衰变链Decay chain

α 衰变使质量数减 4，β 衰变不改变质量数，因此同一衰变链中各核素的质量数除以 4 的余数相同，形成 4n（钍系，始于 ²³²Th）、4n+2（铀系，始于 ²³⁸U）、4n+3（锕系，始于 ²³⁵U）三个天然系列；4n+1 的镎系始于 ²³⁷Np，因半衰期较短在自然界已基本消失，终止于 ²⁰⁹Bi（实际上也极缓慢地衰变为 ²⁰⁵Tl）。

Alpha decay lowers the mass number by 4 and beta decay leaves it unchanged, so every member of a chain has the same remainder on division by 4. This gives three natural series: 4n (thorium, from ²³²Th), 4n+2 (uranium, from ²³⁸U) and 4n+3 (actinium, from ²³⁵U). The 4n+1 neptunium series, from ²³⁷Np, has essentially died out in nature because of its shorter half-lives; it ends at ²⁰⁹Bi, which itself decays extremely slowly to ²⁰⁵Tl.

当母体半衰期远长于子体时，经过足够长时间，各子体的放射性活度都与母体相等，称为长期平衡，如铀矿中的 ²³⁸U 与 ²²⁶Ra。若母体半衰期只是稍长于子体，则达到暂时平衡，这是 ⁹⁹Mo/⁹⁹ᵐTc 发生器（“母牛”）的原理。贝特曼方程给出了衰变链中各核素数量随时间变化的通解。

When the parent's half-life is far longer than its daughters', after enough time every daughter reaches the same activity as the parent: secular equilibrium, as between ²³⁸U and ²²⁶Ra in uranium ore. When the parent is only somewhat longer-lived, transient equilibrium results, the principle of the ⁹⁹Mo/⁹⁹ᵐTc generator ('cow'). The Bateman equations give the general solution for the amounts of each nuclide over time.

1902–1903 年卢瑟福和索迪研究钍的放射性，发现其放出的“钍射气”（氡-220）自身也有放射性，提出元素依次嬗变的观点。1913 年索迪和法扬斯提出放射性位移定律，把衰变产物排入周期表，索迪并据此提出“同位素”概念。铀系中的氡-222 是室内天然辐射的主要来源。

In 1902–03 Rutherford and Soddy, studying thorium, found its 'emanation' (radon-220) was itself radioactive and proposed successive transmutation of elements. In 1913 Soddy and Fajans formulated the radioactive displacement law, placing decay products in the periodic table, and Soddy introduced the concept of isotopes. Radon-222 from the uranium series is the main source of natural radiation indoors.