For years, my wife and I have had lots of alcohol around the house that we haven’t drunk. A few months ago, I realized that very small amounts make an excellent solvent to wash off the writing from our calendar. But yesterday I came up with an even better idea.
On Friday she brought home a digital colorimeter that can be attached via USB to a laptop, or it could transmit data with Bluetooth to an app on a phone or tablet.
I started with a brown-colored German liqueur (35% alcohol)
Using successive dilutions with water, I prepared, from the original, three other standard solutions of 17.5%, 8.75% and 2.19% alcohol. I also made a 4.38% solution that we used later as our unknown.
We calibrated the instrument with a blank (water) and then used the 35% solution to find the optimum wavelength. Out of the 4 choices, a 565 nm wavelength gave us the best results, which looked like the following:
By interpolating (see black line), the absorbance reading of 0.11 for the “unknown” corresponded to an alcohol concentration of 4.47%, only off by 0.09% (a 2 percent experimental error) from the 4.38 that it was supposed to be.
When you try different wavelengths with the colorimeter, you are reminded that absorbance has to be near the range of 0.2 to 0.5 to get a linear relationship. The alcohol solution works well because it is homogenous, free of turbidity, and it does not chemically react in the presence of light. Other factors are taken care of by the instrument itself—it comes with identical cuvettes, which provide the same path length for the light trying to get through. For example the same colored solution will look darker in a wider glass. Also, the light beamed through is also approximately monochromatic, that is of a single frequency, which ensures that the Beer-Lambert Law will hold.
If you can think of better things to do with alcohol than colorimetry experiments( after all, it’s a good fire-starter; good for calorimetry experiments and good fuel for an alcohol cannon) you can use the beautiful blue copper-ammonia complex. The intensity of the blue will be proportional to the concentration of copper ions, and can be used to determine the concentration of Cu2+ in an unknown. These concentrations work well:
The procedure from which I took the table mentions the use of a spectrophotometer, but I am willing to bet that it would work with the Vernier probe or its equivalent.
This November morning, like the previous three, was atypically warm for eastern Canada. I stepped out early to look at the sky, and I noticed two stars very close to the moon. Often, moonlight bleaches out stars in proximity of its boundaries, unless there is a lunar eclipse, which wasn’t the case. So they must have been bright stars.
When I consulted the software Stellarium, I realized the moon was sitting on the lion’s shoulder(constellation Leo), and the two visible stars, which were closer to the moon than the chart below suggests, were Algieba and Regulus. Interestingly each star is really a binary system. If, in each case, you consider the apparent magnitude of the brighter member of the binary, we get 2.08 and 1.35 for Algieba and Regulus, respectively. Among the 10 000 stars that are visible to the naked eye in ideal conditions, they rank as 51st and 22nd brightest. (On the scale, the lower the number is, the brighter the star.)
How bright stars seem to us depends on their intrinsic brightness and on their distance from Earth. Both Algieba and Regulus are close enough for their distance to be determined by parallax. For stars close to the Earth, this was possible even before measurements relied on the very sensitive WFC3 of the Hubble space telescope or ESA’s Gaia. With these we can now obtain much smaller angle differences ( 10 to 40 microarc seconds) and come up with more accurate values for distance and also measure distances for stars as distant as 10 000 light ears away. The parallax technique is based on the idea that your finger seems to move against the background of the room when viewed from either the left or right eye. That movement decreases as you move your finger farther away from you. Replace the finger with the star whose distance you want to measure, and let the two different viewpoints be the earth at opposite ends of its movement around the sun. From the angle created by the different positions(see figure 1), the width of the Earth’s orbit and basic trigonometry, one can then calculate the distances.
Algieba and Regulus are 125.64 and 79.3 light years away, and as is the case for any two non-equidistant stars, by looking at them and the moon, we look at different pasts simultaneously. We see Algieba the way it was 125 years ago before the airplane was invented; the way Regulus was 79 years ago when Franklin Delano Roosevelt made his Four Freedoms speech. But of course the moon’s image that comes to us is only about 1.3 seconds old.
The formula M = m – 5 log[ d/10 ] can give us a star’s absolute magnitude(M) or intrinsic brightness from its apparent magnitude (m) and distance(d) in parsecs (light years divided by 3.26) And it turns out that Algieba(- 0.85) is more intrinsically bright than Rigel (- 0.58).
The intrinsic brightness depends on both the star’s surface area and temperature. If we could indirectly measure temperature, not only would we be able to calculate the area and therefore the star’s radius, but we would have enough data to infer something about where the star is standing in its evolution.
To understand why, let’s sidestep with a bit of chemistry. When zinc oxide (ZnO) is added to burning methanol in the above video, we see blue emissions along with sparks and beautiful flashes of red and green. Why? To what energy level ZnO’s electrons get promoted and then descend again depends on the temperature of the flame. ZnO leads to red emissions between 568 to 704 °C degrees, but the compound emits green light between 704 to 948 °C. You could get a more detailed and characteristic record of those transmissions by looking at the emitted light with a spectroscope. In the 1860s Angelo Secchi, an Italian astronomer attached a spectroscope to a telescope and he noticed that stars could be grouped according to their spectra.
Although the mechanism was not understood at the time, the idea is similar to what happens to the zinc oxide, except that the star’s surface is more or less at one specific temperature. Depending on the temperature, only certain ion and/or neutral atoms in its atmosphere will “peak” because their emissions will only occur at that temperature. For example in Figure 2, if we would see lines from magnesium +1 (astronomers strangely represent this as Mg II because Mg I is reserved for neutral magnesium), silicon +1 (Si II) and hydrogen (H), the spectral type would be AO and the star’s surface temperature, according to the graph would be at about 10 000 K. That almost describes the brighter member of Regulus’ spectrum, except that it also has a bit of neutral helium(He) emissions, classifying Regulus as B8, which matches a temperature of about 12 500 K, much higher than our sun’s 5800K. On the other hand, Algieba is cooler than our sun because in its spectrum iron (Fe I) and calcium +1 (Ca II) dominate, and its K1 classification corresponds to a surface temperature of only about 4500 K.
And now comes the most interesting part. With both the temperature and luminosity we can refer to the Hertzprung-Russell diagram ( Figure 3)
If we look at the (spectral class, absolute magnitude) coordinate of Regulus(B8, -0.58), we notice that it lies on the graph’s main diagonal of main sequence stars. Main sequence stars, like about 90% of stars in the universe, are busy fusing hydrogen into helium. But Regulus is at the upper left hand side of the diagonal, which means that it will leave the main sequence sooner than most other stars. It will run out of hydrogen fuel at its core because although it has more fuel than a star like our sun and is thus more massive, that extra mass creates a higher core temperature. That dramatically increases the rate at which the hydrogen is fused into helium. Roughly speaking, a star’s time spent on the main sequence is inversely proportional to its mass raised to the power of 2.5.
Algieba’s coordinates (K1, -0.85) place it among the island of orange-red stars that are no longer on the main sequence. These are the red giants. Without hydrogen at the core, they lose radiative pressure to counter the gravitational attraction of mass at the core. But this compression increases the temperature and ignites hydrogen fusion in a shell surrounding the stellar core. This makes the whole star swell up, while the outer shell remains cooler, leading to its characteristic reddish color.
We started with a simple observation about stars in close vicinity of the moon that were not bleached by its light, and it led us to peel some of the layers of astronomical knowledge.