[Illustration: Graph: Number of coins at indicated ratios vs.
Copper/gold ratio]
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.