Nuclear Binding Energy Calculator

📐 计算公式

结合能 BE = Δm × c²；质量亏损 Δm =（Z × m_质子 + N × m_中子）− m_核，其中 Z 为质子数、N 为中子数、A = Z + N；因表中常给出原子质量，计算时以氢原子质量替代质子质量，即 Δm = Z × m_氢 + N × m_中子 − m_原子；单位换算 1 u = 931.494 MeV/c²，故 BE(MeV) = Δm(u) × 931.494；结合能越大表示核子结合越牢固。

Find the energy released when nucleons bind into a nucleus, from mass defect times c². For nuclear physics learning and nuclear reaction energy assessment.

质量亏损 Δm (u)

Formula & Standard References

Item	Formula / Note	Source / Standard
Mass defect	Δm = Zm_p + Nm_n − M	Nuclear physics
Binding energy	B = Δm·c²	Einstein 1905
Energy conversion	1 u = 931.494 MeV/c²	CODATA 2018
Binding per nucleon	B/A peaks ~8.8 MeV at Fe-56	Binding energy curve
Semi-empirical formula	Weizsäcker formula (Bethe-Weizsäcker)	Weizsäcker 1935
Coulomb term	Coulomb term in SEMF	Nuclear models

📌 计算说明

1 u·c² ≈ 931.5 MeV。
铁-56 总结合能约 492 MeV。

📐 Physical Constants

Constants used on this page and their authoritative sources, for verification and citation

Constant	Value	Unit	Source
Atomic mass constant (1 u)	1.66053906660e-27	kg	CODATA 2018
Energy equivalent of 1 u	931.49410242	MeV	CODATA 2018 (= 1 u·c²)
Speed of light in vacuum c	299 792 458	m·s⁻¹	SI defining constant (exact)
Elementary charge e	1.602176634e-19	C	SI defining constant (exact)

Note: binding energy = Δm·c², with Δm from the difference between constituent nucleon masses and the nuclear mass; nucleon masses follow CODATA 2018 / AME2020 atomic mass evaluation.

📚 深度解析：原子核结合能

💡 常见使用场景

质量亏损 Δm 转总结合能 BE = Δm·c²。
核稳定度与释放能量评估。
对比不同核的总结合能。

质量亏损 0.528u

总结合能 BE = 0.528 × 1.492×10⁻¹⁰ J ≈ 7.88×10⁻¹¹ J，或 0.528 × 931.5 ≈ 491.8 MeV。

单位换算

1 MeV = 1.602×10⁻¹³ J，故 491.8 MeV ≈ 7.88×10⁻¹¹ J。

❓ 常见问题（FAQ）

结合能越大越稳定吗？: 总结合能随核子数增大，判断稳定性要看比结合能（每核子），见 binding-energy-per-nucleon。
质量亏损从哪来？: 组成核的核子总静质量大于原子核实质量，差额即结合能对应质量。

原子核结合能计算器