What Flowers Do With Light

What does a flower do with light? In a nutshell, some of the light that reaches a flower’s petals is absorbed; some is transmitted through its anatomy and the rest is reflected towards the sky and towards the eyes of pollinators and admirers. But from such a summary, a number of questions can germinate.

How does light get absorbed in flowers?

To attract a variety of pollinators flowers contain pigments, which are compounds whose valence electrons can be excited and “promoted” by wavelengths of visible light. Strictly speaking, colour is characterised by the frequency of photons, not wavelength. The higher the frequency, the more energetic the photon is. But if the medium of comparison (air in our case with flowers) is constant, we can also consistently associate colour with wavelength, keeping in mind that longer wavelengths are associated with less energetic photons.

A pigment’s  molecular structure affects the separation in energy levels for electrons. If the gap is narrow, electrons can be more easily excited and “jump” to a higher level by absorbing longer wavelengths of the spectrum. But how exactly does a specific structure facilitate a jump?

The gap between pi bonding orbitals, π,  (formed from constructive interference of their wavelike characteristics) and pi antibonding orbitals, π*, (from destructive interference) decreases as the number of combining pi orbitals increases. This occurs with more conjugation of double bonds. from http://butane.chem.uiuc.edu

In the above diagram we start with ethylene (C₂H₄), a molecule that acts as a hormone for some ripening fruits. Ethylene has no colour because, with a single C=C bond, the energy gap is too large for any wavelength of visible spectrum to be absorbed. No removal implies no leftover (reflected) wavelengths for organisms to perceive. If a molecule features a single bond in between a pair of double bonds ( a so called conjugated system), the energy gap shrinks.

lycopene

Eventually, if enough alternating double bonds appear, the energy-gaps will be small enough and the molecule will have colour; it will be a pigment.

A variety of Calendula officinalis, a type of marigold whose petals contain a wealth of carotenoids including 5 different carotenes and 4 different lycopenes

One such pigment is lycopene, a reddish compound often associated with tomatoes but which is in fact a fairly common natural product that’s also found in a variety of flower petals such as those of orange marigolds. Of lycopene’s 13 C=C bonds, 11 are conjugated, allowing it to absorb in the longer wavelengths of the visible range, specifically with absorption-peaks at 443 (blue), 471(turquoise)and 502 nm (green). Since the electrons’ transitions remove those colors from white light, we see what’s left over: the reddish end of the spectrum.

So we know the story for a particular molecule. What about the absorption and reflection in the whole flower?

The bluish starflower absorbs in the ultraviolet range, and it also absorbs heavily in the green to red region, reflecting hues of violet to turquoise. What’s unexpected is that only shorter wavelengths of red are absorbed. Longer wavelengths of red are reflected even more than those of the blue region. So in essence we are perceiving an overall composition without realising it.

A starflower’s response to light. Also taken from How to colour a flower: on the optical principles of flower coloration, but I added labels for clarity’s sake.

Wavelengths absorbed, reflected and transmitted by the compounds of a white hibiscus. The arrows on the x axis provide the approximate range of wavelengths associated with each main colour.

A white hibiscus absorbs some violet and indigo, leaving 5 other spectral colours and their hues to reflect and mix, and we see white. What’s also interesting is that, as pointed out in this recent study (May 2016), all white flowers reflect very little ultraviolet. But as we shall see shortly, pigments don’t tell the entire story behind the hibiscus’ color.

Why isn’t pigmentation the only factor affecting reflection?

As pointed out by the botanists who authored the study I mentioned, the petal’s thickness and the flower’s heterogeneous interior also influence what we see. This can at times involve iridescence. In iridescence, the pigment is not the cause of selective reflection. The physical structure can cause specific wavelengths to interfere constructively or destructively. This happens in the layers of soap bubbles, butterflies and also in the coloured base of the otherwise white petals of Hibiscus trionum.  Its patch appears blue, green, and yellow depending on the angle from which it is viewed. It’s attributed to cuticular striations(see B in diagram) that appear only over the coloured parts. When in an experiment, epoxy was used to replicate the structures(C), white light produced a variety of colours.

from http://aob.oxfordjournals.org/content/105/4/505/F3.expansion.html

How much light does a flower transmit and reflect compared to what it absorbs, and why?

Given the variety of interiors and the host of pigments found across different species of flowers, the proportions of reflected and transmitted light are actually similar. This may seem surprising.  But it’s understandable when we recall that all showy flowers co-evolve with organisms who help spread their pollen. The biochemistry and anatomy of flowers has to be adjusted to pollinators’ visual systems so they could respond to the flowers’ cues and be of service to them. It’s a function that serves them well because of the nectar or spare pollen they offer. Humans are further rewarded with the flowers’ beauty.

