Key Equations

Atomic Structure & Nuclear Stability — AQA A-Level Physics

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Specific charge
$$\text{specific charge} = \frac{Q}{m}$$
  • Where:
    • $Q$ = total charge (C)
    • $m$ = total mass (kg)
Used for particles, ions and nuclei. For ions, Q depends on electrons gained/lost. For nuclei, Q = Ze.
Alpha decay
$${}_{Z}^{A}X \longrightarrow {}_{Z-2}^{A-4}Y + {}_{2}^{4}\alpha$$
  • Where:
    • $A$ = nucleon number
    • $Z$ = proton number
    • $X$ = parent nucleus
    • $Y$ = daughter nucleus
Alpha particle = helium-4 nucleus. Nucleon number drops by 4, proton number drops by 2.
Beta-minus decay
$${}_{Z}^{A}X \longrightarrow {}_{Z+1}^{A}Y + {}_{-1}^{0}\beta + {}_{0}^{0}\bar{\nu}_{e}$$
  • Where:
    • $A$ = nucleon number (unchanged)
    • $Z$ = proton number (increases by 1)
Neutron → proton + electron + anti-electron neutrino.
Beta-plus decay
$${}_{Z}^{A}X \longrightarrow {}_{Z-1}^{A}Y + {}_{+1}^{0}\beta + {}_{0}^{0}\nu_{e}$$
  • Where:
    • $A$ = nucleon number (unchanged)
    • $Z$ = proton number (decreases by 1)
Proton → neutron + positron + electron neutrino.
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