colour = Wavelength nonsense, plus a large number of 'personal theories' that PF mods would normally stamp on. I think any thread that drifts into how we see colour should probably be shunted, PDQ, into a Forum that's more appropriate to Psychology.

 

[madness]

It's still based on quantum principles. That means only photons of a relatively narrow range of energy values (seen more below) will be absorbed that would cause the proper excitation of the electron, which is the trigger that ultimately leads to the brain perceiving the stimulus (after a very complicated process; @evan-e-cent gave a more detailed description in post #67). Any more energy or less energy in the photon, and the excitation does not happen.
It's the photon energy that is critical here. (And the photon energy is directly proportional to its frequency, so if you had to pick between frequency and wavelength here, frequency would be the one to choose, given its proportionality to energy).
That's not correct. It is certainly not what I meant convey anyway.

“Red” photoreceptor cones are not particularly sensitive to blue light even though blue light has a higher photon energy. And that is completely consistent with the underlying quantum nature at its core. Just because a photon's energy is significantly greater than the allowed change of electron energy states it does not mean that the electron will necessarily absorb some or all of that energy. Instead, quantum theory predicts that that the electron state will likely not be impacted by the photon at all.

(Light frequencies anywhere from near-infrared all the way through ultraviolet will be absorbed by the eye in one way or another. It’s just that a particular color cone type is only sensitive to photon energies within a limited range. And that is not inconsistent with quantum theory.)

Let me illustrate a more simple example.

Consider a light source with a uniform spectrum of light (with no gaps in the spectrum, and let’s assume the spectrum spans at least the visible band, if not the infrared and ultraviolet too). Shine that light through a cold gas (any gas will work, but hydrogen or neon might make good choices), then observe the resulting spectrum. You'll notice that now there are very narrow gaps (called spectral lines) in the resulting spectrum (after passing through the gas)! Photon energies higher than a given spectral line passed right through the gas as did photons of lower energies. Only certain energies are absorbed.*

*(In this simple gas case, the spectral lines are not infinitesimally thin, but do contain a very small bandwidth, which can be explained by the Doppler effect of the moving gas molecules. It's way more complex for [non-gaseous] huge molecules working together as a tissue.)

The molecular structures of human photoreceptors are far, far more complex than a simple gas (not to mention not being in a gaseous state). There’s more complex mechanisms for absorption and thusly the absorption bandwidths are larger than the simple gas example. Yet extraordinarily more complex as they may be, they still follow the same quantum rules.

This whole post is still clinging to the idea that phototransduction is caused by an excitation of an electron into another energy level, which has been repeatedly demonstrated not to be the case in this thread. As I and evan-e-cent have said, it is a conformal change in the structure of a macromolecule (and by the way, the majority of macromolecular physics is treated with classical rather than quantum principles). The process is related to chemical bonding and activation energies, not excitation of electrons into discrete bands.

 

[sophiecentaur]

caused by an excitation of an electron into another energy level,

Yes; very annoying. But you have to remember that the Hydrogen Atom model is a hard one to shift. In many eyes, QM starts and stops with it - although how that could ever square with infra red and microwave transitions, I cannot imagine. The first QM lesson shows a ladder of energy levels and photons shifting 'an electron' between them - but there is quite a bit more to learn , isn't there? That includes the energy states of molecules and the bulk properties of matter. Pity to spoil a good story with some facts, though.

 

[madness]

Yes; very annoying. But you have to remember that the Hydrogen Atom model is a hard one to shift. In many eyes, QM starts and stops with it - although how that could ever square with infra red and microwave transitions, I cannot imagine. The first QM lesson shows a ladder of energy levels and photons shifting 'an electron' between them - but there is quite a bit more to learn , isn't there? That includes the energy states of molecules and the bulk properties of matter. Pity to spoil a good story with some facts, though.

I don't think this thread has come anywhere close to explaining how a macromolecule can undergo a conformal change in the presence of light in a narrow range of frequencies/wavelengths. The activation energy picture would suggest a frequency threshold above which the change in structure will occur. The hydrogen atom picture could explain it, but we're looking at chemical bonds rather than a ladder of electron energy levels here.