Other Sources:

• Absorbing Light with Organic Molecules

http://butane.chem.uiuc.edu/pshapley/GenChem2/B2/1.html

• Three Routes to Orange Petal Color via Carotenoid Components in 9 Compositae Species  

https://www.jstage.jst.go.jp/article/jjshs/76/3/76_3_250/_pdf

• Visible Spectrum of Lycopene

Click to access LycopeneSpectrum.pdf

• Wavelength versus Color

http://pages.cs.wisc.edu/~yetkin/code/wavelength_to_rgb/wavelength.html

• Floral Iridescence, Produced by Diffractive Optics, Acts As a Cue for Animal Pollinators

http://science.sciencemag.org/content/323/5910/130.full

• Structural colour and iridescence in plants: the poorly studied relations of pigment colour 

http://aob.oxfordjournals.org/content/105/4/505/F3.expansion.html

Probability In Unexpected Places

When I was young my Mom would say that you often find things when you’re not looking for them. It took me longer than it should have to realise that the truism is based on probability. We typically look for a lost item only briefly after we’ve lost it. Or occasionally we decide to look for objects that someone else may have lost in the sand. But for those of us who are not professional treasure hunters, we spend most of our days preoccupied with other goals. Yet for the bulk of the time when we are not actively seeking, our eyes are still open to the possibility of finding something. So it’s more probable that we stumble upon a lost item when we have time on our side.

Few of us think of everyday things mathematically and out of the few who do, fewer still apply the often non-intuitive formulas of probability. How many of us would guess that in baseball,  a 0.350 hitter (someone who gets a hit in 35% of his at bats) is more than twice as likely to get 3 hits out of 4 at bats when compared to a player who only hits 0.250? To calculate each probability we have to first get the possible combinations of outs and hits in 4 at bats which amounts to dividing the permutations (4 X 3 X 2) by the number of permutations per combination(3 X 2 X 1). This yields 4.  In turn that number has to be multiplied by the probability of getting a hit raised to the power of hits and also multiplied by the probability of not getting a hit, raised by the difference between at bats and hits. A mouthful indeed!

For the 0.350 hitter,  P(x) = (4  X  3 X 2)/(3 X 2 X 1)*0.350³ * 0.650¹ = 0.111, but for the 0.250 hitter, P(x) = (4  X  3 X 2)/(3 X 2 X 1)*0.250³ * 0.750¹ = 0.0469. Since 0.111/0.0469 =2.38, the 0.350 hitter is more than twice as likely to go 3 for 4 in a game.

DJ LeMahieu, one of only two MLB players to hit close to 0.350 in 2016 (he hit 0.348), had 69 four-at-bat games in the 146 games he played. He went ¾, 8.7 % of the time . His teammate Gerardo Parra who hit 0.253 did it only in 2 of 52 four-at-bat-games, or 3.8% of the time. The ratio was 2.26 for the two players , very close to the theoretical expectation of 2.27.

As we move from the Newtonian level of large bats making contact with baseballs to the sublime level of quantum mechanics, we still encounter probability. Why for instance is atomic nitrogen’s electron configuration  like the one indicated with the green tick mark?

Why aren’t the first two electrons at the 2p level paired up in the same orbital? In the first setup, repulsion among electrons in a single orbital is avoided. But in the actual configuration something else is going on as well.  As such, each electron can exchange places with any of the two other electrons since all three have the same spin, so we have a total of 6 permutations.

The incorrect setup would imply that the lone electron could only exchange with one other electron from the filled orbital since only one of those would have the same spin. The multiple possibilities of the first scenario— the one following the first of so-called Hund’s rules—stabilise the atom and is the one actually found in nature. (For a more rigorous treatment and to see how Hund’s first rule does not always apply to molecules, consult this review paper.)

A simpler example of probability at work in the realm of chemistry occurs when a drop of vegetable colouring is added to a glass of undisturbed water. The molecules of dye are in constant motion. Those within the drop are more likely to collide with themselves than with water. But eventually, those self-collisions will lead molecules away from the pack and towards the edge of the drop. There, they will be closer to moving water molecules.  Collisions with water will divert the dye towards areas where there are more water molecules than dye, increasing the probability that subsequent encounters will be with other molecules of the universal solvent. Since that original drop represented just one small zone out of the total volume of solution, it becomes extremely unlikely that the dye will reconvene to its point of origin. (Unless of course we evaporate the water!)

So without stirring, the dye will spread uniformly and dissolve thanks to the heat in the environment that powers their motion, and thanks of course to probability.