“Well, think of a series of lakes connected by waterfalls. At the top, the highest lake has an enormous supply of water. Following the waterfall coming out of the lake you find a smaller lake and then maybe a medium-sized lake, and after another waterfall, a smaller lake, then a tiny lake, and so on.
“As long as that big lake on top is full or nearly full, all the other lakes, whether they are small or medium-sized, will still be getting water as fast as it pours out. But if you cut off the supply of water from the upper lake to the next lake, then the smaller lakes will in time run dry. The same thing works with the radioactivity. In this series headed by uranium, as long as uranium is present all the other elements below it are kept supplied so that they don’t run out.”
“I understand that,” said Bill, “but how do we use that to date a painting?”
“One of the pigments used by artists for over 2000 years is known as lead white and it is made from lead metal. The lead metal in turn is extracted from a rock called lead ore, in a process called smelting. The radioactive lead, this lead-210 that I mentioned, behaves like ordinary lead metal and goes along with it.
“The radium, which has a fairly long half-life, doesn’t follow the lead metal, but is removed with other waste products in a material called slag. Since the longer-lived ancestor of the lead-210 is removed, the supply of lead-210 is cut off. (Or we can say that one of the waterfalls is shut off.) The lead-210 will then decay with its 22-year half-life.”
The radioactive series that starts with uranium is like a series of lakes connected by waterfalls. As long as uranium, the big one on top, has water in it, the others will be full and the falls will keep flowing. But when the first waterfall is shut off, the small lakes below it will run dry.
“I get it,” said Bill. “That means that when you take a sample of old lead white paint, there shouldn’t be any radioactive lead-210 left.”
“That’s right. But that would only be true if you removed all the radium. Actually, in the smelting process it’s more usual to remove only 90 or 95% of the radium. In that case, the lead-210 would decay only until the amount left would be equal to the small amount of radium that wasn’t removed. In effect, this would be like shutting off only part of the waterfall.”
“So what do you find,” asked Harley, “if you measure the radioactivity in a sample of lead white paint?”