IChO 1998 · Theory problem 2

Dating historical events using Pb-210; separation of radionuclides for nuclear medicine

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Part A: Dating Historical Events Using Pb-210

Nathan Thompson, one of the first inhabitants of Lord Howe Island, decided to plant some European deciduous trees in his garden. Unfortunately the exact timing of the planting of the seeds is not known. Over the years, pollen produced by the European oak and elm accumulated at the bottom of the lake near Nathan’s house. Very small quantities of radioactive Pb-210 (half-life = 22.0 years) were deposited at the same time. Note that the European oak and elm trees pollinate in their first year of growth.

In 1995, a team of researchers sampled a sediment core from the bottom of the lake. The sediment core was cut into 1 cm slices and examined for pollen and radioactive Pb-210.

The examination of the sediment core found that:

  • Pollen of European oak and elm first occur at a depth of 50 cm.
  • The activity of Pb-210 at the top of the sediment core is 356 Bq/kg and at 50 cm depth 1.40 Bq/kg.

2.1 In what year did Nathan Thompson plant the seeds?

Radioactive Pb-210 is one of the daughters of U-238. U-238 is present in the earth’s crust and for some reason a certain amount of Pb-210 rains out of the atmosphere and attaches itself to sediment particles that accumulate at the bottom of lakes.

  • The U-238 decay chain is:
Figure 1

* Very short half-lives: minutes and days

2.2 Which step in the decay scheme explains how Pb-210 ends up in rainwater while its parent U-238 is only present in the earth’s crust?

Part B: Separation of Radionuclides for Nuclear Medicine Applications.

The Ga-67 is used to image lymphoma. It is preferentially produced by bombarding a target enriched in Zn-68 (> 98%) with high energy protons for 11 hrs. Zn-68 has a natural abundance of 18.8%. Due to the target design other radionuclides may be produced (see Table 1). Twelve hours after the end of bombardment, Ga-67 is bound on a cation exchange. Then the other radionuclides and the Zn-68 are eluted in the wash solution leaving Ga-67 bound to the column.

Table 1

Radionuclide Half-life
Co-55 18.2 hr
Ni-57 36.0 hr
Co-57(daughter of Ni-57) 270 days
Cu-64 12.7 hr
Cu-67 61.7 hr
Zn-65 244 days
Ga-67 78.35 hr
Ga-66 9.4 hr

Cu-64 and Co-55 have ideal half-lives for use in nuclear medicine applications and it would be useful to isolate them from the wash solution.

The distribution coefficient \(D\) is a measure of the partition of a metal ion between the ion-exchange resin and the eluant.

For a given ion-exchange resin and eluant, \(D\) is given by

\[ D= \frac{\text{radioactivity per mg of resin}} {\text{radioactivity per }\mathrm{cm^3}\text{ of eluant}} \]

For a reasonable separation of two metal ions their \(D\) values should differ by at least 10 units.

2.3 The wash solution is evaporated to dryness and the residue resuspended in a small amount of 0.2 M \(\ce{HCl}\) 96 % methanol and loaded onto an anion exchange column. Use the distribution coefficients \(D\) given in Figures 1 and 2 and rank the best solvent systems (from given alternatives) for eluting Cu-64 and Co-55.

2.4 Having isolated relevant radionuclides, the presence of some long-lived radionuclides could interfere with medical use of Cu-64 or Co-55 or Ga-67. Indicate which of the following statements is either true or false (one or more may be true).

a) Ni-57 may be present as a contaminant of Co-55.

b) Co-57 will interfere with the medical use of Co-55.

c) Cu-67 will interfere with the medical use of Cu-64.

d) Ga-66 will interfere with the use of Ga-67.

e) Ga-67 will interfere with the medical use of Cu-64.

2.5 If radionuclide contamination of Cu-64 or Co-55 or Ga-67 occurred, which method would reduce the amount of radionuclide contaminant/s? Indicate which of the following statements is either true or false. ( one or more may be true).

a) Remove Ni-57 before isolating Co-55.

b) Separate the Ni-57 from the bombarded target material before isolating the Ga-67.

c) Separate the radionuclides closer to the end of bombardment.

d) Allow the Ni-57 to decay before isolation of Co-55.

2.6 If zinc of natural isotopic abundance, instead of enriched Zn-68, was bombarded with high energy protons, indicate which of the following statements is either true or false. (one or more may be true).

a) Ga-67 would be produced at 5 fold higher yields.

b) Ga-67 would be produced at 5 fold lower yields.

c) Ga-67 would be produced at lower yields and contamination of Cu-64, Co-55, Co-57, Ni-57 would increase.

d) Ga-67 would be produced at lower yields and contamination of Cu-64, Co-55, Co-57, Ni-57 would remain the same.

Figure 2

Figure 1. Distribution coefficients, \(D\) of metal ions between anion exchange resin and 96 % methanol at varying \(\ce{HCl}\) concentrations. (note \(D\) value for \(\ce{Zn}\) > 1000)

Figure 3

Figure 2. Distribution coefficients, \(D\) of metal ions between anion exchange resin and 55 % isopropyl alcohol at varying \(\ce{HCl}\) concentrations.