 

[sophiecentaur]

, but we're looking at chemical bonds rather than a ladder of electron energy levels here.

Of course we should be but, from what is written in this thread, I doubt that everyone in thinking along those lines. The term 'electron energy level' is not an apt description of what happens in a molecule yet it still turns up in 'explanations' of complex processes due to the energy states of systems with a large number of charges.
And we are nowhere near a description of that.
But I take the key word Colour (in the title) as involving much more than the interaction of a photon with a molecule. However the retinal cells are stimulated, there is the important process of the way the three resulting signals are treated by the nervous system and how the sensation of colour is arrived at, along with the way it's categorised in the brain. That 'top down' study will avoid the risk of oversimplification of the word Colour.

 

[madness]

But I take the key word Colour (in the title) as involving much more than the interaction of a photon with a molecule. However the retinal cells are stimulated, there is the important process of the way the three resulting signals are treated by the nervous system and how the sensation of colour is arrived at, along with the way it's categorised in the brain. That 'top down' study will avoid the risk of oversimplification of the word Colour.

I fully understand this, but what you have to consider is that the brain can only work with the signals it transduces at sensory receptors. Of course, the perception of colour is a complex and poorly understood process, but it all starts with the conversion of light into electrical signals at the retina (unless you are dreaming or hallucinating!).

 

[Ygggdrasil]

I don't think this thread has come anywhere close to explaining how a macromolecule can undergo a conformal change in the presence of light in a narrow range of frequencies/wavelengths. The activation energy picture would suggest a frequency threshold above which the change in structure will occur. The hydrogen atom picture could explain it, but we're looking at chemical bonds rather than a ladder of electron energy levels here.

The activation energy picture is not really an accurate way of looking at photochemical reactions such as the photoisomerization of retinal. In this case, you can think of the first step as a chemical reaction between retinal (R) and a photon of a specific wavelength that changes R from its ground state to its excited state (R*).

Remember that the bond order, a measure of the strength of a chemical bond, can be calculated by taking the number of electrons in bonding orbitals and subtracting the number of electrons in anti-bonding orbitals (then dividing by two). Therefore, by promoting an electron from a bonding orbital to a non-bonding or anti-bonding orbital, you are decreasing the bond order of chemical bonds in retinal. This can, for example, make one of the C-C bonds in retinal resemble more of a single bond (around which rotation can occur) rather than a double-bond (around which rotation is forbidden at typical temperatures). This free rotation about one of the bonds means that when the molecule relaxes back into its ground state, it has some probability of relaxing into the trans- configuration and some probability of relaxing into the cis-configuration.

As to why absorbtion spectra of molecules are much wider than typical atomic spectra, this is due to the fact that molecules have vibrational and rotational states in addition to different electronic states: see https://www.physicsforums.com/threa...t-of-absorption-emission-spectroscopy.433712/. Band theory is not really applicable to this case.

 

[collinsmark]

I didn't mean to use the band theory application of the LED semiconductors as anything more than an analogy. Sometimes studying more simple systems can lead to insights of more complex ones. It was just an analogy. (I thought I made that clear. Did I? I thought so anyway.)

In the case of the simple gas absorption spectra the photon energy absorbed ultimately gets converted to other types of energy. In the case of a monotonic gas like neon, this is translational energy (heat on the macroscopic scale). [Edit: not to mention other photons in the infrared and microwave regions as the result of the atom interacting with other atoms in the gas -- again, ultimately heat though.] In the case of more complicated hydrogen molecules it also involves changes in rotational energy in addition to translational -- and the initial absorption mechanism is also more complex since two hydrogen atoms are initially bonded. We don't need to rely on quantum mechanics (QM) to macroscopically describe the thermal activity of the gases, but QM is necessary to describe the mechanism of that initial photon absorption.

In the case of the even more complicated protein molecule that photon energy ultimately becomes not just changes in translational and rotational energies, but also conformational and vibrational changes (and there may be more vibrational modes than you can shake a stick at). We don't necessarily need QM to model the resulting conformational, vibrational, rotational and translational characteristics. We can use the tools of chemistry and classical physics for most of those.

