\[A = -\frac{dN}{dt} = \lambda N = \frac{\ln2}{t_{1/2}}\cdot\frac{m N_A}{M},\qquad A(t) = A_0e^{-\lambda t}\]
含义Meaning
单位时间的衰变数，SI 单位贝克勒尔（1 Bq = 1 次衰变/秒），旧单位居里（1 Ci = 3.7×10¹⁰ Bq，约等于 1 g ²²⁶Ra 的活度）。
Decays per unit time; SI unit becquerel (1 Bq = 1 s⁻¹); the curie (1 Ci = 3.7×10¹⁰ Bq) is roughly 1 g of ²²⁶Ra.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(A\) | 活度activity | Bq |
| \(m\) | 核素质量mass of nuclide | g |
| \(M\) | 摩尔质量molar mass | g·mol⁻¹ |
推导Derivation
活度即衰变速率 \(\lambda N\)；N 由质量换算 \(N = mN_A/M\)。
Activity is λN with \(N = mN_A/M\).
比活度 \(A/m = \lambda N_A/M\)：半衰期越短、质量数越小，比活度越高。
Specific activity λN_A/M is higher for short-lived, light nuclides.
适用条件与局限Assumptions & limitations
活度不等于剂量：生物效应还取决于辐射类型、能量、吸收方式（Gy、Sv）。
Activity is not dose; biological effect depends on radiation type and energy (Gy, Sv).
例题Worked example
1 g ²²⁶Ra（t½ = 1600 a）：A = 0.693/(1600×3.156×10⁷ s) × 6.022×10²³/226 = 3.66×10¹⁰ Bq ≈ 1 Ci。
1 g ²²⁶Ra: A ≈ 3.66×10¹⁰ Bq ≈ 1 Ci.