UV-vis made simple: all about beer

The basis of most spectrophotometry is the concept in figure 1: when one inputs energy into a molecular bond, it becomes excited.

To make this easier to visualize; we can assume molecular bond as a spring. The two balls connected by the spring are molecules, such as hydrogen, or any kind of molecule really; for ease of explanation, let’s call these balls and spring a system.  Generally speaking, since room temperature (or any temperature above 0 K, or absolute zero) will always give the system energy bigger than 0 (through heat; since heat is basically a kinetic energy on the molecular level, we can talk about this more if you want.), the balls and spring will always contract and expand. If energy is put into the system, it’s as if we’re pulling the two balls apart even more, therefore increasing the frequency of contraction and expansion; just like every spring we can see in life. How do we put energy into the system? In the case of Spectrophotometry, it’s most likely some kind of light, whether it’s UV + Visible light (UV-Vis Spec), Infra red (IR-Spec), or (if I’m not mistaken) a wide range, or continuum of wavelength (Atomic Absorption Spec).

To make things a little easier, in figure 2 the increase in energy is represented in energy level diagram; The Y-axis represents Energy level.  To go from E1 à E2, one has to put in energy. The difference between E1 and E2 is ΔE. In the case for all spectrophotometry, ΔE is always bigger than 0; that is to say that energy will always shift upwards, or in other words, excitation always happen. Since the energy source in spectophotometry  is almost always light, we can represent  ΔE as: ΔE = hv. ΔE = hv is the equation that relates energy to the frequency of the light; h in this case is a constant called the plank’s constant, while v is the frequency of light. But we never express light in terms of frequency you said? Correct!. We express light in terms of wavelength (nanometers; nm). To relate frequency to wavelength there’s a simple equation: v = c/λ, where c is the speed of light (3x108m/s), and λ is the wavelength. All of these equations are hard to memorize you say? Again, correct. Though E = hv is a very commonly used equation, remembering v = c/ λ can be hard. The trick is, since the unit for v (frequency) is 1/sec, and c is m/sec, and wavelength is m (or nm), in order to get 1/sec, c (m/sec) has to be the nominator (the one on the top), while wavelength (m) has to be the denominator (the one on the bottom). I hope that helps a little.  Another idea is the idea that different molecular bonds require very different specific wavelength to excite. Why? Think back to the energy level diagram; different structure excitation have a very specific energy level gap, that is the energy required to excite a specific structure is, again, very specific. And if we need a specific energy, according to E = hv, we need a specific frequency. If we need a specific frequency, according to v = c/ λ, we require a very specific wavelength; this is why different molecules require different wavelength to excite, such as 260 nm to excite DNA.

Now enough of this mumbo jumbo about excitation and the planck dude, let’s move on to actual spectrophotometry.

UV-Vis: all about beer

As one of the most widely used tool, not to mention the simplicity, and versatility (works for DNA, Proteins, etc2..), UV-Vis is a very very important tool to understand. It will be a little disappointing to know, however that after going through a page of that long mumbo jumbo on energy, molecular bonds, and frequency, in UV-Vis, none of those matter too much; the idea behind UV-Vis can be summarized in figure 3. In accordance with the excitation we talked about above, when we shine light (in this case, UV and visible wavelength) towards molecules (such as DNA, or protein), the molecules will absorb the light (energy) and got excited  to a higher energy level. Say we shine light into a solution of DNA (using 260 nm wavelength), the molecules will absorb the light (energy), and in the process goes up in energy level. Now the harsh reality; we do not care about how much the energy goes up (ΔE), though we can fairly easily calculate it. All we care about is how much light is absorbed, since that is synonymous to how much DNA there is to absorb the light. How do we express or quantify light? By using intensity. Simply speaking, intensity measures how much photon are hitting a surface area at a given time, A.K.A, don’t worry about it, just think of intensity as how much light there is. Since we care about how much light is absorbed, we want to know if there is any difference between the initial intensity, and the final intensity. Sadly, because the difference in this intensity can range from 0 to a huuuuge number, it is hard to express it as a difference (ΔI), we therefore express it in terms of absorbance. As in figure 3, absorbance is expressed in terms of logs of division (taking the log of a division between to numbers), this makes it easier to express numerically. Notice that since the initial intensity (Io) is always bigger or equal to the final intensity (If) (since the minimum final intensity happens when nothing absorbs the light, therefore is equal to the initial intensity), the ratio between the two (Io/If) is always bigger than 1.  Therefore, absorbance is always bigger than log of 1, or always bigger than 0; it means that the lowest absorbance is always 0 and never negative; see? Expressing it in terms of absorbance makes it a lot easier! A good practice: IF the absorbance is 0.1, what is the ratio between Io and If? Does it mean that the solution contain (approximately) a lot of a particular molecule? What if the absorbance is 2? What percentage of the initial intensity is absorbed in each case (when A = 0.1 and A = 2)?

Now that we know what absorbance is, how do we use it??? Now comes the two drunken master by the name Beer and lambert; they came up with beer-lambert law. Simply speaking, beer lambert law is just a way to figure out the concentration of a molecule in a solution if the absorbance is known. Beer lamber law is: A = e l c; where A is absorbance, e has a lot of names but one of them is extinction coefficient (some call them the molar absorbtivity), l is cell (tube) length, and c is concentration in Molars. But if we want to measure the concentration, not only do we have to measure the absorbance, but we also have to know the extinction coefficient for the particular molecule (remember that every molecule is different!). Thankfully, the extinction coefficient is calculated empirically, or through experiment; we can find the extinction coefficient for many molecules used in research in a lot of manuals, internet, and the memories of good professors. Say we are measuring the concentration of a DNA solution, using a cell with 1 cm thickness. By asking our good ol’ professor, we find out that the extinction coefficient for DNA is 0.030 (μg/ml)-1 cm-1.  Now we can simply take around 1.1 ml of the solution, pipette it into the cell, and take the reading. We found out that the absorbance is 0.5. Can we calculate the molarity? Hell yea. In fact, the professor is nice enough to give us an extinction coefficient that is already in μg, so we don’t have to calculate the mass of the DNA from the molarity (which can be very very very very hard, unless we use approximation). Isn’t UV-Vis nice?

As we see, UV-Vis cares not about the Energy absorbed (though, technically the energy corresponds to the wavelength, but we can find the list of wavelength for most molecules, again, in books and the interwebz), it cares only about the intensity. Heck, most UV-Vis now don’t even tell us the intensity anymore, they just display the absorbance, and makes the process a lot quicker. Even Heck-er, some UV-Vis can just calculate the concentration by us telling it the extinction coefficient, so that we don’t have to do anything anymore. But still, the science behind the equipment is fun AND informative, so why not learn it? Not to mention it’s easy too.

Now UV-Vis goes deeper than this, but that’s for another day. There’s the fact that UV-Vis is additive (we can just add the absorbance to get the concentration, since it’s linear) and the optical rotation spectrophotometry, which is basically just UV-Vis but uses an extra concept. For now though, I think we can safely say that we are UV-Vis Wizards now.