Roman lead and modern physics

Researchers looking for dark matter signals like to use Roman lead, in particular the lead found in old Roman shipwrecks, which has caused tension between physicists and archaeologists. The reason Roman lead is valuable is that Roman lead is less radioactive than recently mined lead. Lead is primarily used in particle physics experiments as a shielding agent, in that it prevents outside particles from entering a detector and giving false signals. If the lead is radioactive though, the decay of the lead itself will generate noise in the detector. Mined lead is partly made of \(^{210}Pb\), which has a half-life of 22.2 years. If Roman lead was mined 1713 years ago, what is the ratio of the amount of \(^{210}Pb\) in the Roman lead now versus when it was mined?

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