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How are mass and energy related, and what happens to mass in nuclear reactions?

State the mass-energy equivalence E=mc2E = mc^2, describe the mass defect and binding energy of a nucleus, and outline nuclear fission and fusion as reactions that convert mass into energy.

A Regents Physics answer on mass-energy equivalence and nuclear physics: Einstein's E=mc2E = mc^2, the mass defect and binding energy, the universal mass unit, and nuclear fission and fusion as mass-to-energy conversions, using the Reference-Table equation, with worked examples.

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  1. What this topic is asking
  2. Mass-energy equivalence
  3. The mass defect and binding energy
  4. Nuclear fission and fusion
  5. Reference Tables note
  6. Try this

What this topic is asking

This dot point covers the relationship between mass and energy and its role in the nucleus. The Physical Setting/Physics course asks you to state Einstein's mass-energy equivalence E=mc2E = mc^2, to describe the mass defect and binding energy of a nucleus, and to outline nuclear fission and fusion as reactions that convert a tiny amount of mass into a large amount of energy. The Regents tests the E=mc2E = mc^2 calculation and the conceptual link between mass defect and binding energy.

Mass-energy equivalence

The factor c2=9.00×1016c^2 = 9.00 \times 10^{16} m squared per second squared is huge, so converting even a gram of mass releases an enormous amount of energy. This is why nuclear reactions, which convert measurable amounts of mass, release far more energy than chemical reactions, which do not. The equation also underlies the use of the universal mass unit (u), with the Reference Tables giving 11 u =931= 931 MeV, a direct mass-to-energy conversion.

The mass defect and binding energy

This is one of the more subtle Regents ideas. Putting nucleons together releases energy (the binding energy), and that released energy comes from a loss of mass, the mass defect. The same amount of energy must be supplied to break the nucleus apart. The binding energy explains why nuclei are stable and is the source of the energy in fission and fusion.

Nuclear fission and fusion

Fission powers nuclear reactors and fission weapons; fusion powers the Sun and stars (where hydrogen fuses into helium). Both release energy for the same fundamental reason: the products are more tightly bound (more binding energy per nucleon) than the reactants, so mass is lost and converted to energy. Fusion releases even more energy per unit mass than fission, which is why it is pursued as a future energy source.

Reference Tables note

The Reference Tables print E=mc2E = mc^2 in the Modern Physics section, the speed of light c=3.00×108c = 3.00 \times 10^8 m/s in the constants list, and the conversion 11 universal mass unit =931= 931 MeV (with 11 MeV =1.60×10−13= 1.60 \times 10^{-13} J). There is no separate half-life formula on the tables, so radioactive-decay half-life is reasoned from decay data or repeated halving rather than a printed equation. You recall the mass-defect and binding-energy concepts and the descriptions of fission and fusion.

Try this

Q1. State the equation relating mass and energy, naming each symbol. [2 points]

  • Cue. E=mc2E = mc^2: EE is energy, mm is mass, cc is the speed of light.

Q2. State why nuclear reactions release so much more energy than chemical reactions. [1 point]

  • Cue. They convert measurable amounts of mass to energy via E=mc2E = mc^2, and c2c^2 is enormous; chemical reactions do not convert appreciable mass.

Exam-style practice questions

Practice questions written in the style of NYSED exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Regents (style)2 marksPart B-2 (constructed response). In a nuclear reaction, a mass of 2.0×10−32.0 \times 10^{-3} kg is converted entirely into energy. Using c=3.00×108c = 3.00 \times 10^8 m/s, calculate the energy released. Show the equation, substitution and answer.
Show worked answer →

A 2-point constructed-response calculation using the Reference-Table equation E=mc2E = mc^2.

Equation: E=mc2E = mc^2.
Substitution: E=(2.0×10−3)(3.00×108)2=(2.0×10−3)(9.00×1016)E = (2.0 \times 10^{-3})(3.00 \times 10^8)^2 = (2.0 \times 10^{-3})(9.00 \times 10^{16}).
Answer: E=1.8×1014E = 1.8 \times 10^{14} J.

Markers reward the equation from the tables, squaring the speed of light correctly, and the energy in joules. The enormous energy from a tiny mass reflects the very large value of c2c^2.

Regents (style)2 marksPart B-2 (constructed response). State what is meant by the mass defect of a nucleus, and explain how it is related to the energy released when the nucleus forms.
Show worked answer →

A 2-point constructed-response conceptual item on the mass defect.

Mass defect (1 point): the mass defect is the difference between the total mass of the separate nucleons (protons and neutrons) and the smaller mass of the assembled nucleus.
Relationship (1 point): when the nucleus forms, this missing mass is converted to energy (the binding energy) according to E=mc2E = mc^2 and released; the same energy would be needed to pull the nucleus apart again.

Markers reward defining the mass defect as the missing mass and linking it to the binding energy via E=mc2E = mc^2.

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