📚 IB Physics: Nuclear Physics Key Points | IB 物理：核物理 考点精讲
Nuclear physics is a fascinating and vital topic in the IB Physics syllabus, covering the structure of the nucleus, radioactive decay, nuclear reactions, and the vast energy contained within atomic nuclei. Understanding these concepts not only prepares students for examinations but also illuminates the science behind nuclear power, medical imaging, and the fundamental forces of nature.
核物理是 IB 物理课程中一个迷人而重要的主题，涵盖原子核结构、放射性衰变、核反应以及原子核中蕴藏的巨大能量。理解这些概念不仅有助于学生备考，还能揭示核能、医学成像和自然界基本力背后的科学原理。
1. Nuclear Structure and Notation | 原子核结构与符号
The atomic nucleus is composed of protons and neutrons, collectively called nucleons. The number of protons Z defines the chemical element, while the total number of nucleons is the mass number A. The neutron number N is given by N = A – Z. Isotopes are nuclei with the same Z but different N, meaning they belong to the same element but have different masses.
原子核由质子和中子组成，统称为核子。质子数 Z 决定元素种类，核子总数 A 为质量数，中子数 N = A – Z。同位素是指质子数相同而中子数不同的核素，即同一元素但质量不同。
A nuclide is symbolised as ᴬZX, where the mass number A is written as a superscript and the atomic number Z as a subscript. For example, carbon-12 is written as ¹²₆C, and uranium-235 as ²³⁵₉₂U.
核素用符号 ᴬZX 表示，质量数 A 写在左上角，质子数 Z 写在左下角。例如碳-12 写作 ¹²₆C，铀-235 写作 ²³⁵₉₂U。
The size of a nucleus is on the order of 10⁻¹⁵ m, and its density is enormous, around 10¹⁷ kg m⁻³. The strong nuclear force binds nucleons together, overcoming the electrostatic repulsion between protons.
原子核的尺寸约为 10⁻¹⁵ m，密度极大，约 10¹⁷ kg m⁻³。核子之间通过强核力结合，以克服质子间的静电排斥力。
2. Radioactive Decay | 放射性衰变
Unstable nuclei undergo radioactive decay, a spontaneous and random process in which they emit radiation to become more stable. The decay of a particular nucleus is unaffected by physical conditions such as temperature or pressure, and it follows a statistical pattern for a large number of nuclei.
不稳定原子核会发生放射性衰变，这是一个自发且随机的过程，通过放出辐射变得更稳定。单个核的衰变不受温度、压力等物理条件影响，但对于大量原子核，衰变遵循统计规律。
The probability that a given nucleus will decay per unit time is constant, known as the decay constant λ (lambda). Different isotopes have widely different decay constants, reflecting their degree of instability.
一个核在单位时间内发生衰变的概率是恒定的，称为衰变常数 λ。不同同位素的衰变常数差异很大，反映了其不稳定程度。
3. Alpha, Beta, and Gamma Decay | α、β 和 γ 衰变
Radioactive decay can occur in several forms, the most common being alpha (α), beta (β), and gamma (γ) decay. Each type involves the emission of different particles or photons and changes the nucleus in characteristic ways.
放射性衰变有几种常见形式：α 衰变、β 衰变和 γ 衰变。每种类型都放出不同的粒子或光子，并以特定方式改变原子核。
In alpha decay, a heavy nucleus emits an alpha particle, which is a helium-4 nucleus (⁴₂He). The mass number decreases by 4 and the atomic number by 2. For example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He.
在 α 衰变中，重核放出一个 α 粒子，即氦-4 核（⁴₂He）。质量数减少 4，质子数减少 2。例如：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。
Beta-minus (β⁻) decay involves a neutron transforming into a proton, with the emission of an electron (⁰₋₁e) and an antineutrino (ν̄ₑ). The atomic number increases by 1, while the mass number remains unchanged. Example: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ.
β⁻ 衰变中，一个中子转变成一个质子，并放出一个电子（⁰₋₁e）和一个反中微子（ν̄ₑ）。原子序数增加 1，质量数不变。例如：¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ。
Beta-plus (β⁺) decay occurs in proton-rich nuclei, where a proton converts into a neutron, emitting a positron (⁰₊₁e) and a neutrino (νₑ). The atomic number decreases by 1, with no change in mass number.
β⁺ 衰变发生在质子过多的核中，一个质子转变成中子，放出一个正电子（⁰₊₁e）和一个中微子（νₑ）。原子序数减少 1，质量数不变。
Gamma decay is the emission of a high-energy photon (γ) from an excited nucleus. It usually follows alpha or beta decay when the daughter nucleus is left in an excited state. Gamma emission does not change the mass or atomic number.
γ 衰变是激发态原子核放出高能光子 (γ)。它通常发生在 α 或 β 衰变之后，子核处于激发态。γ 辐射不改变原子核的质量数或质子数。
4. Half-Life and Decay Constant | 半衰期与衰变常数
The half-life T½ is the time required for half of the radioactive nuclei in a sample to decay. It is related to the decay constant by T½ = ln(2) / λ. Half-lives range from fractions of a second to billions of years.
半衰期 T½ 是放射性样品中一半原子核发生衰变所需的时间。它与衰变常数的关系为 T½ = ln(2) / λ。半衰期从不到一秒到数十亿年不等。
The number of undecayed nuclei N at time t follows an exponential decay law: N = N₀ e⁻λᵗ, where N₀ is the initial number. This equation assumes a large number of nuclei and is the foundation for all radioactive dating and activity calculations.
t 时刻未衰变核的数量 N 遵循指数衰变规律：N = N₀ e⁻λᵗ，其中 N₀ 为初始核数。该方程基于大数核的统计行为，是所有放射性定年和活度计算的基础。
N = N₀ e⁻λᵗ and T½ = ln 2 / λ
5. Activity and the Decay Law | 活度与衰变定律
The activity A of a radioactive sample is the number of decays per unit time, given by A = λN. Its SI unit is the becquerel (Bq), where 1 Bq equals one decay per second. Activity also decays exponentially: A = A₀ e⁻λᵗ.
