Isotopes

Discussion

nuclear models

This page is mostly just a pile of notes. There is very little prose here.

proton πρῶτον "at first"

• Shell model. Similar to chemistry — electrons in orbitals. Two sets of orbitals, however, one for protons, one for neutrons. Completely filled orbitals are stable. For a nucleus with an intermediate number of nucleons, one can ignore the nucleons in complete shells, but when the number of nucleons added to a complete shell is large, a different model is needed.
• Maria Goeppert-Mayer (1906–1972) Germany–USA, Hans Jensen (1907–1973) Germany
  • Magic numbers of protons and/or neutrons like the completed shells of chemistry: 2, 8, 20, 28, 50, 82, 126, and maybe others.
  • protons 2, 8, 20, 28, 50, 82, 114, 164, 210, 274, 354
  • neutrons 2, 8, 20, 28, 34 (new!), 50, 82, 126, 184, 228, 308, 406, 524, 644, 722
  • The latest predictions for the next shell closures are Z = 120, 124, or 126, and N = 184, or 172.
  • Similar to an electron's motion in an atom, nucleonic orbits bunch together forming shells, and nuclei having filled nucleonic shells (nuclear 'noble gases') are exceptionally stable. This happens for specific 'magic' numbers of protons (Z = 2, 8, 20, 28, 50 and 82) and neutrons (N = 2, 8, 20, 50, 82 and 126).
  • Doubly magic isotopes are rigidly spherical: ⁴He, ¹⁶O ⁴⁰Ca, ⁴⁸Ca, ⁴⁸Ni, ²⁰⁸Pb, ¹⁰⁰Sn, ¹³²Sn
• Liquid drop model (collective model). Used for heavy nuclei with a large number of nucleons in the outermost, incomplete shell. Nucleons are treated collectively, like the molecules in a drop of water. Density, charge distribution, and surface tension.
• Interacting boson model. Nucleons pair up. (Akito Arima and Francesco Iachello)

Even numbers of protons and even numbers of neutrons are most stable. There are no stable elements heavier than bismuth (Z = 83). Two elements below Z = 83 do not exist naturally. Surprise, surprise, they have odd atomic numbers.

• Technetium Tc (Z = 43)
  Italy 1937, Carlo Perrier & Emilio Segre
  Technetium is a man-made element. It is often used in medical research, and is produced in nuclear reactors. It is never found on Earth, but has been found in some stars.
• Promethium Pm (Z = 61)
  United States, 1945, J. A. Marinsky, Lawrence Glendenin & Charles D. United States
  Promethium is a radioactive rare-earth metal. It is often used in the nuclear gaging industry for measuring paper and thin plastics and coatings. Promethium salts glow blue/green in the dark. Promethium is not naturally occurring on Earth, it is made in nuclear reactors.

Isotopic ratios (Isotopic signatures)

oxygen-18/oxygen-16

Nearly all the oxygen on the Earth is of one particular isotope, ¹⁶O which makes up 99.76% of all the oxygen around us. The other two stable isotopes (¹⁸O and ¹⁷O) are found only in trace amounts (0.20% and 0.04% respectively). These abundances are stable in the lithosphere, but vary in the atmosphere.

"Oxygen is a unique tracer of the chemical and physical history of geological and extra-terrestrial material since it has three stable isotopes, (masses 16, 17 and 18), which are easily fractionated by numerous processes and it exists abundantly in gases (e.g. carbon dioxide, oxygen), liquids (primarily water) or solids (virtually all rock forming minerals). Measurement of the ratios of the three isotopes can therefore be used to interpret the physical processes experienced by the sample"

"Light water (water with ¹⁶O) evaporates more easily. The ¹⁸O/¹⁶O fraction will be smaller in the snow that falls on a glacier than it is in the ocean from which the water evaporated. As glaciers grows worldwide there is less and less ¹⁶O in the ocean, so the ¹⁸O/¹⁶O ratio of the ocean gets larger. And so does the d¹⁸O ratio. As the world's glaciers grow in volume ¹⁸O values become larger. The oxygen isotope record was recording the size of the ice sheets."

"Precipitation has a ratio of oxygen isotopes present. ¹⁸O is heavier and ¹⁶O is lighter. If the rain is cold it will have a higher ratio of ¹⁸O:¹⁶O and if it is warm the amount of ¹⁶O increases in the ratio. This is due to many mechanisms Look for papers by Dansgaard 1964 to elaborate on this. [Dansgaard, W. "Stable isotopes in precipitation." Tellus. 16 (1964): 436-468.]"

The ratio of ¹⁸O/¹⁶O changes by 700 ppm/°C of mean ocean temperature.

it is estimated that each 1 part per thousand change in δ18O represents roughly a 1.5–2 °C change in tropical sea surface temperatures (Veizer et al. 2000).

hydrogen-1/hydrogen-2 (hydrogen/deuterium)

Because isotopic fractions of the heavier oxygen-18 (¹⁸O) and deuterium (²H) in snowfall are temperature-dependent and a strong spatial correlation exists between the annual mean temperature and the mean isotopic fraction of ¹⁸O or ²H in precipitation, it is possible to derive temperature records from the records of those isotopes in ice cores.