But even with a complex protein, that initial photon absorption does require quantum theory (particularly given the relatively low temperatures and relatively high photon energies in question [we are talking about photons in the visible range here and molecules near room temperture]). Could we use QM to predict the photon energy absorption spectrum of a complex protein practically? Probably not with today's computers or those to come in the near-foreseeable future. But it could be done at least in principle.

And that's the crux of my point. Classical physics cannot adequately model the mechanism of that initial photon absorption even in principle.

And all of this is relevant to this thread. The OP asked about whether the color of light relates to wavelength or frequency. The correct answer is frequency because it relates to the photon's energy. And energy is the correct answer because that's what governs the underlying quantum mechanics of that initial photon absorption (not wavelengths and not length scales of the photoreceptor or what-not).

(And btw, I'm sorry if that is annoying. )

 

[sophiecentaur]

absorbtion spectra of molecules are much wider than typical atomic spectra,

Isn't that a consequence of the Pauli Exclusion Principle that operates in dense materials? Solid state (of which I know a certain amount) exhibits band structures and not lines, as a result of the PEP, too.

 

[sophiecentaur]

(And btw, I'm sorry if that is annoying. )

Not at all. We all need putting straight about things we don't know about.

 

[collinsmark]

Isn't that a consequence of the Pauli Exclusion Principle that operates in dense materials? Solid state (of which I know a certain amount) exhibits band structures and not lines, as a result of the PEP, too.

As I recall it is not necessary to invoke the Pauil Exclusion Principle (PEP) to explain the energy band model of solids. Sure, in any physical real-world solid one can't get away from the PEP, but I'm just saying that I don't think it's necessary to explain the energy bands vs. single values.

If you take just a single electron and place it in a 3-dimensional, vast array of energy wells (and even simple, Dirac delta wells will suffice) -- perhaps an infinite array of potential wells -- and use standard, non-relativistic quantum mechanics to determine the allowed energies of the electron, bands will naturally result. So the band theory of solids is a very basic outcome of QM and doesn't even require the exclusion principle, as I recall.

And fascinating thing is that this problem (as I recall) is it is not too tough to calculate and show. It relies the assumption that the three dimensional array of potential wells can be approximated as infinitely large. This is one of the few cases where having an infinite number of particles actually simplifies the problem rather than making it infinitely complex. I've always found that fascinating.

The buggers are those systems with an in-between number of particles. Using today's computational resources we can use QM to make very precise predictions for a handful of particles (~10 or less maybe?) or for an infinite number of particles, assuming they have an organized structure. It's those in-between number of particles that are the buggers.

Proteins fall into the latter category. It's not that quantum mechanics isn't up for the challenge, but rather it's just that our computers and computational resources are not. But it eases my mind that QM can be used to fully analyze a protein at least in principle anyway.

 

[madness]

Therefore, by promoting an electron from a bonding orbital to a non-bonding or anti-bonding orbital, you are decreasing the bond order of chemical bonds in retinal. This can, for example, make one of the C-C bonds in retinal resemble more of a single bond (around which rotation can occur) rather than a double-bond (around which rotation is forbidden at typical temperatures).

Focussing just on this step, can we understand why only photons in a particular frequency band would do the job? Can we understand how selectivity for different frequency bands in different cells emerges? I would guess that it's actually more complex, and that the selectivity of different cells to different frequency bands requires more of a systems perspective.

By the way, I've found these last few posts to be very informative!

 

[Ygggdrasil]

Focussing just on this step, can we understand why only photons in a particular frequency band would do the job?

Essentially this has to do with the energy difference between the ground state of the molecule (the HOMO — highest occupied molecular orbital) and its excited state (the LUMO — lowest unoccupied molecular orbital). Only photons with energies matching the energy difference between the orbitals (the HOMO-LUMO gap) will be able to promote the electron to its excited state. Interaction with photons of the wrong frequency will promote the electron to "virtual states" but if these virtual states do not match the electronic states of the molecule, they will be extremely short lived, and decay back to the ground state almost immediately with re-emission of the absorbed photon. Only when the electron gets promoted to a stable electronic excited state will the excited state have a long enough lifetime for chemical processes to occur (e.g. the bond rotation required to convert the cis-form to the trans-form).

