rtn. Science of Sunscreen - Atmospheric screening. In the last post discussing sources of ultraviolet radiation (UV) I discussed the expected “black body” curves according to Planck’s radiation law. We saw there that the UV component was relatively smaller than that due to visible light for a body with the surface temperature of our closet star (our sun). One can split the UV region into UV-A (315-400 nm), UV-B (280-315 nm) and UV-C(100-280 nm) where I indicate the respective wavelength ranges in brackets. The top figure shows a plot of energy from the sun per unit area per wavelength reaching different altitudes above earth. It turns out that the earth’s atmosphere acts as first important sunscreen. For example, go to altitude zero (surface) and follow the two curves (black and red) to top right. You see that curves start just after a wavelength of 290 nm. This means that on earth surface we have no UV-C to contend with (at this stage). This part of the UV spectrum powers the ozone (3 oxygen atoms joined)-oxygen cycle and is thereby expended. This also shows why the concern over the ozone hole was raised - over the hole region UV-C levels will be much higher. The red curve sloping up to right is flux expected should the ozone levels deplete by 10 %. Broad-spectrum sunscreens block UV-A and UV-B (the sun protection factor [SPF] is linked to blocking this B component). I will discuss this insightful plot further in the next post on this topic. Ref.: Wikipedia
Image source: Wikipedia Commons (NASA) [flux].
rtn. Science of Sunscreen - Source. I show some important actors in the story about understanding the source of radiation that is of concern here. From top left clockwise I show: Lord Rayleigh (1842-1919) 🇬🇧; Sir James Jeans 🇬🇧(1877-1946); Wilhelm Wien (1864-1928) 🇩🇪, and Max Planck (1858-1947) 🇩🇪. These scientists theorized/modeled and measured the electromagnetic radiation from matter with a certain temperature. Look now at the figure bottom right. This shows model predictions for the so called spectral radiance (energy radiated by a source per surface area per wavelength) for a so called “black body” at a temperature of 1000 kelvin (K) which corresponds to a temperature on the celsius scale of 1000 -273 = 727 deg C. It turns out that Rayleigh and Jeans got it wrong (this led to the so-called ultraviolet catastrophe because of the runaway spectral radiance in the UV region) and that the curves of Wien and Planck were closer to the experimentally observed curve. Planck in turn outdid Wien who had a more empirical approach. Planck introduced the idea of a quantum of energy (= hf, where h is the so called Planck constant and f is the frequency of electromagnetic wave). Planck’s radiation law can also be applied to the sun, our closest star. Our sun has a surface temperature close to 6000 K. Now look at the black body curves (Planck version) for bodies at various temperatures (bottom left). The green curve is close to the one for the sun. The curve is a plot of spectral energy density per wavelength. Now note that the wavelength range for ultraviolet radiation is 100-400 nm. It is clear that the peak spectral density occurs at wavelengths higher than for UV. In fact the peak region overlaps the visible (to humans) part of the electromagnetic spectrum. Nonetheless, UV still poses risks to life - more on this in future posts.
Image sources: Wikipedia Commons.
rtn. Science of Rings - thermal expansion. Another consideration in choosing a ring is the thermal expansion of the metal. Temperature is a measure of the mean energy of motion of atoms and molecules making up the ring metal. If the temperature in the environment increases (e.g. if you buy a ring in New York in December and arrive in Cape Town a few days later, the ring will experience a temperature change of about +30 degrees celsius) the average energy of motion of the constituent ring particles will increase. As a result of this extra energy the particles take up more space since the amplitude of their vibrations increases. Due to the large number of particles involved, this microscopic effect becomes discernible as an increase in the length dimensions of the ring (e.g. the diameter increases). This means the ring will fit more loosely. If you instead move to a colder environment the length dimensions contract, causing a tighter fit of the ring. I assume here negligible changes to the length dimensions of the finger. The expansion/contraction characteristics of metals can be quantified by means of the linear thermal expansion coefficient. I show these for common ring metals. The units are parts per million (ppm) [change in length dimension] per degree change in temperature. So for the New York-Cape Town scenario, a pure silver ring will be the most loose fitting (relative to other ring types, assuming all rings had the same initial diameter or inner circumference) on arrival in Cape Town. One lesson from this: when fitting a ring for purchase consider leaving some room for expansion and contraction and also consider the temperature changes (relative to when you do the fitting) that you are likely to experience (e.g. winter-summer). Data source: engineeringtoolbox.com.
rtn. Science of Rings - Titanium.
I plot densities for metals commonly used in rings. The units are g per cubic cm. I mainly used engineering toolbox.com to obtain the data. Please let me know of any inaccuracies. Density of a material is temperature dependent. This effect is ignored here. Now look for the metal with the lowest density. You will see it is titanium (Ti). Assume you want a ring of a certain volume. Of the metals shown, the ring of this volume made from Ti will be the lightest. Ti has the highest strength-to-density ratio of metals shown. Ti is also corrosion resistant (therefore good to wear in environments like pools and sea, and therefore of benefit to those with skin allergies - Ti is therefore hypoallergenic), biocompatible (non-toxic and not rejected by the body) [one reason why it is used for joint replacements and dental implants]. It is noteworthy that some 24 karat gold rings can contain up to 1 part per 100 Ti and still meet the karat criteria. I suppose, from above, that the alloy will be for example more dent resistant. Ti rings are also generally made from alloys. Two common alloys are classified as “commercial pure” (99.2 % pure Ti) and “aircraft grade” (90 % pure Ti). My ring shown top left is made from Ti, I hope “commercial pure” ! I will discuss testing ring elemental content in a future post. Of course metal costs also need to be considered. On this score titanium rings also do very well. See an upcoming post on ring costs. Main source: Wikipedia.