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Natural decay series and what a measurement sees

Natural decay series and what a measurement sees

Uranium and thorium are never alone. Each heads a chain of decays that ends at a stable isotope of lead, and in an undisturbed mineral every member of the chain is present at the same activity as its head. Almost every practical difficulty with natural radioactivity comes from the disturbances: a gas that escapes, an element that dissolves where its parent does not, a process that keeps one element and discards another. This note works through those disturbances with figures computed from the nuclide table, and it is explicit about the chain members that table does not carry.

Three chains

The principal path of each chain is listed below, with the members that have a page on this site linked. Several members branch — Bi-212 decays both by alpha and by beta, and Ac-227 and Bi-211 split in the same way — and only the main path is shown. Of the 36 members listed, 15 are carried in the table this site works from; the others are mostly short-lived, and their absence matters in specific places that are pointed out below.

K-40 is the fourth natural radionuclide that matters in practice, and it is not a chain: it decays in one step, mostly to calcium and partly to argon, and its 1461 keV photon, emitted in 10.7% of decays, is present in almost every gamma spectrum ever taken of a natural material.

Secular equilibrium and how it breaks

When a parent lives far longer than its daughters, each daughter's activity rises until it equals the parent's, and from then on the whole chain decays at the parent's pace. This is secular equilibrium, and the time to reach it is set by the daughter, not the parent: after about 3.32 of its own half-lives a daughter has reached nine-tenths of the parent's activity. In a rock that has sat undisturbed for a million years, every member of the uranium chain is in equilibrium with U-238, and a measurement of any one of them is a measurement of all.

Three things break it. Radon is a noble gas, and a fraction of the radon atoms formed in a mineral grain escapes into pore space and from there into the air; everything below radon is then deficient in the solid and in excess wherever the radon went. Chemistry separates elements that physics had kept together — uranium dissolves readily in oxidising water, thorium hardly at all, and radium follows barium and calcium into sulphate and carbonate precipitates. And processing separates them deliberately: a uranium mill keeps the uranium and sends thorium-230 and radium to the tailings; a refinery producing thorium compounds removes the radium.

The two long-lived breaks in the uranium chain

Two members of the uranium chain live long enough to hold the chain apart for a human timescale. Th-230 (75584 years) means that refined uranium remains, for practical purposes, without radium: a thousand years after refining, Th-230 has grown to 0.91% of the U-234 activity and Ra-226 to 0.172%. Pb-210 (22.20 years) divides the chain a second time. Where radon escaped and later decayed — on the inside of gas processing equipment, in atmospheric deposition, in sediments — Pb-210 is found without the radium that would normally support it; where radon is newly trapped, Pb-210 takes 74 years to reach nine-tenths of equilibrium.

Below Pb-210 the chain closes again quickly. In a freshly separated Pb-210 source, Po-210 — an alpha emitter with no photon line in this table — reaches 84% of the Pb-210 activity after one year and 99% after two, and Bi-210 between them is back in equilibrium within weeks. A Pb-210 source more than a couple of years old is therefore three emitters at nearly equal activity, and its total activity is close to three times the Pb-210 figure alone. A measurement of Pb-210 by its 46.5 keV photon, emitted in 4.25% of decays, says nothing directly about how much Po-210 is there.

Uranium measured through other nuclides

U-238 is difficult to see directly by gamma spectrometry. Its strongest recorded photon above 20 keV is at 49.5 keV and is emitted in only 0.064% of decays. The usual route is through its first two daughters, Th-234 and Pa-234m, which return to equilibrium with U-238 within a year of any chemical separation and whose photons are far more plentiful. Neither is carried in this table, so their energies and yields are not quoted here; a measurement laboratory takes them from an evaluated decay data source and states which.

The 186 keV doublet

The most-used peak in natural-uranium spectrometry is not one peak. U-235 emits a photon at 185.7 keV in 57.2% of its decays; Ra-226 emits one at 186.2 keV in 3.56% of its decays. The two energies are 0.5 keV apart, which a germanium detector does not resolve cleanly at that energy, so the peak area is the sum of both.

How the sum divides depends on the isotopic composition. Natural uranium is 0.7204% U-235 by atoms (CIAAW representative composition); with the half-lives in this table that makes the U-235 activity 4.6% of the U-238 activity. In a sample where Ra-226 is in equilibrium with U-238, U-235 therefore supplies 42% of the counts in the peak and Ra-226 the remaining 58%. The split holds only at equilibrium. A sample depleted in radium, or enriched in it, gives the same peak a different meaning, and the peak alone cannot say which. The usual remedies are to obtain U-235 from its other lines — at 143.8, 163.4, 205.3 keV in this table — or to measure Ra-226 through its short-lived progeny after the sample has been sealed for several weeks so that the radon it produces is retained and comes back into equilibrium.

The same composition data give a check on the equilibrium of uranium itself. Natural uranium is 0.0054% U-234 by atoms, and with the half-lives in this table that makes the U-234 activity 0.99 of the U-238 activity — equilibrium, as it should be for a member that is chemically the same element as its ancestor. Groundwater is the well-known exception, where U-234 is often found in excess: the alpha decay of U-238 recoils the daughter atom out of its lattice site, and the U-234 it becomes is more easily leached than the U-238 left behind.

Separated thorium dims, then recovers

Thorium chemicals behave unexpectedly over time. When thorium is purified, Th-232 and Th-228 come through together — both are thorium — but Ra-228 and Ra-224 are removed. Th-228 then decays with its own half-life of 1.9116 years while its supply, Ra-228, has to grow back from zero with a half-life of 5.75 years. Solving the chain with the half-lives in this table, and treating Ac-228, whose half-life is a matter of hours, as passing straight through:

Everything below Th-228 in the chain has a half-life of days or less, so the rest of the chain follows Th-228's curve within weeks. Ac-228, above Th-228, follows Ra-228 instead, and its activity rises from zero over the same years. The lower part of the chain includes Tl-208, which emits the most penetrating photon in any of the natural chains. The dose rate from a stock of thorium compound — thoriated welding electrodes, thorium nitrate, older optical glass — therefore depends on when the thorium was purified, and a measurement made a few years after manufacture can be a little under half of what the same material gives a few decades later.

Activity concentration in grams

The IAEA's General Safety Requirements Part 3 use 1 Bq/g for any member of the uranium or thorium chains, and 10 Bq/g for K-40, as the activity concentrations above which an industrial activity involving natural material is brought under the requirements for planned exposure situations. Translating those figures into composition shows what kind of material they catch.

Computed from the specific activities in this table with CIAAW standard atomic weights and isotopic abundances (K-40 at 0.0117% of potassium atoms).

The materials that do exceed the uranium and thorium figures are a familiar list: scale and sludge from oil and gas production, in which radium co-precipitates with barium sulphate; phosphate rock and some of the gypsum produced from it; zircon and monazite sands; filter media from water treatment that removes uranium or radium; and some residues from metal smelting and coal combustion. In each the concentration was raised by a process, which is also why the chain in those materials is rarely in equilibrium.

What the calculators here do with a chain

Every calculator on this site works on one nuclide at a time. The page for Ra-226 gives the air kerma rate constant for Ra-226's own photons, and those are weak; the photon field of an aged, sealed radium source comes mostly from Pb-214 and Bi-214, which are not in the table. That page says so, and the full list of such cases is on the limits of this dataset page. The decay calculator also takes one nuclide at a time. The curves in this note were computed with the Bateman solution in the same engine, at build time, for members whose half-lives are in the table and along one branch; the form itself does not build chains.

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