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Module 7: The Nature of Light

Quick questions on Mass-energy equivalence E = mc^2 and nuclear binding energy: HSC Physics Module 7

9short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the kinetic energy in special relativity?
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Splitting the total energy gives kinetic energy as:
What are unit conventions?
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For atomic and nuclear calculations, the unified atomic mass unit is convenient:
What is energy in a chemical bond?
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For comparison, chemical-bond energies are of order eV per molecule, six orders of magnitude smaller than nuclear binding energies. That is why nuclear reactions release millions of times more energy per atom than chemical reactions.
What is deuteron binding energy?
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Δm=(mp+mn)−md=(1.00728+1.00866)−2.01355=2.39×10−3\Delta m = (m_p + m_n) - m_d = (1.00728 + 1.00866) - 2.01355 = 2.39 \times 10^{-3} u. Eb=2.39×10−3×931.5=2.23E_b = 2.39 \times 10^{-3} \times 931.5 = 2.23 MeV. Per nucleon: 1.111.11 MeV.
What is iron-56 binding energy?
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Δm≈0.528\Delta m \approx 0.528 u. Eb≈492E_b \approx 492 MeV. Per nucleon: ≈8.79\approx 8.79 MeV - the peak of the binding-energy curve.
What is fission energy release?
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When U-235 captures a neutron and fissions into Ba-141 + Kr-92 + 3 neutrons, the mass defect is approximately 0.2150.215 u, giving about 200200 MeV per fission event. A reactor running at 11 GW thermal fissions about 3×10193 \times 10^{19} U-235 atoms per second.
What is q1?
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State the mass-energy equivalence relation and the energy equivalent of 1 u1 \text{ u} in MeV. [2 marks]
What is q2?
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The binding energy of a 4^4He nucleus is 28.3 MeV28.3 \text{ MeV}. Calculate the mass defect in atomic mass units. [3 marks]
What is q3?
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A D-T fusion reaction 12H+13H→24He+n^2_1 \text{H} + ^3_1 \text{H} \to {}^4_2 \text{He} + n releases 17.6 MeV17.6 \text{ MeV}. (a) Calculate the mass defect in u and in kg. (b) Compare the energy released per kilogram of fuel with chemical combustion (∼5×107 J/kg\sim 5 \times 10^7 \text{ J/kg}). (c) Justify why fusion is more energy-dense than fission per unit reactant mass.

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