Energy Released in Radioactive Decay | 放射性衰变释放的能量

📚 Energy Released in Radioactive Decay | 放射性衰变释放的能量

Radioactive decay releases energy when an unstable nucleus transforms into a more stable configuration. This energy appears as kinetic energy of emitted particles and gamma photons. The source of the energy is a small loss of mass, described by Einstein’s mass-energy equivalence.

放射性衰变在不稳定原子核转变为更稳定组态时释放能量。这些能量表现为发射粒子和γ光子的动能。能量来源于微小的质量损失，由爱因斯坦的质能等价关系描述。

1. Mass-Energy Equivalence and Atomic Mass Unit | 质能等价与原子质量单位

Einstein’s relation E = mc² shows that mass can be converted into energy. In nuclear physics, masses are conveniently expressed in atomic mass units, u. One atomic mass unit is defined as 1/12 of the mass of a carbon-12 atom.

爱因斯坦关系 E = mc² 表明质量可以转化为能量。在核物理中，质量通常用原子质量单位 u 表示。一个原子质量单位定义为碳-12 原子质量的 1/12。

1 u = 1.6605 × 10⁻²⁷ kg

1 u c² = 931.5 MeV

This conversion factor is the key to all decay-energy calculations: a mass loss of 1 u releases 931.5 MeV of energy.

这个换算因子是所有衰变能计算的关键：质量亏损 1 u 释放 931.5 MeV 能量。

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

The binding energy of a nucleus is the energy required to separate it into its individual protons and neutrons. The mass of a nucleus is always less than the sum of its separated nucleons; this difference is the mass defect. Multiplying the mass defect by c² gives the binding energy.

原子核的结合能是将它拆散为单个质子和中子所需的能量。原子核的质量总是小于其分离核子质量之和；这个差值就是质量亏损。将质量亏损乘以 c² 即得结合能。

Δm = Z m_p + N m_n − m_nucleus

BE = Δm c²

The binding energy per nucleon increases from light nuclei up to iron-56 and then decreases. A decay is energetically allowed if the products have greater binding energy per nucleon than the parent, so energy is released as the system becomes more tightly bound.

每个核子的结合能从轻核到铁-56 逐渐增大，之后又下降。如果产物的每个核子结合能大于母核，则衰变在能量上是允许的，系统变得更紧密时释放能量。

3. Mass Defect in Decay Processes | 衰变过程中的质量亏损

In any spontaneous decay, the total rest mass of the products is less than the rest mass of the parent. This mass

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