含义Meaning
同温同压下，气体的扩散（隙流）速率与其摩尔质量的平方根成反比。
At equal temperature and pressure, effusion rate is inversely proportional to the square root of molar mass.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(r\) | 扩散 / 隙流速率rate of effusion / diffusion | mol·s⁻¹ |
| \(M\) | 摩尔质量molar mass | g·mol⁻¹ |
推导Derivation
隙流速率正比于分子平均速率 \(\bar v\)。
Effusion rate is proportional to the mean molecular speed \(\bar v\).
由分子运动论 \(\bar v = \sqrt{8RT/(\pi M)} \propto 1/\sqrt{M}\)（T 相同）。
Kinetic theory: \(\bar v = \sqrt{8RT/(\pi M)} \propto 1/\sqrt{M}\) at fixed T.
取两种气体之比即得。
Take the ratio for two gases.
适用条件与局限Assumptions & limitations
严格适用于隙流（小孔直径远小于平均自由程）；宏观扩散只是近似。
Strictly for effusion through a hole much smaller than the mean free path; bulk diffusion only approximately.
两气体须在同温下比较。
Compare at the same temperature.
例题Worked example
²³⁵UF₆ 与 ²³⁸UF₆ 的速率比仅 √(352/349) = 1.0043，所以气体扩散法浓缩铀需要上千级。
²³⁵UF₆ vs ²³⁸UF₆: rate ratio √(352/349) = 1.0043, so diffusion enrichment needs over a thousand stages.