Economics Dynamics Problems 66

Economics Dynamics Problems 66 - 50 Economic Dynamics It is...

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50 Economic Dynamics It is possible to estimate λ l 0 for an authentic painting. It is also possible to estimate λ l 0 for the lead in the painting under investigation. If the latter is absurdly large rel- ative to the former, then we can conclude that it is a forgery. A very conservative estimate would indicate that any value for λ l 0 in excess of 30,000 disintegra- tions per minute per gram of white lead is absurd for an authentic painting aged 300years.Using22yearsforthehalf-lifeoflead-210,thenthevalueof λ is(ln2 / 22) and e 300 λ = e (300 / 22) ln 2 = 2 (150 / 11) To estimate the present disintegration rate of lead-210 the disintegration rate of polonium-210 is used instead because it has the same disintegration rate as lead- 210 and because it is easier to measure. In order, then, to authenticate the ‘Disciples at Emmaus’, purported to be a Vermeer, it is established that the disintegration rate of polonium-210 per minute per gram of white lead in this particular painting is 8.5 and that of radium-226 is 0.8.
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