Monday, March 11, 2013

Living with Chemicals: Betacarotene

The Chemical (Systematic name): 1,3,3-Trimethyl-2-[3,7,12,16-tetramethyl-18-(2,6,6-trimethylcyclohex-1-en-1-yl)octadeca-1,3,5,7,9,11,13,15,17-nonaen-1-yl]cyclohex-1-ene
You probably know it as: Betacarotene
The structure:

File:Beta-Carotin.svg


In the next few blog entries for "living with chemicals" I'm going to be focusing on some of the amazing chemicals that make sight possible. We're going to start with the chemical betacarotene, which you've probably heard helps you see better at night. You may have even been told that eating carrots helps you see better at night because of the high betacarotene content.

While it is true that betacarotene is necessary for night vision (it's converted to Vitamin A which is converted to retinal which is necessary for sight), it won't help you see better at night unless you have a real deficiency. However, as is true with many myths, the story behind the myth is more interesting than the myth itself. During WWII, the Britain's Royal Air Force developed a new radar system (the Airborne Interception Radar). This gave them a huge advantage for shooting down Nazi planes. So, to keep the Nazi's from realizing they had a new tool they spread the rumor that their soldiers ate lots of carrots to help them see better in the dark.

And it worked so well that people believe it to this day!

Betacarotene is also interesting because it's a really long molecule. There are 22 conjugated carbon-carbon bonds (the alternating single and double bonds you see along the chain). This actually means that betacarotene is good evidence that quantum mechanics is a valid theory (that may sound like a leap, but let me explain). Some of the most simplistic models of electrons describe them as orbiting around a single atom. That may make sense, but it's wrong. In systems like betacarotene the electrons actually move freely down the entire chain. In fact, they exist as a wave that exists everywhere along the chain at the same time. We can model the electron system using the energy level diagram below:



Only two electrons can occupy each level, so in total 11 energy levels are filled. As the energy level gets higher the space between levels gets smaller and smaller. When light interacts with this system an electron is promoted from the n = 11 level to the n = 12 level. But this can't happen when just any light comes along, it must be light whose energy is equal to the spacing between the two levels - which turns out to be ~480 nm, a nice blue color. So that's why carrots are orange, they reflect orange light and absorb blue light. But we can still learn something cool if we model the system as a particle in a box. The energy of the particle in a box levels can be calculated by:

E = {n^2}\frac{{{h^2}}}{{8m{L^2}}}

Where n is the energy level, h is the Plank constant, m is the mass of the electron, and L is the length. The difference between level 11 and level twelve is:

\Delta E = {E_{12}} - {E_{11}} = \left( {{{12}^2} - {{11}^2}} \right)\frac{{{h^2}}}{{8m{L^2}}}

Which can be rearranged so that we can calculate the length of the chain in betacarotene:

L = \sqrt {\left( {{{12}^2} - {{11}^2}} \right)\frac{{{h^2}}}{{8m\Delta E}}}  = 1.89{\rm{ nm}}

Which is a pretty good answer for the length of that long chain in betacarotene, especially since we used a very simple model to get the answer. So next time you bite into a carrot, take a look at its nice orange color and remember that without quantum mechanics it wouldn't be orange at all.