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Internat'l Law

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Abstract:

Using uranium isotope ratios in a representative DU sample as reported by the DoD, the alpha emissions of depleted uranium (DU) represent 57% of the alpha emissions observed from natural uranium (NU). However, this is only half of the story. Since any sample of DU or NU that is six months beyond the uranium purification process contains radioactive decay products that are emitting beta and gamma radiation, any comparison of radioactivity of DU relative to NU should take these additional emissions into account. When that is done, it is found that DU has 75% of the radioactivity found in NU. Thus statements that "DU is much less radioactive than NU" are deliberately misleading.

This article shows in detail the mathematical calculations used and the isotope concentrations assumed in order to arrive at the above conclusions. It also describes the effects that transuranic contamination (plutonium, amerecium and neptunium) might have on the inherent radioactivity of DU and evaluates the significant consequences that contamination with Np-235 would have on the environment and human health.

Introduction

In order to play down the radioactive nature of depleted uranium, government, industry and military spokespersons frequently state that DU is "40% less radioactive than natural uranium." This often leaves the desired impression that DU is less than half as radioactive as natural uranium, which is entirely false. The same statement could be phrased differently and with less ambiguity as follows: "DU still retains 60% of the radioactivity of natural uranium". This is the figure that most anti-DU activist use. Yet, as we shall see, even this figure does not accurately represent the total radiation released by DU.

Radioactive Decay Calculations

To see where the 60% figure comes from, a little simple math is required along with data on the isotopic composition of natural uranium and depleted uranium, which is given in Tables Ia and Ib.

Radioactive decay follows first-order reaction kinetics. That means that the rate of decay of a substance follows the rate law expressed by:

• kt = ln( a/(a-x) )	(Equation 1)
  

where "k" is the isotope's "decay rate constant", "a" is the amount of material at time zero and "(a-x)" is the amount of substance at time "t" after "x" amount of material has decayed.

Table Ia. Isotope Composition of Natural Uranium (NU)

Table Ib. Isotope Composition of Depleted Uranium (DU)

The rate constants given in Table Ia and Ib for each isotope can be calculated using Equation 1 by substituting the isotope's half-life for "t", the number "1" for "a" and the number "0.5" for "(a-x)" and solving for "k". This works because the amount of material remaining after one half-life is, of course, one-half of the amount you started with.

For example, for U-238, the calculation is:

• k t = ln ( a / (a-x) )
• k (4.51x109) = ln ( 1 / 0.5) = ln (2.0) = 0.6931
• k = 0.6931 / (4.51x109) = 1.54x10-10

Once the decay rate constants for all of the isotopes have been calculated, Equation 1 can then be used to calculate a value for "x", the amount of material that has undergone radioactive decay in a given time "t". For the calculations of interest in this paper, the starting amount for each isotope, "a" will be the amount present in 1 gram of NU or DU, which is calculated from the percent composition of these two materials and is given in column 4 of Tables Ia and Ib. To simplify calculations, the time period used in the equation will be 1 year, so "t" equals 1.0 .

For example, for U-238, the amount of U-238 that will have decayed in 1 year's time, "x", if we start with 0.993 gram of U-238 (the amount in 1 gram of NU) will be:

• k t = ln ( a / (a-x) )

(Note: You will need to use the anti-log "exp" function in a Microsoft Excel spreadsheet to solve this equation, as most calculators do not provide sufficient decimal places to handle the calculation.)

• exp (k t) = a / (a-x)                                                   ( Equation 2 )

• (a-x) = a / (exp (k t) )

• x = a - a / (exp (k t) ) = a ( 1 - 1/( exp (k t) )           (Equation 3)

• x = ( 0.993 grams) ( 1 - 1/(exp (1.54x10-10)))  = 1.53x10-10 grams

Finally, to convert this mass "m" to actual number of alpha decay events "N", we must know how many atoms "N" this represents. We use the isotope's mass weight "MW" (238 grams/mole for U-238) and Avogadro's number, A = 6.023x1023 atoms per mole:

• N = (A) (m) / (MW)                                                  ( Equation 4 )

N = ( 6.023x1023 ) (1.53x10-10 ) / (238) = 3.87x1011 alpha particles emitted from 0.993 grams of U-238 in 1 year's time.

Using this same sequence of math calculations for each of the remaining six entries in Tables Ia and Ib, you will obtain the results shown in Tables IIa and IIb.

Table IIa. Alpha Radioactive Emissions of Natural Uranium (NU).

Table IIb. Alpha Radioactive Emissions of Depleted Uranium (DU).

Now that we have figures for the total alpha emissions for both NU and DU, we can determine how much less alpha radiation is emitted by DU compared to NU:

• DU / NU = 4.66x1011 / 8.17x1011 = 0.57 = 57%          ( Equation 5 )
  

So DU gives off 57% of the alpha radiation observed for the same mass of NU. This is where the 60% figure comes from and how it is calculated.

