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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
14short 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 famous equation?Show answer
In Einstein's 1905 special relativity, the total energy of a free particle of rest mass $m$ moving at speed $v$ is:
What is the kinetic energy in special relativity?Show answer
Splitting the total energy gives kinetic energy as:
What is unit conventions?Show answer
For atomic and nuclear calculations, the unified atomic mass unit is convenient:
What is mass defect and binding energy?Show answer
The mass of a bound nucleus is less than the sum of the masses of its free constituents (protons and neutrons). The difference is the mass defect:
What is three worked examples?Show answer
Deuteron binding energy. $\Delta m = (m_p + m_n) - m_d = (1.00728 + 1.00866) - 2.01355 = 2.39 \times 10^{-3}$ u. $E_b = 2.39 \times 10^{-3} \times 931.5 = 2.23$ MeV. Per nucleon: $1.11$ MeV.
What is pair production and annihilation?Show answer
The cleanest demonstrations of $E = m c^2$ are at particle level:
What is energy in a chemical bond?Show answer
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?Show answer
$\Delta m = (m_p + m_n) - m_d = (1.00728 + 1.00866) - 2.01355 = 2.39 \times 10^{-3}$ u. $E_b = 2.39 \times 10^{-3} \times 931.5 = 2.23$ MeV. Per nucleon: $1.11$ MeV.
What is iron-56 binding energy?Show answer
$\Delta m \approx 0.528$ u. $E_b \approx 492$ MeV. Per nucleon: $\approx 8.79$ MeV - the peak of the binding-energy curve.
What is fission energy release?Show answer
When U-235 captures a neutron and fissions into Ba-141 + Kr-92 + 3 neutrons, the mass defect is approximately $0.215$ u, giving about $200$ MeV per fission event. A reactor running at $1$ GW thermal fissions about $3 \times 10^{19}$ U-235 atoms per second.
What is quoting $E = m c^2$ when the particle is moving?Show answer
That formula is only the rest energy. The total energy of a moving particle is $E = \gamma m c^2$.
What is confusing mass defect with the masses themselves?Show answer
$\Delta m$ is a small difference, often $10^{-3}$ u or less; the binding energy in MeV is the headline result.
What is saying mass is destroyed in a nuclear reaction?Show answer
Mass and energy are equivalent forms; what is conserved is total relativistic energy (which includes rest energy). It is more accurate to say "rest mass is converted to other forms of energy".
What is treating chemical and nuclear energy releases as the same scale?Show answer
Chemical reactions release of order eV per atom; nuclear reactions release of order MeV per nucleon - a factor of one million larger.