Deuterium values are expressed as δD, which is defined as:

where (²H/¹H)_sample is the ratio of deuterium to ordinary hydrogen in sample corresponding to a particular datum, and (²H/¹H)_V-SMOW is the ratio of deuterium to ordinary hydrogen in Vienna Standard Mean Ocean Water (V-SMOW).

The deuterium content distribution is well documented over East Antarctica and over a large range of temperatures (−20° to −55° C); there is a linear relationship between the average annual surface temperature and the snow deuterium content. The slope of this δD/surface temperature relationship was found by Jouzel et al. (1993, 1996) and Petit et al. (1999) to be 9‰ per °C. Further details on the methodology are presented in Jouzel et al. (1987), Lorius et al. (1985), and Petit et al. (1999).

The record presented by Jouzel et al. (1987), based on data in a 2083-meter ice core from the Russian Vostok station in central east Antarctica, was the first such record to span a full glacial-interglacial cycle. Drilling continued at Vostok until January 1998, reaching a depth of 3623 m, and a corresponding time of ~420 kyr BP. More recently, a 740-kyr deuterium record has been extracted from an ice core taken at Dome C (EPICA Community Members, 2004). Deuterium fractions were determined in meltwater from 55-cm long sections of the ice core the surface down to the bottom of the core.

Heavy water is more readily condensed or deposited from vapor, causing its distribution to differ somewhat from ordinary, light water.

carbon-13/carbon-12

"Carbon atoms occur in three different masses, or isotopes. Unlike high-temperature processes in deep Earth, low- temperature, biological processes, such as photosynthesis, are sensitive to the differences in mass, and actively sort different carbon isotopes. Thus, the ratios of carbon isotopes in organic materials — plants, animals, and shells — vary, and also differ from those in the carbon dioxide of the atmosphere and the oceans."

• carbon fixation — (binding the gaseous CO₂ to dissolved compounds inside the plant
  the first step in photosynthesis — production of sugars (and other organic compounds) from water, CO₂, and sunlight
  • C3
    • CO₂ molecules incorporated into the three carbon molecule glycerate 3-phosphate. (The 3 refers to the place on the molecule where the phosphate is attached, not to the number of carbon atoms.) The enzyme used for this, rubisco, is the most common protein on the planet.
    • C3 plants lose about 25 to 50 percent of the energy they capture during photosynthesis to a process called photorespiration. In photorespiration, oxygen is fixed instead of carbon dioxide. (Photorespiration is an evolutionary relic. C3 plants evolved 500 or more million years ago when the atmosphere was higher in CO₂ and lower in oxygen.) The rate of this unwanted process is higher at higher temperatures.
    • Most plants use C3 carbon fixation.
    • ~95% of Earth's biomass?
    • C3 plants are noticeably deficient in heavy isotopes of carbon.
  • C4
    • CO₂ molecules incorporated into the four carbon compounds oxaloacetate and malate
    • A newer form of carbon fixation that arose 65 million years ago. C4 plants eliminate photorespiration by fixing CO₂ to a 4 carbon molecule in one cell and then passing this molecule on to another cell that is kept relatively oxygen free. "It is thought that the primary selective mechanism for the development of C4 photosynthesis is the low level of CO₂ that has prevailed during the last 50 to 60 million years." "C4 carbon fixation has evolved on several occasions in different groups of plants, so is an example of convergent evolution."
      • More efficient at carbon fixation than C3 at high temperatures. Thus C4 plants are typically found in the tropics.
      • C4 plants keep their stomata closed more than C3 plants. This reduces water loss due to transpiration. Thus C4 plants are typically found in savanna ecosystems.
      • C4 fixation uses two ATP while C3 uses only one. At colder temperatures, this higher energy cost is not offset by increased efficiency in fixing carbon. C4 plants cannot compete with C3 plants in cool, moist environments.
    • C4 carbon fixation has evolved on several occasions in different groups of plants, but is typically found in tropical grasses like maize, sorghum, amaranth, finger millet, fonio (a variety of crabgrass), sugarcane, switch grass. (Also found in poinsettia, and lambsquarter a.k.a. pigweed.) Note that the first five examples are cereal crops.
    • ~5% of Earth's biomass, <1% of plant species
    • C4 plants are still deficient in heavy isotopes of carbon, but less so than C3 plants; that is, C4 plants are richer in heavy carbon that C3 plants.
  • CAM (crassulacean acid metabolism)
    • CO₂ is converted to an inorganic acid (malate) during the night and released back into the plant as CO₂ during the day
    • Found in many families of plants, but typically found in arid plants like cacti and succulents, (also pineapple, which are bromeliads, and some orchids)
    • <1% of Earth's biomass? 3~4% of all plant species.

