Binding Energy and Nuclear Stability | 结合能与核稳定性

📚 Binding Energy and Nuclear Stability | 结合能与核稳定性

Nuclear reactions release energies millions of times greater than typical chemical reactions. The fundamental reason is that a small amount of mass disappears when nucleons bind together, and this mass difference is converted into energy. In this article, we connect mass defect, binding energy, binding energy per nucleon and the stability curve, with a strong focus on CIE A-Level Physics requirements.

核反应释放的能量比一般化学反应高数百万倍。其根本原因在于核子结合时会有少量质量消失，这些质量差被转化为能量。本文将围绕质量亏损、结合能、比结合能以及核稳定性曲线展开，紧扣 CIE A-Level 物理考点。

1. Mass Defect and E = mc² | 质量亏损与质能方程

The mass defect Δm of a nucleus is defined as the difference between the total mass of its separate protons and neutrons and the mass of the nucleus itself. When nucleons join together, the bound system has slightly less mass than the sum of its parts.

原子核的质量亏损 Δm 定义为组成它的独立质子和中子总质量与原子核自身质量之差。当核子结合在一起时，形成的束缚系统质量略小于各部分质量之和。

This missing mass is not lost; it is converted into energy when the nucleus is formed. Einstein’s mass-energy relation gives the binding energy:

这些亏损的质量并没有消失，而是在原子核形成时转化为能量。爱因斯坦质能关系给出结合能：

E = Δm c²

In SI units, Δm is in kilograms, c = 3.00 × 10⁸ m s⁻¹, and E is measured in joules. For a single nucleus, this energy is extremely small in joules, so nuclear physicists often use MeV and atomic mass units.

在国际单位制中，Δm 以千克为单位，c = 3.00 × 10⁸ m s⁻¹，能量 E 以焦耳为单位。对单个原子核而言，这个能量以焦耳表示非常小，因此核物理中常用 MeV 和原子质量单位。

Δm = (Z mₚ + N mₙ) − M

Here Z is the proton number, N is the neutron number, mₚ is the proton mass, mₙ is the neutron mass, and M is the mass of the assembled nucleus.

其中 Z 是质子数，N 是中子数，mₚ 是质子质量，mₙ 是中子质量，M 是形成后的原子核质量。

2. Atomic Mass Unit and Energy Equivalence | 原子质量单位与能量当量

In nuclear physics, masses are usually measured in unified atomic mass units, u. By definition, 1 u is exactly one twelfth of the mass of a neutral carbon-12 atom. In kilograms, this is approximately:

在核物理中，质量通常以统一原子质量单位 u 表示。根据定义，1 u 严格等于中性碳-12 原子质量的十二分之一。换算成千克约为：

1 u ≈ 1.661 × 10⁻²⁷ kg

Using E = mc², one atomic mass unit is equivalent to 931.5 MeV of energy. This conversion is essential in binding energy calculations.

利用 E = mc²，一个原子质量单位相当于 931.5 MeV 的能量。这个换算关系在结合能计算中至关重要。

1 u ≈ 931.5 MeV/c²

To convert a mass defect given in u into energy in MeV, we multiply by 931.5 MeV/c². To convert from MeV to joules, use 1 MeV = 1.602 × 10⁻¹³ J.

要将以 u 表示的质量亏损转换为以 MeV

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