In nuclear reactions, part of the mass is converted into energy. We study Einstein’s principle of mass-energy equivalence and its applications.
Basic Knowledge
Mass-energy equivalence（Einstein, 1905）:E = mc²（c = 3.0 × 10⁸ m/s）
The energy equivalent of mass 1 u (atomic mass unit = 1.66 × 10⁻²⁷ kg) is approximately 931.5 MeV
Mass defect (binding energy):
The mass of a nucleus is smaller than the sum of the masses of its constituent nucleons (protons + neutrons). The mass difference Δm has already been released as binding energy:Δm = Zm_p + Nm_n − M_核、E_結合 = Δm × c²
Nuclear fission and nuclear fusion:
・Nuclear fission: A heavy nucleus（such as ²³⁵U）absorbs a neutron and splits → enormous energy release → nuclear reactors and atomic bombs
・Nuclear fusion: Light nuclei（²H + ³H → ⁴He + n）combine → even greater energy → the Sun’s energy source, hydrogen bombs, and ITER
Conservation laws in nuclear reactions: conservation of mass number (A), conservation of charge number (Z), and conservation of energy and momentum.
E = mc²（mass-energy equivalence. Even a small m gives a large amount of energy because c² is enormous）
Mass defect Δm（the difference between the actual mass of a nucleus and the sum of the nucleon masses）
Binding energy（the energy that binds nucleons in a nucleus. Δmc²）
Nuclear fission (fission)（a heavy nucleus splits. ²³⁵U + n → fission fragments + neutrons + energy）
Nuclear fusion (fusion)（light nuclei combine. The main energy source of the Sun）
Chain reaction（neutrons produced by fission trigger subsequent fissions. Controlled in nuclear reactors）
Further Exploration (Background and Significance)
If 1 g of mass were completely converted into energy: E = mc² = 0.001 × (3×10⁸)² = 9 × 10¹³ J. This is equivalent to the explosive energy of approximately 20,000 tons of TNT. Mass changes in chemical reactions are too small to measure, but nuclear reactions produce mass defects at measurable levels.
The Sun’s energy mainly comes from nuclear fusion through the proton-proton chain reaction (pp chain), in which approximately 4× 10⁹ kg of mass is converted into energy every second. The Sun has been shining for about 5 billion years and will continue to shine steadily for about another 5 billion years.
Fusion power（ITER: International Thermonuclear Experimental Reactor）is expected to be a next-generation energy source because its fuel is abundant and its waste problem is smaller than that of fission. However, plasma confinement technology remains a challenge (it is a field that has been said to be “always 20 years from practical use”).
- E = mc²（mass-energy equivalence）
- 1 u ≈ 931.5 MeV
- Mass defect Δm → binding energy Δmc²
- Nuclear fission: heavy nucleus + n → fission fragments + energy
- Nuclear fusion: light nuclei combine → energy (the Sun’s source)
- Conservation laws: A, Z, energy, and momentum
- A nuclear reactor controls the chain reaction
Notes (Easily Confused Points)
① Mass defect Δm has not “disappeared”; it was released as binding energy when the nucleus formed. ② The energy released by both fission (heavy nucleus → lighter nuclei) and fusion (light nuclei → heavier nucleus) comes from mass defect. ③ Always check the conservation laws (A and Z) in nuclear reactions. ④ “E = mc²” is rest-mass energy; for moving particles, the exact relation is E² = (pc)² + (mc²)².
Practice
- Find the energy released in a nuclear reaction with mass defect Δm = 3.0 × 10⁻²⁹ kg（c = 3.0 × 10⁸ m/s）.
- Explain the difference between nuclear fission and fusion in terms of “nuclear size (heavy or light)” and “how energy is released.”
- In the nuclear reaction ²H + ³H → ⁴He + ?, answer ?. Then verify the conservation of mass number and proton number.