  "The different isotope ratios for the two kinds of plants propagate through the food chain, thus it is possible to determine if the principal diet of a human or an animal consists primarily of C3 plants (rice, wheat, soybeans, potatoes) or C4 plants (corn, corn-fed beef and chicken, synthetic products derived from corn) by isotope analysis of their flesh and bones. Similarly, marine fish contain more 13C than freshwater fish, with values approximating the C4 and C3 plants respectively."

  • Pollan, Michael. Omnivore's Dilemma. New York: Penguin, 2006.
    • "There are some 45,000 items in the average American supermarket and more than a quarter of them contain corn."
    • Of the 38 ingredients it takes to make a McNugget, there are at least 13 that are derived from corn. 45 different menu items at McDonald's are made from corn. [publisher's blurb]
    • "When you look at the isotope ratios, we Americans look like corn chips with legs." Todd Dawson
• marine vs. aquatic fish
• the Seuss effect — identifying carbon from fossil fuels, δ¹³C
  • The secular decrease in coral δ¹³C can be ascribed to the Seuss effect, which is due to uptake by the oceans of atmospheric CO₂ that has been progressively depleted in ¹³C by combustion of fossil fuels

sulfur-34/sulfur-32

Similarly, sulfur comes in two stable isotopes: sulfur 32 and sulfur 34. Sulfur eating bacteria prefer the slightly lighter sulfur 32. (It's easier to chemically pull the lighter isotope out of a molecule than the heavier.) The concentration of this isotope in their waste products is as much as 7 percent greater than it is in their food sources. When sulfur rich minerals are found in nature it can be determined if the sulfur came had a geologic or biologic origin by looking at the ratio of ³⁴S:³²S.

nitrogen-15/nitrogen-14

• herbivores vs. carnivores
• When an animal eats, it tends to excrete more of the lighter nitrogen 14, while the heavier nitrogen 15 accumulates in body tissues—becoming more concentrated with each rung up the food chain. As a result, carnivores tend to have much higher levels of nitrogen 15 than omnivores or herbivores.
• fish eaters have more nitrogen 15 in their bones than meat eaters
• however cats have nitrogen ratios similar to vegan humans since they process proteins more efficiently

boron-11/boron-10

δ¹¹B in biogenic carbonates as a proxy for paleo pH

"Boron is common in the ocean and in some plankton, such as the ubiquitous formanifera, take it up by accident while seeking carbon to build their shells. And, depending on how acidic the waters are [that is, how much CO₂ there is in the atmosphere], formanifera take up different proportions of the two available isotopes, boron 10 and boron 11. Measure the ratio between the two and you have the pH of the water in which the organism lived."

Boron-11 trifluoride is used in the semiconductor industry.

argon-36/argon-38/argon-40

The most abundant isotope of argon in the universe is ³⁶Ar (~85%), but is the most abundant isotope on Earth is ⁴⁰Ar (>99%). What's going on here?

Given enough time, Earth's atmosphere will leak away into space. Light elements like hydrogen and helium don't stick around for long. You'd have a hard time finding either one. Heavier molecules like nitrogen, oxygen, and carbon dioxide and heavier elements like argon, linger. Life keeps the atmosphere full of nitrogen, oxygen, and carbon dioxide to the best of its ability. Life doesn't need argon, so it is being replenished some other way. The sun and Jupiter are giants balls of gas. The sun is so hot that all this gas has ionized into plasma, but that doesn't affect the isotopic composition of these relatively heavy gases. Whatever argon they have in them is left over from the birth of the solar system.

Primordial argon in the Earth's atmosphere and even its crust is certainly long gone. The Earth doesn't have enough gravity to keep it down. Whatever's left of the primordial argon is buried in the mantle and deeper. Some of this gas does manage to seep out, however. If we look at the ratio of ³⁶Ar to ³⁸Ar for the Sun, Earth, and Jupiter, we get similar numbers. (See the table below.) These hints at a common origin for the three bodies in the solar system.

Earth's crust may be low in argon, but like a banana it's high in potassium (~3%). One particular isotope, ⁴⁰K, is unstable and decays into ⁴⁰Ar. This radiogenic argon leaks out from the Earth just like the primordial argon, but because potassium is so so common and the crust is nearer to the surface than the mantle is, the radiogenic ⁴⁰Ar is the dominant isotope in Earth's atmosphere (>99%). The sun and Jupiter are mostly hydrogen with a little bit of helium thrown in for fun. They don't contain much potassium as a fraction of their bloated masses. Not much potassium means not much ⁴⁰Ar.

Like Earth, Mars is solid. Like Earth and bananas, Mars is probably loaded with potassium. Like Earth, most of the argon in Mars' atmosphere is radiogenic ⁴⁰Ar. Unlike the other solar system bodies mentioned in this section, Mars is noticeably low in the lightest stable isotope of argon, ³⁶Ar. Mars has less gravity than Earth and no magnetic field to protect its atmosphere. As a result, Mars's atmosphere is leaking away into space much faster than Earth's. The lightest isotope always leaves the quickest, so bye bye ³⁶Ar.