\[t_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda},\qquad N = N_0\left(\frac12\right)^{t/t_{1/2}}\]
含义Meaning
放射性核数减少一半所需的时间，对给定核素为常数，与起始量无关。
The time for half the nuclei to decay — a constant for each nuclide, independent of the starting amount.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(t_{1/2}\) | 半衰期half-life | s, a |
推导Derivation
令 \(N = N_0/2\)：\(1/2 = e^{-\lambda t_{1/2}}\)，取对数 \(t_{1/2} = \ln2/\lambda\)。
Set \(N = N_0/2\) and take logs.
代回得到以 2 为底的形式，便于整数个半衰期的计算。
Substituting back gives the base-2 form.
适用条件与局限Assumptions & limitations
与衰变定律相同的统计前提。半衰期跨度极大：²¹²Po 0.3 μs，²³⁸U 4.47×10⁹ a，¹²⁸Te 约 2×10²⁴ a。
Same statistical premise. Half-lives range from 0.3 μs (²¹²Po) to 4.47×10⁹ a (²³⁸U) and beyond.
例题Worked example
¹³¹I（t½ = 8.02 d）经 40 天剩余 (1/2)^(40/8.02) ≈ 3.1%。
¹³¹I (8.02 d) after 40 days: (1/2)^4.99 ≈ 3.1 % remains.