Unfortunately, this figure is correct only the very instant that a pure sample of NU or DU has been produced in the factory or mill. The reason is that all of the uranium isotopes, as they give off alpha particles, produce radioactive decay products that immediately begin contaminating the pure uranium sample and undergoing radioactive decay themselves, giving off their own radioactive emissions. After a sample of NU or DU is six months old, the above figures are no longer correct. The decay products, called daughter isotopes, are giving off beta particles and gamma rays. These must be added to the alpha radiation calculated above, and this will result in a different percentage figure for the amount of radiation given off by DU as compared to NU.

The relevant daughter isotopes for each of the uranium isotopes listed above are shown in the following radioactive decay series. Th represents thorium; Pa represent protactinium. Read the "»»" symbol as "producing" or "yielding".

U-238 which emits alpha »»

	     Th-234 (half-life = 24.1 days) which emits beta + gamma »»

		  Pa-234 (half-life = 6.75 hours) which emits beta + gamma »»

			U-234 (half-life = 247,000 years).

U-236 which emits alpha »»

            Th-232 (half-life = 14 billion years)

U-235 which emits alpha + gamma »»

            Th-231 (half-life = 25.5 hours) which emits beta + gamma »»

                              Pa-231 (half-life = 32,500 years)

U-234 which emits alpha + gamma »»

            Th-230 (half-life = 80,000 years)

The complete radioactive decay series for each of these is much longer, but for practical purposes once the chain has hit an isotope with a very long half-life, any additional decay becomes insignificant (at least for the duration of our life times).

Due to the relatively short half-lives of Th-234, Pa-234, and Th-231, after a sample of uranium is about six-months old, the concentrations of these three isotopes reach a "steady state" in which one atom decays for every new atom formed. This means that for every alpha particle emitted by U-238, forming a Th-234 atom, a different Th-234 atom decays, giving off its beta and gamma radiation and forming a Pa-234 atom. But as soon as this Pa-234 atom is formed, a different Pa-234 atom decays, giving off its beta and gamma radiation and forming a U-234 atom. So for every alpha decay of U-238 there are four additional radiation events taking place as well. The number of alpha emissions for U-238 in Tables IIa and IIb must be multiplied by 5 to account for all of the radiation events taking place! Tables IIIa and IIIb list the multipliers for each isotope and show the totals for alpha, beta and gamma radiation produced by NU and DU.

Table IIIa. Total Radioactive Emissions of Natural Uranium (NU).

Table IIIb. Total Radioactive Emissions of Depleted Uranium (DU).

Now applying Equation 4 for the DU/NU ratio

• DU / NU = 21.04x1011 / 28.25x1011 = 0.75 = 75%                  ( Equation 5 )
  

Thus in terms of TOTAL RADIOACTIVE EMISSION, DU is 75% as radioactive as NU.

The Effects of Other Contaminants

The Department of Energy has admitted that the DU stockpiles contain radioactive waste from nuclear reactor cores and that plutonium, americium and neptunium are present in DU. This is also evidenced by the presence of U-236 which could only have come from reactor cores. The presence of these transuranic elements complicates the picture somewhat, but the same analysis can be used to determine the effects that these elements have on the total radioactivity of DU. All that needs to be known are the percentage amounts of these elements in a 1 gram sample of DU.

S. F. Boulyga of the Research Center Juelich in Juelich Germany reported [Journal of Analytical Atomic Spectroscopy Vol. 16(11), 2001 (pp. 1283-1289) ] finding Pu-239, Pu-240 and Am-241 in a sample taken from a DU penetrator shell. He reported 1.7x10-9 gram (1.7 nanograms) of Am-241 and 3.1x10-5 gram (31 micrograms) of U-236 in a 1 gram DU sample. This is 10 times the amount of U-236 reported by DoD and used in the above calculations (Table 1b).

For the sake of calculations, if you were to assume that the Pu-239 and Pu-240 each had the same concentration as the Am-241 in the sample, and to use Boulyga's experimentally determined concentration of U-236 in the above calculations, you would find that these changes only increase the percentages of DU radiation compared to NU radiation by about 1%.

However, once Neptunium enters the picture, the situation changes drastically. Neptunium 237, like plutonium and amerecium, does not appreciably change the percentages. But Neptunium 235, with a 410 day half-life, creates a big spike in radioactivity. Even at the extremely low concentration of 1.7 nanograms per gram of DU, Np-235 triples the alpha radiation over natural uranium and doubles the total alpha, beta and gamma radiation over natural uranium.

In light of these results, it is unfortunate that a careful isotopic analysis of the actual composition of DU penetrator shells has not been published that includes a full accounting of all of the transuranium isotopes present. If even small amounts of Np-235 are found to contaminate the DU used in manufacturing these weapons, the radiation impact on the environment and on human health is many times greater than currently assumed.

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Last Revised: 12/21/2004
Copyright 2003 by Dan Bishop, All Rights Reserved
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