Key Equations

Nuclear Energy & Binding Energy — AQA A-Level Physics

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Mass-energy equivalence
$$E = mc^2$$
  • Where:
    • $E$ = energy (J)
    • $m$ = mass (kg)
    • $c$ = speed of light = 3.0 × 10⁸ m s⁻¹
Applies to all nuclear reactions. A small mass defect corresponds to a large energy release.
Mass defect
$$\Delta m = Zm_p + (A - Z)m_n - m_{\text{total}}$$
  • Where:
    • $Δm$ = mass defect (kg or u)
    • $Z$ = proton number
    • $A$ = nucleon number
    • $mₚ$ = proton mass
    • $mₙ$ = neutron mass
    • $m_total$ = measured nuclear mass
Total mass of separated nucleons minus measured mass of nucleus.
Average kinetic energy of a thermal neutron
$$E = \frac{3}{2}kT$$
  • Where:
    • $E$ = kinetic energy (J)
    • $k$ = Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹
    • $T$ = temperature (K)
At T = 300 K, E ≈ 0.04 eV. This is the energy needed for neutrons to induce fission in U-235.
Number of nuclei from mass
$$N = \frac{m \times N_A}{M}$$
  • Where:
    • $N$ = number of nuclei
    • $m$ = mass of sample (g)
    • $N_A$ = Avogadro constant = 6.02 × 10²³ mol⁻¹
    • $M$ = molar mass (g mol⁻¹)
Used to find the number of atoms in a sample for activity and energy calculations.
Binding energy from mass defect
$$E = \Delta m \, c^2$$
  • Where:
    • $E$ = binding energy (J)
    • $Δm$ = mass defect (kg)
    • $c$ = speed of light (m s⁻¹)
Convert Δm from u to kg first (1 u = 1.661 × 10⁻²⁷ kg), or use 1 u = 931.5 MeV directly.
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