Nuclear Energy | 核能

📚 Nuclear Energy | 核能

Nuclear energy arises from changes in the nucleus of an atom. When a nucleus undergoes fission or fusion, a small fraction of its mass is converted into a large quantity of energy according to Einstein’s equation E = mc². This topic is included only in the International A-level specification, where you must be able to calculate mass defect, binding energy, and the energy released in nuclear reactions, as well as understand the physics of nuclear reactors and fusion.

核能来源于原子核的变化。当原子核发生裂变或聚变时，其质量的一小部分会按照爱因斯坦方程 E = mc² 转化为大量能量。本主题仅包含在国际 A-level 考纲中，你需要能够计算质量亏损、结合能以及核反应释放的能量，并理解核反应堆的工作原理与聚变物理。

1. Mass–Energy Equivalence | 质能等价

In 1905, Einstein proposed that mass and energy are equivalent. The relationship is given by:

E = mc²

where E is energy in joules, m is mass in kilograms, and c is the speed of light in a vacuum, 3.00 × 10⁸ m s⁻¹. Because c² is an enormous number, even a tiny mass corresponds to a very large quantity of energy. This principle underpins all nuclear energy calculations.

其中 E 是以焦耳为单位的能量，m 是以千克为单位的质量，c 是真空中的光速，数值为 3.00 × 10⁸ m s⁻¹。由于 c² 是一个极其巨大的数值，即使极小的质量也对应着巨大的能量。这一原理是所有核能计算的基础。

In nuclear physics, masses are often quoted in atomic mass units (u), where 1 u = 1.661 × 10⁻²⁷ kg. The corresponding energy equivalent is 1 u = 931.5 MeV. This conversion factor is essential for calculation questions.

在核物理中，质量常用原子质量单位（u）表示，1 u = 1.661 × 10⁻²⁷ kg。其对应的能量当量为 1 u = 931.5 MeV。这个换算因子在计算题中至关重要。

2. Mass Defect | 质量亏损

When nucleons (protons and neutrons) combine to form a nucleus, the mass of the nucleus is found to be less than the total mass of the individual nucleons. This difference is called the mass defect, Δm.

当核子（质子和中子）结合形成原子核时，原子核的质量小于各独立核子的总质量。这个差值称为质量亏损 Δm。

For a nucleus with Z protons and N neutrons, the mass defect is:

Δm = Zmₚ + Nmₙ − mₙᵤₖ

where mₚ is the proton mass, mₙ is the neutron mass, and mₙᵤₖ is the mass of the nucleus. This “missing” mass has been converted into energy, which is released when the nucleus forms.

其中 mₚ 为质子质量，mₙ 为中子质量，mₙᵤₖ 为原子核质量。这部分”消失”的质量已转化为能量，在原子核形成时释放出来。

Worked example: The mass of a helium-4 nucleus is 4.00150 u. The proton mass is 1.00728 u and the neutron mass is 1.00867 u. Helium-4 contains 2 protons and 2 neutrons.

示例：氦-4 原子核的质量为 4.00150 u。质子质量为 1.00728 u，中子质量为 1.00867 u。氦-4 含有 2 个质子和 2 个中子。

Total nucleon mass = 2(1.00728) + 2(1.00867) = 4.03190 u

核子总质量 = 2(1.00728) + 2(1.00867) = 4.03190 u

Δm = 4.03190 − 4.00150 = 0.03040 u

E = Δmc² = 0.03040 × 931.5 = 28.3 MeV

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