The Physics
Opus in profectus


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nuclear models

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

proton πρῶτον "at first"

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.

Table of nuclides

isotopic ratios (isotopic signatures)


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.

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:

δD = 

2H  −  2H

2H  × 100
1H 1H 1H
    sample   V‑SMOW   V‑SMOW  

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 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."


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.



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.


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 by by 36Ar.

36Ar 38Ar 40Ar 36Ar:38Ar:40Ar
Earth 0.3336% 0.0629% 99.6035% 5.3:1:1583
Mars 0.92% 0.22% 98.86% 4.2:1:452
Jupiter 84.8% 15.2% none? 5.6:1:none?
Sun 84.6% 15.4% 10−4 5.5:1:10−5


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.