Can we understand how selectivity for different frequency bands in different cells emerges? I would guess that it's actually more complex, and that the selectivity of different cells to different frequency bands requires more of a systems perspective.

All opsins contain the same chromophore (11-cis retinal), yet different opsins have different sensitivities to different frequencies of light. This can occur because the retinal chromophore lies buried deep within a pocket in the opsin protein. The chromophore makes extensive non-covalent interactions with parts of the protein, and these interactions can affect the distribution of electrons throughout the retinal molecule, therefore, changing the energies of the molecular orbitals and the HOMO-LUMO gap. You can essentially think of this as the protein applying an external electric field to the molecule which can change the potential energy function of the electrons in 11-cis retinal. Thus, the frequency selectivity of cone cells depends entirely on the type of opsin protein they make.

This strategy has also been used on fluorescent proteins. Many fluorescent proteins have identical or very similar chromophores, but by introducing specific mutations around the chromophore-binding site, scientists have been able to fine tune the colors of the fluorescent proteins in order to generate a rainbow of colors:

 

[madness]

Essentially this has to do with the energy difference between the ground state of the molecule (the HOMO — highest occupied molecular orbital) and its excited state (the LUMO — lowest unoccupied molecular orbital). Only photons with energies matching the energy difference between the orbitals (the HOMO-LUMO gap) will be able to promote the electron to its excited state. Interaction with photons of the wrong frequency will promote the electron to "virtual states" but if these virtual states do not match the electronic states of the molecule, they will be extremely short lived, and decay back to the ground state almost immediately with re-emission of the absorbed photon. Only when the electron gets promoted to a stable electronic excited state will the excited state have a long enough lifetime for chemical processes to occur (e.g. the bond rotation required to convert the cis-form to the trans-form).

Very cool. So, if two photons at exactly half the energy were to arrive simultaneously, they might achieve the same result, but the intermediate state is so short lived that any delay in their arrival times would stop this from happening. Is this correct or incorrect?

I suppose this is also where the classical picture breaks down entirely, since classically you would expect that a photon at a higher energy than required would just induce some additional rotational or translational energy, or perhaps just excite the electron to an even higher state.

All opsins contain the same chromophore (11-cis retinal), yet different opsins have different sensitivities to different frequencies of light. This can occur because the retinal chromophore lies buried deep within a pocket in the opsin protein. The chromophore makes extensive non-covalent interactions with parts of the protein, and these interactions can affect the distribution of electrons throughout the retinal molecule, therefore, changing the energies of the molecular orbitals and the HOMO-LUMO gap. You can essentially think of this as the protein applying an external electric field to the molecule which can change the potential energy function of the electrons in 11-cis retinal. Thus, the frequency selectivity of cone cells depends entirely on the type of opsin protein they make.

I see, it's interesting that there is a purely molecular basis for all of this.

This strategy has also been used on fluorescent proteins. Many fluorescent proteins have identical or very similar chromophores, but by introducing specific mutations around the chromophore-binding site, scientists have been able to fine tune the colors of the fluorescent proteins in order to generate a rainbow of colors:

I've come across opsins mostly in the context of optogenetics, where the most commonly used opsins are channelrhodopsin and halorhodopsin. They have really revolutionised neuroscience research.

 

[Ygggdrasil]

Very cool. So, if two photons at exactly half the energy were to arrive simultaneously, they might achieve the same result, but the intermediate state is so short lived that any delay in their arrival times would stop this from happening. Is this correct or incorrect?

Yes, this is correct. This is what occurs in two photon absorption and other nonlinear optical phenomena.

I suppose this is also where the classical picture breaks down entirely, since classically you would expect that a photon at a higher energy than required would just induce some additional rotational or translational energy, or perhaps just excite the electron to an even higher state.

Light cannot really induce many changes in translational energy due to conservation of momentum. Light can excite rotational or vibrational excited states, but these are also quantized. The basic idea is that if the energy of the ground state + the energy of the photon gives an energy that is an eigenvalue of your particular molecule's hamiltonian, you will get a stable, stationary state. Otherwise, the resulting state will be a very unstable virtual state that will quickly revert back to the ground state.

