In a Museum
The Problem
You are a curator working with the ancient coin collection of a large museum. A donor has just given the museum a group of 50 gold coins presumably about 1500 years old. After months of careful study, you have satisfied yourself that most of those coins are genuine specimens of that period. Judging from your experience, you decide that a small group of five are definite forgeries.
However, there are three others that you suspect are also fakes, but you are not quite certain. You know that both genuine minters and forgers often tried to save money by diluting their gold with less expensive metals such as silver and copper. Since the chances are slim that the forger’s product has the same concentration of gold, silver, and copper as the genuine coins, you realize that a chemical analysis would help you decide if the doubtful pieces were real or fake.
An accurate chemical analysis would require a sample of such size that the coin would be ruined as a museum specimen. You need an analytical method that can be applied to an infinitesimal sample.
The Solution
You are not a scientist but you’ve heard about neutron activation analysis. Therefore, you contact a radiochemist at a local university who is an expert in this field.
He decides to use a sampling technique developed by scientists at Brookhaven National Laboratory for sampling metal objects of archaeological interest. You obtain from him a set of 50 quartz plates that have been ground on one side. Following his instructions, you carefully scrape away a small area on the edge of each coin. You then rub each freshly cleaned area across the ground surface of one plate leaving a minute streak of metal similar to a pencil mark.
At the scientist’s laboratory, each plate is carefully placed inside a quartz tube. No attempt is made to weigh the tiny streak of metal since you wish only to compare the ratios of the metal concentrations. However, because the samples make a rather bulky package, the scientist is concerned with the uniformity of the neutron flux that each sample will “see”. He therefore also places in each tube an exactly equal weight of a gold—silver—copper alloy wire (of known proportions) to act as a standard neutron-flux monitor. The tubes are then sealed and taken to a reactor to be irradiated for 12 hours.
After the samples are removed from the reactor, the scientist carefully breaks open each of the quartz tubes and places the sample and the standard piece of wire in separate numbered plastic capsules with lids. For an accurate comparison, each capsule is prepared in the same manner. About 4 hours after the samples are removed from the reactor, he begins the radioactivity measurements.
The sample capsules are loaded into an automatic sample-changing mechanism that places each one into an identical position above a lithium-drifted germanium detector. (See the chapter beginning on [page 19].) Gamma-ray spectra are collected all day, first from a sample, then from its accompanying standard. Each count takes 2 minutes, and 3 minutes are required between counts for data printout and sample changing. A typical gamma-ray spectrum looks like the one in the [figure on the next page]. Notice that only gold (gold-198) and copper (copper-64) show up in this short counting time. Later on, radioactivity from silver (silver-110m) can be measured using a longer counting time. This can be done because while the activation products from copper and gold have relatively short half-lives (12.8 hours and 2.7 days, respectively), that from silver has a half-life of 270 days. To increase the sensitivity of the analysis for silver, the scientist repackages and re-irradiates the samples and wires for 100 hours. Silver-110m is one of two radioactive isotopes of silver that have the same mass. In this case, one has a higher energy than the other and decays in a different way. This is known as an isomeric state and it occurs for many other elements as well as for silver.
The spectrum obtained from a streak of metal on a quartz plate after a 3-hour exposure to neutrons in a reactor and a 6-hour delay before counting. The activation products of gold and copper are obviously present and are easily measured in only 1 minute.
The spectrum obtained from the same streak of metal after re-exposure to neutrons for 100 hours and a delay of approximately 2 months before counting. Activation products from gold and copper have decayed away and the gamma-ray spectrum of silver-110m is now observed. In this case the sample is closer to the detector than for the earlier measurement and the measurement takes 100 minutes.
Two months later, the scientist repeats the procedure of counting the samples and standards, except that this time the plastic capsules are closer to the detector, each count is for 100 minutes, and the sample changer operates for about a week. A typical spectrum looks like that in the [figure on page 39].
The scientist can now compute ratios for the three elements in each sample and compare them with the standard, but he decides that a computer could do it faster and with fewer errors. The data collected during the two series of counts are therefore sent to a data processing center where, in a matter of minutes, a computer does the following for each of 50 samples:
1. Finds the 0.411-MeV gamma-ray peak for gold-198.
2. Determines the total counts in the peak.
3. Repeats the process for the corresponding wire standard.
4. Corrects the total count for the wire for the small amount of radioactive decay that occurred in the few minutes between the sample count and the standard count.
5. Computes the ratio: [total count for sample/total count for standard (corrected)]
6. Repeats all the above for the 0.511-MeV gamma ray for copper-64 and (in the longer counts) for the 0.658-MeV gamma ray for silver-110.
7. Computes the ratios: [sample to standard (for copper)/sample to standard (for gold)] and [sample to standard (for silver)/sample to standard (for gold)].
8. Tabulates and prints the ratios found in Step 7.
Radioactivity ratios for 50 “gold” coins. Above are the silver to gold ratios. There are two groups of genuine coins. Five known forgeries show considerably higher ratios than the genuine coins. Two of the suspect coins also show high ratios but the third, suspect A, shows a ratio that falls into one of the genuine groups. Below are the copper to gold ratios. Again there are two groups of genuine coins. (The same coins make up the two groups here as above.) The five known forgeries again show higher ratios than the genuine ones and again the same two suspects appear to be forgeries. Suspect A, however, shows a ratio similar to one group of the genuine specimens. One therefore concludes that suspect A is genuine and that B and C are not.
For example, suppose for sample 1 there are 20,000 counts in the 0.412-MeV peak (gold), 190 counts in the 0.511-MeV peak (copper), and 450 counts in the 0.654-MeV peak (silver). Suppose also that standard 1 yielded 10,000, 500, and 400 counts for these three peaks (corrected for decay), respectively. Then the ratio for gold would be (20,000/10,000) = 2.00, the ratio for copper would be (190/500) = 0.380, and the ratio for silver would be (450/400) = 1.13.
Finally, the activity ratio of copper to gold would be (0.380/2.00) = 0.190, and the activity ratio of silver to gold would be (1.13/2.00) = 0.565.
Because each sample was irradiated with an identical standard, and counted in an identical arrangement, the last two ratios will be the same for different samples if, and only if, the concentrations of gold, silver, and copper in those samples are in identical proportions. This will be true no matter where in the reactor or for how long the irradiation took place.
Now the scientist presents the data to you. You immediately see that (a) the good coins fall into two groups, one with a silver to gold activity ratio of approximately 0.56 and a copper to gold ratio of approximately 0.20 and a second group with these ratios approximately 0.51 and 0.18; (b) the coins you were certain were forgeries have distinctly higher ratios ranging from 0.60 to 0.65 for silver to gold and from 0.23 to 0.30 for copper to gold; and (c) of the three suspected coins, two have ratios that fall into the range of the known forgeries, but one, with ratios of 0.552 and 0.198, is probably genuine.
You present the result to the museum director in the form of a graph (see the [figure on page 41]) and a few weeks later, 43 coins are added to the permanent exhibits of the museum, while 7 are discarded.