放射性样品的活度 A 是指单位时间内发生的衰变次数，A = λN。国际单位是贝克勒尔 (Bq)，1 Bq 表示每秒一次衰变。活度也遵循指数衰减：A = A₀ e⁻λᵗ。
When solving half-life problems, students often use the relation N = N₀ (1/2)ⁿ, where n = t / T½ is the number of half-lives elapsed. This is equivalent to the exponential form and is particularly useful when t is a multiple of T½.
在求解半衰期问题时，学生常用 N = N₀ (1/2)ⁿ，其中 n = t / T½ 是经过的半衰期个数。这与指数形式等价，当 t 是 T½ 的整数倍时尤其方便。
The random nature of decay means that individual decay times cannot be predicted, but the average behaviour is described precisely by these laws. Background radiation must always be subtracted when measuring activity in experiments.
衰变的随机性意味着无法预言单个核的衰变时刻，但整体平均行为可由上述规律精确描述。实验中测量活度时，必须扣除本底辐射。
6. Mass-Energy Equivalence | 质能等价
A cornerstone of nuclear physics is Einstein’s mass–energy equivalence, E = mc². This principle shows that mass can be converted into energy and vice versa, and it is the key to understanding nuclear binding energy and the energy released in nuclear reactions.
核物理的基石之一是爱因斯坦的质能等价原理 E = mc²。该原理表明质量可以转化为能量，反之亦然，是理解核结合能与核反应释放能量的关键。
E = mc²
In nuclear physics, the unified atomic mass unit (u) is commonly used: 1 u = 1.661 × 10⁻²⁷ kg. Its energy equivalent is 931.5 MeV. This conversion factor is essential for calculating binding energies from mass differences.
在核物理中，常用统一原子质量单位 u，1 u = 1.661 × 10⁻²⁷ kg，其能量当量为 931.5 MeV。这个转换因子对于从质量差计算结合能至关重要。
7. Binding Energy and Mass Defect | 结合能与质量亏损
The mass of a nucleus is always less than the total mass of its individual protons and neutrons. This difference is the mass defect Δm. The binding energy E_b is the energy equivalent of this mass defect: E_b = Δm c². It represents the energy required to separate the nucleus into its constituent nucleons.
原子核的质量总是小于其单独质子和中子质量之和，这个差值称为质量亏损 Δm。结合能 E_b 是质量亏损的能量当量：E_b = Δm c²，表示将原子核完全分解为核子所需的最小能量。
For example, a helium-4 nucleus has a mass of 4.00151 u, while two protons and two neutrons have a combined mass of approximately 2 × 1.00728 u + 2 × 1.00867 u = 4.03190 u. The mass defect is 0.03039 u, giving a binding energy of about 28.3 MeV.
例如，氦-4 核的质量为 4.00151 u，而两个质子和两个中子的总质量约为 2 × 1.00728 u + 2 × 1.00867 u = 4.03190 u。质量亏损为 0.03039 u，结合能约为 28.3 MeV。
Binding energy per nucleon (E_b / A) is a measure of nuclear stability. It rises steeply for light nuclei, reaches a maximum around iron-56 (≈ 8.8 MeV per nucleon), and then gradually decreases for heavier nuclei. The fusion of light nuclei and fission of heavy nuclei both lead to products with higher binding energy per nucleon, releasing energy.
每个核子的结合能 (E_b / A) 是核稳定性的量度。它对于轻核急剧上升，在铁-56 附近达到最大（约 8.8 MeV/核子），然后对重核逐渐下降。轻核的聚变和重核的裂变都能产生每个核子结合能更高的产物，从而释放能量。
8. Nuclear Fission | 核裂变
Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei, accompanied by the release of energy and several neutrons. A typical reaction is the neutron-induced fission of uranium-235: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + energy.
核裂变是一个重核分裂成两个较轻的核，同时释放能量和若干个中子。典型的反应是中子引发的铀-235 裂变：²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + 能量。
The released neutrons can induce further fission events, leading to a chain reaction. In a nuclear reactor, the chain reaction is controlled using control rods (e.g., boron or cadmium) that absorb neutrons, and a moderator (e.g., water or graphite) that slows down the neutrons to thermal energies where fission probability is higher.
释放出的中子可以引发更多的裂变事件，形成链式反应。在核反应堆中，使用能吸收中子的控制棒（如硼或镉）和慢化剂（如水或石墨）来控制链式反应，慢化剂将中子减速到热中子能量，以提高裂变概率。
Critical mass is the minimum mass of fissile material required to sustain a chain reaction. Issues with fission include radioactive waste, safety risks, and the limited supply of uranium, but it remains a major low-carbon energy source.
临界质量是维持链式反应所需的可裂变物质的最小质量。裂变面临的问题包括放射性废物、安全风险和铀资源的有限性，但它仍是重要的低碳能源。
9. Nuclear Fusion | 核聚变
Nuclear fusion is the combining of light nuclei to form a heavier nucleus, releasing energy. The most studied fusion reactions involve isotopes of hydrogen: deuterium (²₁H) and tritium (³₁H). The reaction ²₁H + ³₁H → ⁴₂He + ¹₀n produces 17.6 MeV of energy.
核聚变是轻原子核结合成较重核的过程，并释放能量。研究最多的聚变反应涉及氢的同位素：氘 (²₁H) 和
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