 

[Apoorv3012]

Consider a beam of light passing through a slab of some refractive index.
We know that the speed and wavelength of the light changes, but its frequency remains the same.
Since the wavelength of the light changes, does its colour change, or does it remain the same as its frequency remains the same.

Does the wavelength really change after refraction?

 

[DaveC426913]

Does the wavelength really change after refraction?

Yes.

 

[Apoorv3012]

Yes.

Thanks Dave ,I read some further on other threads and understood that happens because the light's speed change per medium and since it's frequency remains constant, the wavelength must change.

 

[evan-e-cent]

All the above discussion is very interesting with different perspectives from people coming from different backgrounds, and with different areas of expertise.

I was about to comment on the fact that the basic chemical structure of the light sensing molecule Retinal is the same in all the different color sensing cones but that it may be influenced by hydrogen bonding, weaker Van der Waal's forces, and other electromagnetic effects of the surrounding protein structures when Yggdrasil gave us a much more eloquent description and demonstrated a beautiful example.

Is it true that the speed of light varies with wavelength? I assume this also applies to the speed of light in a vacuum?

I had not appreciated that, but this Wikipedia article uses it to explain how a prism separates colors. Here's the quote.

For electromagnetic waves the speed in a medium is governed by its refractive index according to

where c is the speed of light in vacuum and n(λ0) is the refractive index of the medium at wavelength λ0, where the latter is measured in vacuum rather than in the medium. The corresponding wavelength in the medium is

When wavelengths of electromagnetic radiation are quoted, the wavelength in vacuum usually is intended unless the wavelength is specifically identified as the wavelength in some other medium. In acoustics, where a medium is essential for the waves to exist, the wavelength value is given for a specified medium.

The variation in speed of light with vacuum wavelength is known as dispersion, and is also responsible for the familiar phenomenon in which light is separated into component colors by a prism. Separation occurs when the refractive index inside the prism varies with wavelength, so different wavelengths propagate at different speeds inside the prism, causing them to refract at different angles. The mathematical relationship that describes how the speed of light within a medium varies with wavelength is known as a dispersion relation.

 

[evan-e-cent]

I asked "Has anyone wondered why water is perfectly clear". No one took my bait. Well I will give you my answer anyway.

Vision evolved in water, in species that lived in the sea, or otherwise had eyes that contain water. Any wavelength of light that is absorbed by water would not penetrate the eye and therefore would be invisible. So vision evolved to avoid these wavelengths. Consequently water MUST be transparent as a requirement of the evolutionary process.

 

[rootone]

That kinda makes sense when thinking about UV and beyond, but Infrared and below goes through water quite well, apart from a quite narrow band in the microwwave region, or maybe I'm wrong about that.

 

[collinsmark]

I asked "Has anyone wondered why water is perfectly clear". No one took my bait. Well I will give you my answer anyway.

Vision evolved in water, in species that lived in the sea, or otherwise had eyes that contain water. Any wavelength of light that is absorbed by water would not penetrate the eye and therefore would be invisible. So vision evolved to avoid these wavelengths. Consequently water MUST be transparent as a requirement of the evolutionary process.

I never thought about it like that. Nice insight! Eyes and their photoreceptors wouldn't be so useful if their peak sensitives were at parts of the spectrum readily absorbed by water or even the eyes' own fluids.

That goes along with another nice thing that the peak power spectral density of sunlight falls within the visible range.

 

[sophiecentaur]

I asked "Has anyone wondered why water is perfectly clear". No one took my bait. Well I will give you my answer anyway.

I guess that one reason for our visible range of wavelengths is primarily based on the spectrum of the Sun's light and having a response that covers the black body spectral peak. The fact that water has an appropriate trough in its absorption spectrum is just 'good luck' on our part - mainly on account of the ability of plants to photosynthesise under a significant layer of water. It is another Goldilocks situation, if you like.
As you say, vision developed under water and the photochemistry of vision evolved around this window, just as with photosynthesis. But the absorption of water shows a sharp slope in our visual region (see this wiki link). Even at a depth of a few metres, the red is severely attenuated and colours become bluer and bluer. Our colour vision was evolved in an air environment, I think. This wiki article says that many fish have UV sensitivity in their colour vision- which would make sense, as there's so little red to be seen down there.

