Mass and Energy | 质量与能量

📚 Mass and Energy | 质量与能量

In CIE A Level Physics, the relationship between mass and energy is captured by Einstein’s famous equation E = mc². This principle is essential for understanding nuclear reactions, radioactive decay, and particle interactions. It tells us that mass can be converted into energy and energy can contribute to mass.

在 CIE A Level 物理中，质量与能量的关系由爱因斯坦著名方程 E = mc² 描述。这一原理对理解核反应、放射性衰变和粒子相互作用至关重要。它表明质量可以转化为能量，能量也可以表现为质量。

1. The Mass-Energy Equivalence Principle | 质能等价原理

Einstein’s special theory of relativity shows that mass and energy are equivalent. The total energy E of a particle has a contribution from its rest mass m₀: E₀ = m₀c². Here c is the speed of light in vacuum, c = 3.00 × 10⁸ m s⁻¹. Since c² is huge, a small mass corresponds to a very large energy.

爱因斯坦的狭义相对论指出质量与能量是等价的。粒子的总能量 E 包含来自其静止质量 m₀ 的贡献：E₀ = m₀c²。其中 c 是真空中的光速，c = 3.00 × 10⁸ m s⁻¹。由于 c² 极大，很小的质量就对应非常大的能量。

E₀ = m₀c²

The equation is not just a conversion factor; it states that mass is a form of energy. In nuclear physics, we often deal with rest mass energies because changes in mass are measurable.

该方程不仅仅是一个换算因子，它表明质量是能量的一种形式。在核物理中，我们经常处理静止质量能量，因为质量的变化是可测量的。

2. Rest Energy and the Electronvolt | 静能与电子伏特

The rest energy of a particle is the energy stored in its mass when the particle is at rest. For an electron, mₑ = 9.11 × 10⁻³¹ kg, so E₀ = mₑc² ≈ 8.19 × 10⁻¹⁴ J. This is more conveniently expressed in electronvolts: 1 eV = 1.60 × 10⁻¹⁹ J, so the electron rest energy is about 0.511 MeV.

粒子的静能是粒子静止时储存在其质量中的能量。对电子而言，mₑ = 9.11 × 10⁻³¹ kg，因此 E₀ = mₑc² ≈ 8.19 × 10⁻¹⁴ J。用电子伏特表示更方便：1 eV = 1.60 × 10⁻¹⁹ J，因此电子的静能约为 0.511 MeV。

In A Level calculations, you should be able to convert between joules and electronvolts. The proton and neutron rest energies are about 938 MeV and 940 MeV respectively.

在 A Level 计算中，你应能在焦耳和电子伏特之间转换。质子和中子的静能分别约为 938 MeV 和 940 MeV。

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

Nuclear masses are often given in atomic mass units, u. By definition, 1 u is one twelfth of the mass of a carbon-12 atom, and 1 u = 1.66 × 10⁻²⁷ kg. Using E = mc², 1 u is equivalent to 931.5 MeV. Therefore a mass difference of 1 u corresponds to an energy of 931.5 MeV.

核质量通常以原子质量单位 u 表示。根据定义，1 u 是碳-12 原子质量的十二分之一，且 1 u = 1.66 × 10⁻²⁷ kg。利用 E = mc²，1 u 等价于 931.5 MeV。因此，1 u 的质量差对应 931.5 MeV 的能量。

1 u c² = 931.5 MeV

This conversion is extremely useful in nuclear calculations because mass differences are typically of the order of 10⁻³ u to 10⁻¹ u, giving energies in MeV.

这一换算在核计算中极其有用，因为质量差通常在 10⁻³ u 到 10⁻¹ u 量级，给出的能量以 MeV 为单位。

4. Mass Defect in Nuclei | 原子核的质量亏损

The mass of a nucleus is always less than the sum of the masses of its individual protons and neutrons. For a nucleus with Z protons and N neutrons, the mass defect Δm is:

原子核的质量总是小于其各个质子和中子质量之和。对于含有 Z 个质子和 N 个中子的原子核，质量亏损 Δm 为：

Δm = Z mₚ + N mₙ − m_nucleus

This missing mass has been converted into binding energy. It is important to use nuclear masses consistently. In CIE exams, data may give atomic masses including electrons; you should account for electron masses when required, although often differences cancel.

这些“消失”的质量转化为结合能。一致地使用核质量非常重要。在 CIE 考试中，数据可能给出包含电子的原子质量；需要时应计入电子质量，尽管差异通常会抵消。

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

Binding energy E_b is the energy required to separate a nucleus into its individual nucleons. It is related to the mass defect by:

结合能 E_b 是将原子核拆分为单个核子所需的能量。它与质量亏损的关系为：

E_b = Δm c²

A larger binding energy means the nucleons are more tightly bound. However, total binding energy alone does not determine stability. A heavier nucleus has more nucleons, so it naturally has a larger total binding energy. Stability is better measured by binding energy per nucleon.

结合能越大，核子结合得越紧密。但仅凭总结合能不能决定稳定性。较重的原子核有更多核子，因此总结合能自然更大。稳定性更好地用比结合能（每个核子的结合能）来衡量。

6. Binding Energy per Nucleon Curve | 比结合能曲线

The binding energy per nucleon E_b/A is obtained by dividing the total binding energy by the nucleon number A. It rises rapidly for light nuclei, reaches a maximum of about 8.8 MeV per nucleon near iron-56, and then decreases slowly for heavier nuclei.

比结合能 E_b/A 由总结合能除以核子数 A 得到。它对于轻核迅速上升，在铁-56 附近达到约每核子 8.8 MeV 的最大值，然后对于更重的核缓慢下降。

This curve explains why energy can be released by both fission of heavy nuclei and fusion of light nuclei. Both processes move products toward the more stable middle region of the curve.

这条曲线解释了为什么重核裂变和轻核聚变都能释放能量。两种过程都使产物向曲线中部更稳定的区域移动。

7. Nuclear Fission and Fusion | 核裂变与核聚变

In nuclear fission, a heavy nucleus such as uranium-235 splits into lighter fragments, releasing energy because the products have a higher binding energy per nucleon. A typical fission reaction is:

在核裂变中，铀-235 等重核分裂成较轻的碎片，由于产物的比结合能更高而释放能量。一个典型的裂变反应为：

U-235 + n → Ba-141 + Kr-92 + 3 n + energy

The total mass of products is smaller than reactants, and the energy released is ΔE = Δm c².

产物的总质量小于反应物，释放的能量为 ΔE = Δm c²。

In nuclear fusion, light nuclei such as deuterium and tritium combine to form helium-4. The mass of the helium nucleus is less than the total mass of the reactants, so energy is released. Fusion powers the Sun.

在核聚变中，氘和氚等轻核结合形成氦-4。氦核的质量小于反应物总质量，因此释放能量。聚变为太阳提供能量。

8. Annihilation and Pair Production | 湮灭与电子对产生

Mass–energy equivalence is also demonstrated in particle physics. When a particle and

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Mass and Energy | 质量与能量