放射性测年Radiometric dating

若样品形成时子体为零且之后为封闭体系，年龄 t = (1/λ)·ln(1 + D/P)，D 和 P 分别为子体和母体原子数。选用的核素半衰期应与待测年龄相当：碳-14（5730 年）适合 5 万年以内的有机物；钾-氩（12.5 亿年）适合火山岩；铀-铅（²³⁸U 44.7 亿年、²³⁵U 7.04 亿年）适合最古老的岩石。等时线法可在初始子体含量未知时同时求出年龄和初始比值。

If a sample began with no daughter and stayed a closed system, its age is t = (1/λ)·ln(1 + D/P), where D and P are daughter and parent atoms. The half-life should match the age range: carbon-14 (5730 years) for organic matter up to about 50,000 years, potassium–argon (1.25 billion years) for volcanic rocks, uranium–lead (4.47 billion years for ²³⁸U and 704 million for ²³⁵U) for the oldest rocks. The isochron method gives both the age and the initial ratio when the initial daughter content is unknown.

1905 年卢瑟福提出可用放射性衰变测定岩石年龄。1907 年博尔特伍德根据铀矿中铅的含量首次测得矿物年龄达数亿年，远超当时开尔文估算的地球年龄。1956 年帕特森用铀-铅法测定陨石，得出地球年龄约 45.5 亿年，这一数值沿用至今。

Rutherford suggested in 1905 that radioactive decay could date rocks. In 1907 Boltwood used the lead content of uranium minerals to obtain the first mineral ages, hundreds of millions of years, far beyond Kelvin's estimate of the Earth's age. In 1956 Patterson's uranium–lead dating of meteorites gave the Earth an age of about 4.55 billion years, a figure still accepted.

放射性测年建立了地质年代表，确定了恐龙灭绝（约 6600 万年前）、人类演化和古气候事件的时间。澳大利亚杰克山锆石的铀-铅年龄约 44 亿年，是地球上已知最古老的矿物。测年精度依赖质谱技术（如 TIMS、SHRIMP、加速器质谱）和封闭体系假设的检验。

Radiometric dating built the geological time scale and dated the dinosaur extinction (about 66 million years ago), human evolution and past climate events. Zircons from Jack Hills, Australia, have uranium–lead ages of about 4.4 billion years, the oldest known terrestrial minerals. Precision depends on mass spectrometry (TIMS, SHRIMP, accelerator mass spectrometry) and on testing the closed-system assumption.