 

[Ygggdrasil]

Another reason why vision is confined to the near-IR to near-UV has to do with the fundamental chemistry behind vision. Recall that vision relies upon the absorption of light by a chromophore molecule. The amount of energy that it takes to excite the chromophore is on the order of a few 100 kJ/mol, which corresponds to the energy of photons in the visible range.

If we wanted to engineer an opsin to be sensitive to much lower frequencies, what energy would we want our chromophore to absorb? For example, if you wanted to detect radio frequencies (around 100 MHz), each photon would contain about 0.04 kJ/mol. Therefore, the energy required to excite the chromophore molecule would have to be about 0.04 kJ/mol.

Do you see the problem here? At human body temperature (37^oC, 310K), the amount of thermal energy available is about 2.6 kJ/mol. This means that thermal energy alone will be enough to activate our hypothetical radio-sensitive opsin! The protein would not actually be able to sense radio waves because it would always be on regardless of whether or not radio waves were present.

If you look at calculations like these, you'll see that it is not an accident that animal vision is limited to a small range of the EM spectrum ranging from the near IR to the near UV. At frequencies significantly below the visible region, you get to the point where thermal energy becomes more energetic than the photons and a chromophore would not be able to distinguish thermal energy from the absorption of photons. At frequencies significantly above the visible region, you get into the range of ionizing radiation – photons so energetic that their energies are comparable to the activation energies for breaking chemical bonds. Thus, photons in the far UV and above would destroy components of the cells meant to detect them.

 

[sophiecentaur]

At human body temperature (37oC, 310K), the amount of thermal energy available is about 2.6 kJ/mol. This means that thermal energy alone will be enough to activate our hypothetical radio-sensitive opsin! The protein would not actually be able to sense radio waves because it would always be on regardless of whether or not radio waves were present.

What you would have is effectively a receiver with a really lousy noise figure and you'd have to use a different system for detection. An electronic circuit could do it easily by operating with a narrow enough bandwidth - but that is not a QM based method.
Also, our bodies can cope with existing levels of UV and I should imagine that an alternative biological detection system could work. Again, there are electronic methods for UV imaging. I would suggest that the reason that animals do not use frequencies far outside the human visual range is likely to be that the illumination levels are so much lower. Where it is actually advantageous, some animals can see into IR and UV regions that we can't. We never evolve any characteristic that is not useful to us (or good value, energetically speaking). Lazy development can often correspond to good engineering. (But we would never do it that way because we don't think that way)

 

[collinsmark]

A bit of humor from today's Saturday Morning Breakfast Cereal.

 

[Eltahawy]

HUH? Frequency and wavelength are inverse properties. How can one change and not the other?

For a constant speed of light, but the speed of light changes at different materials

 

[phinds]

For a constant speed of light, but the speed of light changes at different materials

If you are going to respond to a post, be sure you read all of the relevant posts. The issue you are addressing was completely resolved in posts 6, 9, and 10 and you have simply repeated what was said there.

 

[evan-e-cent]

So do we now move onto the mechanism of infrared detection in snakes? Of course IR is still considerably higher energy than the radio waves we were discussing.

I also wonder whether this consideration of energetics has any relevance to the mass fear that radio frequencies could cause problems such as brain cancer in humans. If the energy level is so low it is masked by random thermal energy there probably isn't much chance that it would disrupt covalent bonds such as those in DNA. Ultraviolet light break bonds, and that is how it causes skin cancer. Cells have repair mechanisms to repair DNA damaged by UV light. But that is getting way off topic.

 

[evan-e-cent]

That goes along with another nice thing that the peak power spectral density of sunlight falls within the visible range.

The graph is interesting in that it shows visible light corresponding with the peak produced by the sun. But equally interesting that it does NOT correspond with the light we actually see on the surface of the Earth at sea level!