Isotopes

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© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion

nuclear models

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

proton πρῶτον "at first"

• Shell model. Very 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. Magic numbers of protons and/or neutrons like the completed shells of chemistry: 2, 8, 20, 28, 50, 82, 126, and maybe 184.
• Liquid drop model (collective model). Used for very 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 gauging 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.

[magnify]

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 Daasgarad 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.

• 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:

  δD = {[(²H/¹H)_sample - (²H/¹H)_V-SMOW] (²H/¹H)_V-SMOW} X 1000

  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.

  http://cdiac.ornl.gov/trends/temp/domec/domec.html

  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 savannah 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, switchgrass. (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
• 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

• boron-11/boron-10

  "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-40

  Argon 36 is the most abundant isotope of argon in the universe, but argon 40 is the most abundant isotope on earth. What's up with that?

  Where does one typically find argon on earth? In the atmosphere. And what's the atmosphere exposed to? Why space. And where does the argon on the earth eventually all end up. In space -- the place with the biggest amount of space. And which isotopes get there first? Why the lightest ones, of course. And which are left behind on the crummy rotten old earth? Why the heaviest, of course.

  In the atmosphere of earth, the place where nearly all of our argon lies, argon 36 acccounts for 99.6% of all the argon around, but in space argon 40 makes up a whopping 84.2% of all the argon in all of creation.

Tracers

• beryllium 10

  "[S]unspot activity can be deduced from beryllium-10 traces in Greenland and Antarctic ice cores. The reasoning is as follows: more sunspots imply a more magnetically active sun which then more effectively repels the galactic cosmic rays, thus reducing their production of Be-10 atoms in the Earth's atmosphere. Be-10 atoms precipitate on Earth and can be traced in polar ice even after centuries. Using this approach, scientists … have reconstructed the sunspot count back to the year 850 …."

  "Beryllium 10 produced in the atmosphere by cosmic rays readily attaches to aerosols and gets snowed out onto ice caps, leaving a clear signal in the ice core of variations in the cosmic ray flux …. The decrease in Beryllium 10 since 1900 reflects the decrease in the cosmic ray flux over this period. The reason is that the solar magnetic flux has increased by almost a factor of 2 since 1900, for reasons that are not fully understood."

  Work done with beryllium-10 shows that the sun goes through prolonged period of anomalous behavior in addition to its regular, 11-year cycle.

Summary

• bullet

Problems

practice

1. Write something.
   • Answer it.
2. Write something.
   • Answer it.
3. Write something.
   • Answer it.
4. Write something completely different.
   • Answer it.

conceptual

1. God is in the gaps, as they say.
   The discussion highlighted the magic numbers for protons and neutrons (2, 8, 20, 28, 50, 82, 126), but it also mentioned a few gaps in the nuclides. Namely, there are no stable isotopes with mass number 5 or 8 (numbers that are important later when we study stellar nucleosynthesis) or atomic number 43 or 61 (technetium and promethium). Look closely at the graph of the nuclides and see if you can find any other interesting gaps. (Consider only elements with atomic numbers below lead Z = 82.)
   1. Are there any other atomic mass numbers with no stable isotopes (like 5 or 8)?
   2. What neutron numbers have no stable isotopes?
   3. What do all of these numbers share in common (or maybe, what do they almost all share in common)?
   4. Are there any apparently "non-magic numbers"

Resources

• general
  • ABCs of Nuclear Science, Nuclear Science Division, Lawrence Berkeley National Laboratory (LBNL)
  • Handbook of Isotopes in the Universe, Donald Clayton (2003)
  • Table of the Nuclides
    • Brookhaven National Laboratory
    • International Atomic Energy Agency
    • Korea Atomic Energy Research Institute
    • Los Alamos National Laboratory
• heavy hydrogen
  • Astrophysicists announce surprising discovery of extremely rare molecule in interstellar space (triply deuterated ammonia), Tom Phillips, Caltech Press Release, 29 May 2002.
  • Why is heavy water poisonous? Philip Carlson, PhysLink.com
• isotopic ratios
  • Aber, James S. Paleoclimate Reconstruction, Emporia State University
  • Center for Stable Isotope Biogeochemistry, University of California, Berkeley
  • Dansgaard, W. "Stable Isotopes in Precipitation." Tellus. 16 (1964): 436-468.
  • Dawson, Todd, et al. Stable Isotopes in Plant Ecology. Annual Review of Ecology and Systematics. Vol. 33: (November 2002): 507-559.
  • Omnivore's Dilemma, Michael Pollan (2006)
  • Park, R., and S. Epstein. "Metabolic fractionation of ¹³C and ¹²C in plants." Plant Physiology. 36 (1961): 380-384.
  • Urey, H.C. "The thermodynamic properties of isotopic substances." Journal of the Chemical Society. (1947): 562-581.

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