📚 Energy Released in Radioactive Decay | 放射性衰变中释放的能量
the form of kinetic energy of emitted particles and often electromagnetic radiation. This energy originates from a tiny loss of mass, known as the mass defect, according to Einstein's famous equation E = mc².
放射性衰变是一种自发的核过程，不稳定的原子核转变为更稳定的结构，以发射粒子的动能和通常伴随的电磁辐射形式释放能量。这一能量源自微小的质量损失，即质量亏损，符合爱因斯坦著名的质能方程 E = mc²。
1. Mass Defect and the Source of Decay Energy | 质量亏损与衰变能量来源
Every nucleus has a mass slightly less than the sum of the masses of its individual protons and neutrons. This difference, the mass defect, represents the energy that holds the nucleus together — the binding energy. When a heavy nucleus decays into lighter fragments, the total mass of the products is less than the mass of the original nucleus; the 'missing' mass is converted into kinetic energy and radiation.
每个原子核的质量略小于其质子和中子单独质量之和。这个差值，即质量亏损，代表了将核子结合在一起的能量——结合能。当重核衰变为较轻的碎片时，产物的总质量小于原始核的质量；“丢失”的质量转化为动能和辐射能。
2. Einstein’s Mass–Energy Equivalence | 爱因斯坦质能等价方程
ioactive decay, a small mass difference Δm yields a significant energy release ΔE = Δm c².
基本关系式 E = mc² 将质量与能量联系起来。在放射性衰变中，微小的质量差 Δm 会产生可观的能量释放 ΔE = Δm c²。
ΔE = Δm c²
(MeV), and masses are often expressed in atomic mass units (u), where 1 u = 931.5 MeV/c².
对于核过程，能量以兆电子伏特（MeV）为单位，质量常用原子质量单位（u）表示，其中 1 u = 931.5 MeV/c²。
- 1 u = 1.660539 × 10⁻²⁷ kg
- 1 u c² = 931.494 MeV
Since c² is a huge factor, even a mass loss of 0.001 u releases about 0.93 MeV.
由于 c² 是一个巨大的因子，即使 0.001 u 的质量损失也会释放约 0.93 MeV 的能量。
3. Nuclear Binding Energy and Stability | 核结合能与稳定性
The binding energy per nucleon peaks around iron-56. Nuclei heavier than iron can release energy by splitting (fission) or by decaying into more stable nuclei. Radioactive decay tends to occur for nuclei that lie far from the valley of stability, and the energy released is the difference in binding energies between the parent and daughter nuclei.
每个核子的平均结合能在铁-56附近达到峰值。比铁重的原子核可以通过分裂（裂变）或衰变成更稳定的核来释放能量。远离稳定谷的核倾向于发生放射性衰变，释放的能量是母核与子核结合能之差。
For example, uranium-238 decays by alpha emission into thorium-234, and the total binding energy of the products is greater than that of the parent nucleus, so energy is released.
例如，铀-238通过α衰变变成钍-234，产物的总结合能大于母核，因此释放能量。
4. Alpha Decay Energetics | α衰变能量学
In alpha decay, a heavy nucleus emits a helium-4 nucleus (⁴He). The decay energy, called the Q-value, is shared between the alpha particle and the daughter nucleus as kinetic energy. Because momentum is conserved, the lighter alpha particle carries away most of the kinetic energy.
在α衰变中，重核发射一个氦-4 核（⁴He）。衰变能，即 Q 值，以动能的形式分配给 α 粒子和子核。由于动量守恒，较轻的 α 粒子带走绝大部分动能。
) = 234.043601 u, m(⁴He) = 4.002603 u. Δm = 0.004584 u, which corresponds to Q ≈ 4.27 MeV.
例子：²³⁸U → ²³⁴Th + ⁴He + Q。利用原子质量：m(²³⁸U) = 238.050788 u，m(²³⁴Th) = 234.043601 u，m(⁴He) = 4.002603 u。Δm = 0.004584 u，对应的 Q ≈ 4.27 MeV。
The kinetic energy of the alpha particle can be approximated from the Q-value using conservation of momentum.
α粒子的动能可通过动量守恒由 Q 值近似得到。
E_α = [m_daughter / (m_daughter + m_α)] × Q
For the ²³⁸U decay, this gives E_α ≈ 4.2 MeV, matching the measured value.
对于 ²³⁸U 衰变，得出 E_α ≈ 4.2 MeV，与测量值一致。
5. Beta Decay and the Neutrino | β衰变与中微子
n + neutrino). The decay energy Q is shared between the electron/positron and the antineutrino/neutrino. Consequently, beta particles are emitted with a continuous spectrum of kinetic energies up to the maximum Q-value.
β衰变有两种类型：β⁻（中子 → 质子 + 电子 + 反中微子）和 β⁺（质子 → 中子 + 正电子 + 中微子）。衰变能 Q 在电子/正电子与反中微子/中微子之间分配。因此，β 粒子以连续的动能谱发射，最高可达 Q 值。
Example: Carbon-14 decay: ¹⁴C → ¹⁴N + e⁻ + ν̄ₑ + Q, Q ≈ 0.156 MeV. The electron's kinetic energy varies from zero to nearly 0.156 MeV, with an average around
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