Radium and Forgeries

This is a painting called The Supper at Emmaus. Its subject is the story in the 24th chapter of Luke's gospel, and the story of the painting is itself quite a tale.

It was discovered from obscurity in 1937 by the Dutch painter Hans van Meegeren, and it was acclaimed by experts as a heretofore unknown masterpiece of the legendary 17th century painter Johannes Vermeer. Soon other previous unknown Vermeers began to surface thanks to his efforts. During the occupation by the Nazis, van Meegeren sold some of the paintings to the loathsome Hermann Göring for the equivalent of millions of dollars. After the war, the Dutch were understandably upset about this act of cultural betrayal and van Meegeren was put on trial for his crime. The penalty would have been severe, but van Meegeren dropped a bombshell:

He had not actually sold any Vermeer paintings, he claimed. He had forged all of the paintings, leaving Göring holding a fake rather than an actual cultural treasure. The penalty for such fraud was much less steep, and the authorities were skeptical. Nonetheless, close examination combined with a virtuoso demonstration by van Meegeren demonstrated the truth of the forgery beyond a reasonable doubt. He was convicted of fraud and given a light sentence. Sadly for him, he died of unrelated heart issues just before he began his sentence.

So where's the physics? Both Vermeer and van Meegeren used lead-based paints, which contain radioactive thorium-230. This decays into radium-226, which decays into lead-210, which decays into the stable lead-206. (There's a boatload of other short-lived decay products, but their short lives mean their concentrations are very small at any given time.) When refined, the radium is mostly removed from the lead ore. Now hold that thought for a moment.

The rate at which the number of lead-210 atoms in the paint changes is determined by the rate at which the decaying radium-226 turns into lead-210, minus the rate at which the lead-210 itself changes into lead-206. Mathematically:

The half-life of the radium-226 is about 1600 years and the half-life of the lead-10 is about 22.6 years. It's possible to use these values and integrate the equations precisely, but in this case it's not necessary. It suffices to know that since the paint starts of with almost no radium due to the refining process, almost all of the radioactivity of the sample will be characteristic of the lead-210. Since the first term of the equation above is initially pretty much zero due to the lack of radium, the radioactivity of the lead will decrease due to time as it radiates itself into inert lead-206. Meanwhile the radioactivity due to radium will increase as the thorium decaus into radium, increasing the radium's concentration.

Lead and radium radioactivity can be distinguished easily, and by comparing the ratios in the alleged forgeries to the ratios in verifiable Vermeers it's possible to distinguish them. For reasons of clarity the experiment actually measured the quantity (1 - (Ra/Po)), where Ra is the measured radiation from the radon and Po is the measured radiation from polonium, whose concentration closely tracks that of the lead-210. For the genuine paintings, the values of that quantity are in the .90-.99 range. For the fakes, the values are in the ~0.1 range. This conclusively demonstrates that Vermeer could not have painted the picture above.

This technique was not actually among the ones used during the trial, as it wasn't available at the time. Van Meegeren's innocence (well, lesser guilt) was argued on other evidence and his own demonstrated skill. Nonetheless, some questions remained until this technique was brought to bear on the subject. Good job, science!

[This story appears as a problem in a number of physics texts, but I actually first heard of it in an old Paul Harvey "Rest of the Story" book, of all places.]