Official English text of the problem.

Answers

  • 2.1: Approximately 1819.
  • 2.2: The formation of gaseous radon-222 by alpha decay of radium-226. Radon escapes into the atmosphere, where its decay produces the precursors of Pb-210.
  • 2.3: A suitable elution sequence is: remove Ni-57 using the loading solvent; elute Co-55 with approximately 2 M \(\ce{HCl}\) in 55% isopropyl alcohol; then elute Cu-64 with approximately 1 M \(\ce{HCl}\) in 55% isopropyl alcohol. Approximately 0.01 M \(\ce{HCl}\) in 96% methanol is another suitable cobalt eluent.
  • 2.4: a) False; b) True; c) True; d) False; e) False. Here d) concerns the stated problem of long-lived contamination.
  • 2.5: a) True; b) True; c) True; d) False.
  • 2.6: a) False; b) True, approximately; c) False; d) True, interpreting contamination as the absolute production of contaminants arising from unchanged target construction.

Solution

2.1 — Dating the first pollen

The dating calculation assumes that the sediment originally had the same Pb-210 activity per unit mass as newly deposited surface sediment, and that subsequent activity loss was caused by radioactive decay.

For activity per unit mass \(a\),

\[ a(t)=a_0\,2^{-t/t_{1/2}}. \]

Therefore,

\[ \begin{aligned} t &=\frac{t_{1/2}}{\ln 2}\ln\!\left(\frac{a_0}{a(t)}\right)\\ &=\frac{22.0\ \mathrm{yr}}{\ln 2} \ln\!\left( \frac{356\ \mathrm{Bq\,kg^{-1}}} {1.40\ \mathrm{Bq\,kg^{-1}}} \right)\\ &=175.8\ \mathrm{yr} \approx176\ \mathrm{yr}. \end{aligned} \]

Thus the first pollen was deposited approximately in

\[ 1995-175.8=1819.2. \]

Since the trees pollinate during their first year of growth, the planting year was approximately 1819.

2.2 — Transport from the crust into the atmosphere

The crucial step is

\[ \ce{^{226}_{88}Ra -> ^{222}_{86}Rn + ^{4}_{2}He}. \]

Both mass number and nuclear charge are conserved:

\[ 226=222+4,\qquad 88=86+2. \]

Radon-222, atomic SMILES [222Rn], is a noble gas and can escape from rocks and soil into the atmosphere. Its subsequent radioactive descendants ultimately produce Pb-210. These non-gaseous products attach to atmospheric particles and are carried down by rain.

The emitted alpha particle is a helium-4 nucleus, \(\ce{^{4}He^{2+}}\), SMILES [4He+2]; the equation above uses conventional nuclear notation.

2.3 — Choosing the eluents

A large \(D\) means strong retention on the resin; a small \(D\) favours passage into the eluant. A useful eluent therefore gives the desired metal a relatively small \(D\), while maintaining a difference of at least 10 from metals that must remain on the column.

From the stated definition, \(D\) has units of \(\mathrm{cm^3\,mg^{-1}}\). The following values are approximate graph readings.

Stage Solvent system Relevant \(D\) values Result
Load and wash 0.2 M \(\ce{HCl}\), 96% methanol Ni: no adsorption; Co: about 50; Cu: about 100; Zn: \(>1000\) Ni-57 passes through while Co, Cu and Zn remain retained.
Collect cobalt About 2 M \(\ce{HCl}\), 55% isopropyl alcohol Co: about 2; Cu: about 30; Zn: several hundred Co-55 elutes while Cu and Zn remain more strongly retained.
Collect copper About 1 M \(\ce{HCl}\), 55% isopropyl alcohol Cu: about 6; Zn: about 500 Cu-64 elutes after cobalt has been removed; Zn remains strongly retained.

For the cobalt separation at approximately 2 M acid,

\[ D_{\mathrm{Cu}}-D_{\mathrm{Co}}\approx30-2=28>10. \]

For the subsequent copper–zinc separation,

\[ D_{\mathrm{Zn}}-D_{\mathrm{Cu}}\approx500-6\gg10. \]

Removing nickel during the initial wash is essential: in the isopropyl alcohol system its \(D\) is only 0.1–0.8, so it would accompany a weakly retained cobalt fraction if left on the column.

Figure 1 also supplies a viable cobalt eluent: at approximately 0.01 M \(\ce{HCl}\) in 96% methanol,

\[ D_{\mathrm{Co}}\approx8,\qquad D_{\mathrm{Cu}}\approx60, \]

giving a difference of approximately 52. Cobalt is more strongly retained under this condition than under the proposed isopropyl alcohol condition, but the separation criterion is satisfied.

The solvent components are:

  • Hydrogen chloride, \(\ce{HCl}\), SMILES Cl, used to provide the stated acid concentration.
  • Methanol, \(\ce{CH3OH}\), SMILES CO.
  • Propan-2-ol, or isopropyl alcohol, \(\ce{CH3CH(OH)CH3}\), SMILES CC(O)C.

