放射性活度计算器

A = λ·N

Calculate nuclear decays per unit time in becquerels from decay constant and number of nuclei. Suitable for radiochemistry and nuclear medicine activity quantification.

📐 计算公式
放射性活度 A = 衰变常数 λ × 原子核数 N(Bq,1 Bq 即每秒 1 次衰变);居里换算 A_Ci = A ÷ 3.7×10¹⁰(1 Ci = 3.7×10¹⁰ Bq)。校验:空值或非数值输入会提示并中止计算,不按 0 兜底;仅做非空与数值检查,不做范围校验。判据:λ 或 N 越大活度越强,Bq 与 Ci 两卡均以科学计数法输出。

单位时间衰变数(贝可勒尔)。

Formula & Standard References

Item Formula / Note Source / Standard
Activity definitionA = λN decays per secondNuclear physics
UnitsBq = s⁻¹; 1 Ci = 3.7×10¹⁰ BqSI units
Specific activitya = A/mNuclide properties
Atom countN = m·N_A/MMolar relation
Decay correctionA(t) = A₀e^(−λt)Decay law
MeasurementCoincidence, 4π counting, LSCRadioactivity metrology
📌 计算说明
  • A = λN。
  • 1 Ci = 3.7e10 Bq。

📐 Nuclear Data

Constants used on this page and their authoritative sources, for verification and citation

Constant Value Unit Source
Curie (Ci, non-SI unit) 3.7e10 Bq Historical definition (activity of 1 g of radium-226, exact by convention)
Avogadro constant N_A 6.02214076e23 mol⁻¹ SI defining constant (exact)
Natural logarithm of 2, ln 2 0.6931471805599453 — Mathematical constant (exact)

Note: the becquerel (Bq = s⁻¹) is the SI derived unit of activity; the curie is a historical non-SI unit retained by ICRU, with 1 mCi = 37 MBq.

📚 深度解析:活度(A = λN)

💡 常见使用场景

λ=1e-9 s⁻¹、N=1e20
A = 1e-9 × 1e20 = 1×10¹¹ Bq;核数增到 1e21 则 A=1e12 Bq。
与半衰期换算
若 th=ln2/λ=6.93e8s,则 A=(ln2/th)×N 等价,结果一致。

❓ 常见问题(FAQ)

A=λN 与 A₀e^(−λt) 关系?
前者是瞬时活度定义,后者是其随时间衰减规律,t=0 时一致。
λ 的单位?
λ 单位为 s⁻¹(每秒衰变概率),N 为核数,故 A 为 s⁻¹ = Bq。