Nuclear Chemistry Cheat Sheet
Balancing nuclear equations, decay modes, decay kinetics, binding energy, and fission/fusion.
Keep going with the free Nuclear Chemistry study guide → (graded practice with a subscription).
Nuclear Chemistry
Balancing nuclear equations, decay modes, decay kinetics, binding energy, and fission/fusion.
Conserve A and Z
CORE RULEBoth mass number A (top) and atomic number Z (bottom) are conserved: the sums must match on each side of a nuclear equation.
Particles
REFERENCE| Particle | Symbol (A, Z) |
|---|---|
| alpha | ⁴₂He (4, 2) |
| beta-minus | ⁰₋₁e (0, −1) |
| positron | ⁰₊₁e (0, +1) |
| neutron | ¹₀n (1, 0) |
| proton | ¹₁p (1, 1) |
| gamma | ⁰₀γ (0, 0) |
Decay modes
REFERENCE| Mode | Effect on nucleus |
|---|---|
| alpha | A − 4, Z − 2 |
| beta-minus | A same, Z + 1 (n → p) |
| positron | A same, Z − 1 (p → n) |
| electron capture | A same, Z − 1 (e⁻ on left) |
Multi-step decay counting
CORE RULEFor x alphas + y betas: solve 4x = mass difference and 2x − y = atomic-number difference simultaneously.
Decay kinetics (first order)
CORE RULEDecay is first-order: k = ln2 / t₁/₂ = 0.693 / t₁/₂ (units of inverse time).
Fraction remaining: N/N₀ = e^(−kt) = (1/2)^(t/t₁/₂). Use the half-life form when t/t₁/₂ is a simple ratio.
Activity & dating
CORE RULEActivity is proportional to the atom count, so ln(A/A₀) = −kt substitutes directly, the basis of radiocarbon and other radiometric dating.
Mass defect & binding energy
CORE RULEMass defect Δm = (mass of free protons + neutrons) − (actual nuclear mass). Binding energy BE = Δm·c² (c = 2.998 × 10⁸ m/s).
Binding energy per nucleon
CORE RULEBE/A = total binding energy ÷ A (MeV/nucleon). The curve peaks near iron-nickel (Fe-56 ≈ 8.8 MeV/nucleon), the most stable nuclei.
Fission vs fusion
CORE RULEFission: a heavy nucleus splits into two mid-mass nuclei + neutrons. Fusion: light nuclei combine. Both release energy when products sit higher on the BE/A curve (toward iron-nickel).
Activity A = λN
CORE RULEActivity A = λN, λ = ln2/t₁/₂, N = number of radioactive atoms (from mass via molar mass and Nₐ). SI unit: becquerel (1 Bq = 1 decay/s).