📚 A2 Physics: Radioactive Decay | 放射性衰变 考点精讲
Radioactive decay is a fundamental process in nuclear physics, describing how unstable atomic nuclei release energy or particles to become more stable. In A2 Physics, a thorough understanding of decay laws, half-life, activity, and the properties of different radiations is essential for tackling exam questions and practical applications.
放射性衰变是核物理中的一个基本过程，描述了不稳定的原子核如何释放能量或粒子以变得更稳定。在A2物理中，深入理解衰变规律、半衰期、活度以及不同辐射的特性，对于解答考题和实际应用至关重要。
1. Radioactive Decay and Nuclear Stability | 放射性衰变与原子核稳定性
The stability of a nucleus depends on the balance between the strong nuclear force and the electrostatic repulsion between protons. Nuclei with an excess of neutrons or protons tend to be unstable and undergo radioactive decay to reach a more stable configuration.
原子核的稳定性取决于强核力与质子间静电排斥力之间的平衡。中子或质子过多的原子核往往不稳定，会发生放射性衰变以达到更稳定的构型。
Radioactive decay is a spontaneous and random process. It is not affected by external conditions such as temperature or pressure, and it is impossible to predict exactly when a particular nucleus will decay.
放射性衰变是一个自发且随机的过程。它不受温度、压力等外部条件的影响，也无法精确预测某个特定原子核何时衰变。
During decay, nuclei can emit alpha particles, beta particles, or gamma rays, often transforming into a different element.
在衰变过程中，原子核可发射α粒子、β粒子或γ射线，并常常转变为另一种元素。
2. Decay Constant and the Exponential Law | 衰变常数与指数衰变定律
The decay constant λ (lambda) represents the probability per unit time that a given nucleus will decay. A larger λ indicates a more rapidly decaying isotope.
衰变常数λ表示单个原子核在单位时间内发生衰变的概率。λ越大，表明该同位素衰变得越快。
time t follows the exponential law: N = N₀ e⁻λᵗ, where N₀ is the initial number of nuclei.
在时间t时剩余未衰变的原子核数N遵循指数规律：N = N₀ e⁻λᵗ，其中N₀是初始原子核数。
N = N₀ e⁻λᵗ
This equation shows that the number of radioactive nuclei decreases exponentially with time. The same exponential form applies to the mass of a radioactive sample and to the count rate measured by a detector.
该方程表明放射性核的数量随时间呈指数衰减。同样的指数形式也适用于放射性样品的质量和探测器测得的计数率。
3. Activity and the Becquerel | 活度与贝可勒尔
cays per unit time. It is directly proportional to the number of undecayed nuclei: A = λN.
放射源的活度A定义为单位时间内发生的衰变次数，它与未衰变的核数成正比：A = λN。
A = λN
The SI unit of activity is the becquerel (Bq), where 1 Bq corresponds to one decay per second.
活度的国际单位是贝克勒尔（Bq），1 Bq相当于每秒发生一次衰变。
nential decay: A = A₀ e⁻λᵗ, making it easy to calculate the activity after any given time.
活度同样遵循指数衰减规律：A = A₀ e⁻λᵗ，因此可以方便地计算经过任意时间后的活度。
A = A₀ e⁻λᵗ
In experiments, the measured count rate C is often proportional to the activity, though one must correct for background radiation.
在实验中，测得的计数率C常与活度成正比，但需扣除本底辐射。
4. Half-life and Mean Lifetime | 半衰期与平均寿命
oactive nuclei in a sample to decay. It is related to the decay constant by T½ = ln 2 / λ.
半衰期T½是样品中半数放射性核发生衰变所需的时间。它与衰变常数的关系为 T½ = ln 2 / λ。
T½ = ln 2 / λ
After one half‑life, N = N₀/2; after two half‑lives, N = N₀/4, and so on. This simple fraction approach is useful for quick estimates.
经过一个半衰期，N = N₀/2；经过两个半衰期，N = N₀/4，以此类推。这种简单分数法便于快速估算。
ive nucleus is the average time before decay, given by τ = 1/λ. It is longer than the half‑life.
放射性核的平均寿命τ是衰变前的平均时间，τ = 1/λ。它比半衰期长。
τ = 1 / λ
Knowing T½ allows calculation of the fraction remaining after any time: N = N₀ (1/2)t/T½.
知道了T½，便可以计算任意时间后的剩余比例：N = N₀ (½)t/T½。
5. Radiocarbon Dating | 碳-14 放射性测年
Radiocarbon dating uses the decay of
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