The relevant metal-ion identities are listed below. These SMILES identify isotope and formal ion charge; the graphs do not specify the actual coordination structures or geometries of the adsorbed species.

Metal-ion names SMILES
Copper-64(II); copper-67(II) [64Cu+2]; [67Cu+2]
Cobalt-55(II); cobalt-57(II) [55Co+2]; [57Co+2]
Nickel-57(II) [57Ni+2]
Zinc-65(II); zinc-68(II) [65Zn+2]; [68Zn+2]
Gallium-66(III); gallium-67(III) [66Ga+3]; [67Ga+3]

2.4 — Identifying the interfering radionuclides

Ordinary ion-exchange chromatography separates different elements through their chemical behaviour. It does not usefully separate isotopes of the same element.

Statement Answer Reason
a) Ni-57 may contaminate Co-55. False Under the stated separation conditions, nickel is removed during loading and washing because it is not adsorbed in the methanol system.
b) Co-57 interferes with Co-55. True Both are cobalt isotopes and accompany one another chemically. Co-57 has a half-life of 270 days, much longer than the 18.2 h half-life of Co-55.
c) Cu-67 interferes with Cu-64. True Both are copper isotopes and accompany one another chemically. Cu-67 has a longer half-life: 61.7 h versus 12.7 h.
d) Ga-66 interferes with Ga-67. False, in the stated long-lived-contaminant sense Ga-66 has a half-life of only 9.4 h, compared with 78.35 h for Ga-67. Its contribution decreases preferentially during storage.
e) Ga-67 interferes with Cu-64. False Gallium has already been retained on the first cation-exchange column, while copper enters the wash solution.

For d), the relative activity follows

\[ \frac{a_{66}(t)}{a_{67}(t)} = \frac{a_{66}(0)}{a_{67}(0)} 2^{-t\left( \frac{1}{9.4\ \mathrm h}-\frac{1}{78.35\ \mathrm h} \right)}. \]

After 12 h this ratio is approximately \(0.459\) times its initial value. An initially present Ga-66 impurity can still matter before sufficient decay; it is not the persistent, long-lived impurity described in the question.

2.5 — Reducing contamination

Ni-57 produces Co-57 as it decays. Once formed, Co-57 accompanies Co-55 through chemical separation. Removing the nickel parent early prevents further production of this inseparable cobalt impurity.

Statement Answer Reason
a) Remove Ni-57 before isolating Co-55. True Removing the parent prevents further Co-57 production in material that will supply the cobalt fraction. It cannot remove Co-57 already formed.
b) Remove Ni-57 from the target material before isolating Ga-67. True Earlier nickel removal reduces the time available for Co-57 formation before the subsequent cobalt separation.
c) Separate closer to the end of bombardment. True Less Co-57 forms before separation, and more of the short-lived desired radionuclides survives.
d) Allow Ni-57 to decay before isolating Co-55. False Waiting converts Ni-57 into the problematic Co-57 daughter while Co-55 itself continues to decay.

For example, during the stated 12 h delay, the fraction of Ni-57 that decays is

\[ 1-2^{-12/36.0}=0.206, \]

or about 20.6%. Because Co-57 has a 270-day half-life, almost all daughter atoms formed during this short interval remain present.

The benefit of earlier separation in c) concerns daughter formation and preservation of useful activity. It is not a claim that every impurity benefits from earlier use: short-lived Ga-66 is reduced by allowing it to decay.

2.6 — Replacing enriched zinc with natural zinc

The principal intended production reaction is

\[ \ce{^{68}_{30}Zn + ^{1}_{1}H -> ^{67}_{31}Ga + 2 ^{1}_{0}n}. \]

Mass number and nuclear charge balance:

\[ 68+1=67+2,\qquad30+1=31. \]

For the same number of zinc atoms and the same irradiation conditions, the contribution from this reaction is proportional to the Zn-68 abundance. Using 98% as the approximate enriched abundance,

\[ \frac{Y_{\mathrm{natural}}}{Y_{\mathrm{enriched}}} \approx \frac{18.8}{98} =0.192. \]

Thus the natural-zinc yield is approximately one-fifth of the enriched-zinc yield:

\[ \frac{Y_{\mathrm{enriched}}}{Y_{\mathrm{natural}}} \approx5.21. \]

Accordingly:

Statement Answer Reason
a) Fivefold higher Ga-67 yield. False Natural zinc contains substantially less Zn-68.
b) Fivefold lower Ga-67 yield. True, approximately The abundance estimate gives a reduction by a factor of about 5.2.
c) Lower Ga-67 yield and increased Cu, Co and Ni contaminant production. False, under the intended target-construction assumption Changing zinc enrichment does not increase the amount of the other target materials responsible for these contaminants.
d) Lower Ga-67 yield and unchanged Cu, Co and Ni contaminant production. True, under the same assumption Their absolute production remains approximately unchanged when target construction and irradiation are unchanged.

The distinction is between absolute contaminant production and contamination relative to Ga-67. If contaminant activity remains constant while Ga-67 production falls to about 19%, the contaminant-to-Ga-67 activity ratio increases by about a factor of 5.2.

The solution was checked against the official solution.